Mercurial > octave
changeset 24547:fdc9ce839afd
maint: Remove statistics functions which have been shifted to Octave Forge package.
* NEWS: Announce list of functions removed from core.
* scripts/statistics/center.m, scripts/statistics/corr.m,
scripts/statistics/corrcoef.m, scripts/statistics/cov.m,
scripts/statistics/discrete_cdf.m, scripts/statistics/discrete_inv.m,
scripts/statistics/discrete_pdf.m, scripts/statistics/discrete_rnd.m,
scripts/statistics/empirical_cdf.m, scripts/statistics/empirical_inv.m,
scripts/statistics/empirical_pdf.m, scripts/statistics/empirical_rnd.m,
scripts/statistics/histc.m, scripts/statistics/iqr.m,
scripts/statistics/kendall.m, scripts/statistics/kurtosis.m,
scripts/statistics/mean.m, scripts/statistics/meansq.m,
scripts/statistics/median.m, scripts/statistics/mode.m,
scripts/statistics/module.mk, scripts/statistics/moment.m,
scripts/statistics/prctile.m, scripts/statistics/quantile.m,
scripts/statistics/range.m, scripts/statistics/ranks.m,
scripts/statistics/run_count.m, scripts/statistics/runlength.m,
scripts/statistics/skewness.m, scripts/statistics/spearman.m,
scripts/statistics/statistics.m, scripts/statistics/std.m,
scripts/statistics/var.m, scripts/statistics/zscore.m:
Moved from scripts/statistics/base.
* scripts/module.mk: Update build system. Remove @include for directories
base/, tests/, models/, distributions/.
* octave.texi: Update @detailmenu.
* stats.txi: Rewrite statistics chapter with condensed list of functions.
* scripts/statistics/base/module.mk,
scripts/statistics/distributions/module.mk, scripts/statistics/models/module.mk
scripts/statistics/tests/module.mk:
Removed from build system.
* scripts/statistics/base/cloglog.m, scripts/statistics/base/crosstab.m,
scripts/statistics/base/logit.m, scripts/statistics/base/moment.m,
scripts/statistics/base/ppplot.m, scripts/statistics/base/probit.m,
scripts/statistics/base/qqplot.m, scripts/statistics/distributions/betacdf.m,
scripts/statistics/distributions/betainv.m,
scripts/statistics/distributions/betapdf.m,
scripts/statistics/distributions/betarnd.m,
scripts/statistics/distributions/binocdf.m,
scripts/statistics/distributions/binoinv.m,
scripts/statistics/distributions/binopdf.m,
scripts/statistics/distributions/binornd.m,
scripts/statistics/distributions/cauchy_cdf.m,
scripts/statistics/distributions/cauchy_inv.m,
scripts/statistics/distributions/cauchy_pdf.m,
scripts/statistics/distributions/cauchy_rnd.m,
scripts/statistics/distributions/chi2cdf.m,
scripts/statistics/distributions/chi2inv.m,
scripts/statistics/distributions/chi2pdf.m,
scripts/statistics/distributions/chi2rnd.m,
scripts/statistics/distributions/discrete_cdf.m,
scripts/statistics/distributions/discrete_inv.m,
scripts/statistics/distributions/discrete_pdf.m,
scripts/statistics/distributions/discrete_rnd.m,
scripts/statistics/distributions/empirical_cdf.m,
scripts/statistics/distributions/empirical_inv.m,
scripts/statistics/distributions/empirical_pdf.m,
scripts/statistics/distributions/empirical_rnd.m,
scripts/statistics/distributions/expcdf.m,
scripts/statistics/distributions/expinv.m,
scripts/statistics/distributions/exppdf.m,
scripts/statistics/distributions/exprnd.m,
scripts/statistics/distributions/fcdf.m,
scripts/statistics/distributions/finv.m,
scripts/statistics/distributions/fpdf.m,
scripts/statistics/distributions/frnd.m,
scripts/statistics/distributions/gamcdf.m,
scripts/statistics/distributions/gaminv.m,
scripts/statistics/distributions/gampdf.m,
scripts/statistics/distributions/gamrnd.m,
scripts/statistics/distributions/geocdf.m,
scripts/statistics/distributions/geoinv.m,
scripts/statistics/distributions/geopdf.m,
scripts/statistics/distributions/geornd.m,
scripts/statistics/distributions/hygecdf.m,
scripts/statistics/distributions/hygeinv.m,
scripts/statistics/distributions/hygepdf.m,
scripts/statistics/distributions/hygernd.m,
scripts/statistics/distributions/kolmogorov_smirnov_cdf.m,
scripts/statistics/distributions/laplace_cdf.m,
scripts/statistics/distributions/laplace_inv.m,
scripts/statistics/distributions/laplace_pdf.m,
scripts/statistics/distributions/laplace_rnd.m,
scripts/statistics/distributions/logistic_cdf.m,
scripts/statistics/distributions/logistic_inv.m,
scripts/statistics/distributions/logistic_pdf.m,
scripts/statistics/distributions/logistic_rnd.m,
scripts/statistics/distributions/logncdf.m,
scripts/statistics/distributions/logninv.m,
scripts/statistics/distributions/lognpdf.m,
scripts/statistics/distributions/lognrnd.m,
scripts/statistics/distributions/nbincdf.m,
scripts/statistics/distributions/nbininv.m,
scripts/statistics/distributions/nbinpdf.m,
scripts/statistics/distributions/nbinrnd.m,
scripts/statistics/distributions/normcdf.m,
scripts/statistics/distributions/norminv.m,
scripts/statistics/distributions/normpdf.m,
scripts/statistics/distributions/normrnd.m,
scripts/statistics/distributions/poisscdf.m,
scripts/statistics/distributions/poissinv.m,
scripts/statistics/distributions/poisspdf.m,
scripts/statistics/distributions/poissrnd.m,
scripts/statistics/distributions/stdnormal_cdf.m,
scripts/statistics/distributions/stdnormal_inv.m,
scripts/statistics/distributions/stdnormal_pdf.m,
scripts/statistics/distributions/stdnormal_rnd.m,
scripts/statistics/distributions/tcdf.m,
scripts/statistics/distributions/tinv.m,
scripts/statistics/distributions/tpdf.m,
scripts/statistics/distributions/trnd.m,
scripts/statistics/distributions/unidcdf.m,
scripts/statistics/distributions/unidinv.m,
scripts/statistics/distributions/unidpdf.m,
scripts/statistics/distributions/unidrnd.m,
scripts/statistics/distributions/unifcdf.m,
scripts/statistics/distributions/unifinv.m,
scripts/statistics/distributions/unifpdf.m,
scripts/statistics/distributions/unifrnd.m,
scripts/statistics/distributions/wblcdf.m,
scripts/statistics/distributions/wblinv.m,
scripts/statistics/distributions/wblpdf.m,
scripts/statistics/distributions/wblrnd.m,
scripts/statistics/distributions/wienrnd.m,
scripts/statistics/models/logistic_regression.m,
scripts/statistics/models/private/logistic_regression_derivatives.m,
scripts/statistics/models/private/logistic_regression_likelihood.m,
scripts/statistics/tests/anova.m, scripts/statistics/tests/bartlett_test.m,
scripts/statistics/tests/chisquare_test_homogeneity.m,
scripts/statistics/tests/chisquare_test_independence.m,
scripts/statistics/tests/cor_test.m,
scripts/statistics/tests/f_test_regression.m,
scripts/statistics/tests/hotelling_test.m,
scripts/statistics/tests/hotelling_test_2.m,
scripts/statistics/tests/kolmogorov_smirnov_test.m,
scripts/statistics/tests/kolmogorov_smirnov_test_2.m,
scripts/statistics/tests/kruskal_wallis_test.m,
scripts/statistics/tests/manova.m, scripts/statistics/tests/mcnemar_test.m,
scripts/statistics/tests/prop_test_2.m, scripts/statistics/tests/run_test.m,
scripts/statistics/tests/sign_test.m, scripts/statistics/tests/t_test.m,
scripts/statistics/tests/t_test_2.m,
scripts/statistics/tests/t_test_regression.m,
scripts/statistics/tests/u_test.m, scripts/statistics/tests/var_test.m,
scripts/statistics/tests/welch_test.m,
scripts/statistics/tests/wilcoxon_test.m, scripts/statistics/tests/z_test.m,
scripts/statistics/tests/z_test_2.m:
Removed functions.
| author | Rik <rik@octave.org> |
|---|---|
| date | Sun, 07 Jan 2018 17:13:23 -0800 |
| parents | d3a507ca2d5d |
| children | a00033be2134 |
| files | NEWS doc/interpreter/octave.texi doc/interpreter/stats.txi scripts/module.mk scripts/statistics/base/center.m scripts/statistics/base/cloglog.m scripts/statistics/base/corr.m scripts/statistics/base/corrcoef.m scripts/statistics/base/cov.m scripts/statistics/base/crosstab.m scripts/statistics/base/histc.m scripts/statistics/base/iqr.m scripts/statistics/base/kendall.m scripts/statistics/base/kurtosis.m scripts/statistics/base/logit.m scripts/statistics/base/mean.m scripts/statistics/base/meansq.m scripts/statistics/base/median.m scripts/statistics/base/mode.m scripts/statistics/base/module.mk scripts/statistics/base/moment.m scripts/statistics/base/ppplot.m scripts/statistics/base/prctile.m scripts/statistics/base/probit.m scripts/statistics/base/qqplot.m scripts/statistics/base/quantile.m scripts/statistics/base/range.m scripts/statistics/base/ranks.m scripts/statistics/base/run_count.m scripts/statistics/base/runlength.m scripts/statistics/base/skewness.m scripts/statistics/base/spearman.m scripts/statistics/base/statistics.m scripts/statistics/base/std.m scripts/statistics/base/var.m scripts/statistics/base/zscore.m scripts/statistics/center.m scripts/statistics/corr.m scripts/statistics/corrcoef.m scripts/statistics/cov.m scripts/statistics/discrete_cdf.m scripts/statistics/discrete_inv.m scripts/statistics/discrete_pdf.m scripts/statistics/discrete_rnd.m scripts/statistics/distributions/betacdf.m scripts/statistics/distributions/betainv.m scripts/statistics/distributions/betapdf.m scripts/statistics/distributions/betarnd.m scripts/statistics/distributions/binocdf.m scripts/statistics/distributions/binoinv.m scripts/statistics/distributions/binopdf.m scripts/statistics/distributions/binornd.m scripts/statistics/distributions/cauchy_cdf.m scripts/statistics/distributions/cauchy_inv.m scripts/statistics/distributions/cauchy_pdf.m scripts/statistics/distributions/cauchy_rnd.m scripts/statistics/distributions/chi2cdf.m scripts/statistics/distributions/chi2inv.m scripts/statistics/distributions/chi2pdf.m scripts/statistics/distributions/chi2rnd.m scripts/statistics/distributions/discrete_cdf.m scripts/statistics/distributions/discrete_inv.m scripts/statistics/distributions/discrete_pdf.m scripts/statistics/distributions/discrete_rnd.m scripts/statistics/distributions/empirical_cdf.m scripts/statistics/distributions/empirical_inv.m scripts/statistics/distributions/empirical_pdf.m scripts/statistics/distributions/empirical_rnd.m scripts/statistics/distributions/expcdf.m scripts/statistics/distributions/expinv.m scripts/statistics/distributions/exppdf.m scripts/statistics/distributions/exprnd.m scripts/statistics/distributions/fcdf.m scripts/statistics/distributions/finv.m scripts/statistics/distributions/fpdf.m scripts/statistics/distributions/frnd.m scripts/statistics/distributions/gamcdf.m scripts/statistics/distributions/gaminv.m scripts/statistics/distributions/gampdf.m scripts/statistics/distributions/gamrnd.m scripts/statistics/distributions/geocdf.m scripts/statistics/distributions/geoinv.m scripts/statistics/distributions/geopdf.m scripts/statistics/distributions/geornd.m scripts/statistics/distributions/hygecdf.m scripts/statistics/distributions/hygeinv.m scripts/statistics/distributions/hygepdf.m scripts/statistics/distributions/hygernd.m scripts/statistics/distributions/kolmogorov_smirnov_cdf.m scripts/statistics/distributions/laplace_cdf.m scripts/statistics/distributions/laplace_inv.m scripts/statistics/distributions/laplace_pdf.m scripts/statistics/distributions/laplace_rnd.m scripts/statistics/distributions/logistic_cdf.m scripts/statistics/distributions/logistic_inv.m scripts/statistics/distributions/logistic_pdf.m scripts/statistics/distributions/logistic_rnd.m scripts/statistics/distributions/logncdf.m scripts/statistics/distributions/logninv.m scripts/statistics/distributions/lognpdf.m scripts/statistics/distributions/lognrnd.m scripts/statistics/distributions/module.mk scripts/statistics/distributions/nbincdf.m scripts/statistics/distributions/nbininv.m scripts/statistics/distributions/nbinpdf.m scripts/statistics/distributions/nbinrnd.m scripts/statistics/distributions/normcdf.m scripts/statistics/distributions/norminv.m scripts/statistics/distributions/normpdf.m scripts/statistics/distributions/normrnd.m scripts/statistics/distributions/poisscdf.m scripts/statistics/distributions/poissinv.m scripts/statistics/distributions/poisspdf.m scripts/statistics/distributions/poissrnd.m scripts/statistics/distributions/stdnormal_cdf.m scripts/statistics/distributions/stdnormal_inv.m scripts/statistics/distributions/stdnormal_pdf.m scripts/statistics/distributions/stdnormal_rnd.m scripts/statistics/distributions/tcdf.m scripts/statistics/distributions/tinv.m scripts/statistics/distributions/tpdf.m scripts/statistics/distributions/trnd.m scripts/statistics/distributions/unidcdf.m scripts/statistics/distributions/unidinv.m scripts/statistics/distributions/unidpdf.m scripts/statistics/distributions/unidrnd.m scripts/statistics/distributions/unifcdf.m scripts/statistics/distributions/unifinv.m scripts/statistics/distributions/unifpdf.m scripts/statistics/distributions/unifrnd.m scripts/statistics/distributions/wblcdf.m scripts/statistics/distributions/wblinv.m scripts/statistics/distributions/wblpdf.m scripts/statistics/distributions/wblrnd.m scripts/statistics/distributions/wienrnd.m scripts/statistics/empirical_cdf.m scripts/statistics/empirical_inv.m scripts/statistics/empirical_pdf.m scripts/statistics/empirical_rnd.m scripts/statistics/histc.m scripts/statistics/iqr.m scripts/statistics/kendall.m scripts/statistics/kurtosis.m scripts/statistics/mean.m scripts/statistics/meansq.m scripts/statistics/median.m scripts/statistics/mode.m scripts/statistics/models/logistic_regression.m scripts/statistics/models/module.mk scripts/statistics/models/private/logistic_regression_derivatives.m scripts/statistics/models/private/logistic_regression_likelihood.m scripts/statistics/module.mk scripts/statistics/moment.m scripts/statistics/prctile.m scripts/statistics/quantile.m scripts/statistics/range.m scripts/statistics/ranks.m scripts/statistics/run_count.m scripts/statistics/runlength.m scripts/statistics/skewness.m scripts/statistics/spearman.m scripts/statistics/statistics.m scripts/statistics/std.m scripts/statistics/tests/anova.m scripts/statistics/tests/bartlett_test.m scripts/statistics/tests/chisquare_test_homogeneity.m scripts/statistics/tests/chisquare_test_independence.m scripts/statistics/tests/cor_test.m scripts/statistics/tests/f_test_regression.m scripts/statistics/tests/hotelling_test.m scripts/statistics/tests/hotelling_test_2.m scripts/statistics/tests/kolmogorov_smirnov_test.m scripts/statistics/tests/kolmogorov_smirnov_test_2.m scripts/statistics/tests/kruskal_wallis_test.m scripts/statistics/tests/manova.m scripts/statistics/tests/mcnemar_test.m scripts/statistics/tests/module.mk scripts/statistics/tests/prop_test_2.m scripts/statistics/tests/run_test.m scripts/statistics/tests/sign_test.m scripts/statistics/tests/t_test.m scripts/statistics/tests/t_test_2.m scripts/statistics/tests/t_test_regression.m scripts/statistics/tests/u_test.m scripts/statistics/tests/var_test.m scripts/statistics/tests/welch_test.m scripts/statistics/tests/wilcoxon_test.m scripts/statistics/tests/z_test.m scripts/statistics/tests/z_test_2.m scripts/statistics/var.m scripts/statistics/zscore.m |
| diffstat | 191 files changed, 4689 insertions(+), 16602 deletions(-) [+] |
line wrap: on
line diff
--- a/NEWS Sun Jan 07 09:57:32 2018 -0800 +++ b/NEWS Sun Jan 07 17:13:23 2018 -0800 @@ -84,7 +84,127 @@ ** The following statistical functions have been moved from core Octave to the statistics package available from Octave Forge. - table -> crosstab + BASE + cloglog.m + table.m --renamed to --> crosstab.m + logit.m + prctile.m + probit.m + qqplot.m + + DISTRIBUTIONS + betacdf.m + betainv.m + betapdf.m + betarnd.m + binocdf.m + binoinv.m + binopdf.m + binornd.m + cauchy_cdf.m + cauchy_inv.m + cauchy_pdf.m + cauchy_rnd.m + chi2cdf.m + chi2inv.m + chi2pdf.m + chi2rnd.m + expcdf.m + expinv.m + exppdf.m + exprnd.m + fcdf.m + finv.m + fpdf.m + frnd.m + gamcdf.m + gaminv.m + gampdf.m + gamrnd.m + geocdf.m + geoinv.m + geopdf.m + geornd.m + hygecdf.m + hygeinv.m + hygepdf.m + hygernd.m + kolmogorov_smirnov_cdf.m + laplace_cdf.m + laplace_inv.m + laplace_pdf.m + laplace_rnd.m + logistic_cdf.m + logistic_inv.m + logistic_pdf.m + logistic_rnd.m + logncdf.m + logninv.m + lognpdf.m + lognrnd.m + nbincdf.m + nbininv.m + nbinpdf.m + nbinrnd.m + normcdf.m + norminv.m + normpdf.m + normrnd.m + poisscdf.m + poissinv.m + poisspdf.m + poissrnd.m + stdnormal_cdf.m + stdnormal_inv.m + stdnormal_pdf.m + stdnormal_rnd.m + tcdf.m + tinv.m + tpdf.m + trnd.m + unidcdf.m + unidinv.m + unidpdf.m + unidrnd.m + unifcdf.m + unifinv.m + unifpdf.m + unifrnd.m + wblcdf.m + wblinv.m + wblpdf.m + wblrnd.m + wienrnd.m + + MODELS + logistic_regression.m + + TESTS + anova.m + bartlett_test.m + chisquare_test_homogeneity.m + chisquare_test_independence.m + cor_test.m + f_test_regression.m + hotelling_test.m + hotelling_test_2.m + kolmogorov_smirnov_test.m + kolmogorov_smirnov_test_2.m + kruskal_wallis_test.m + manova.m + mcnemar_test.m + prop_test_2.m + run_test.m + sign_test.m + t_test.m + t_test_2.m + t_test_regression.m + u_test.m + var_test.m + welch_test.m + wilcoxon_test.m + z_test.m + z_test_2.m ** Other new functions added in 4.4:
--- a/doc/interpreter/octave.texi Sun Jan 07 09:57:32 2018 -0800 +++ b/doc/interpreter/octave.texi Sun Jan 07 17:13:23 2018 -0800 @@ -714,10 +714,8 @@ * Descriptive Statistics:: * Basic Statistical Functions:: -* Statistical Plots:: * Correlation and Regression Analysis:: * Distributions:: -* Tests:: * Random Number Generation:: Sets
--- a/doc/interpreter/stats.txi Sun Jan 07 09:57:32 2018 -0800 +++ b/doc/interpreter/stats.txi Sun Jan 07 17:13:23 2018 -0800 @@ -19,13 +19,14 @@ @node Statistics @chapter Statistics -Octave has support for various statistical methods. This includes -basic descriptive statistics, probability distributions, statistical tests, -random number generation, and much more. +Octave has support for various statistical methods. The emphasis is on basic +descriptive statistics, but the Octave Forge statistics package includes +probability distributions, statistical tests, random number generation, and +much more. -The functions that analyze data all assume that multi-dimensional data -is arranged in a matrix where each row is an observation, and each -column is a variable. Thus, the matrix defined by +The functions that analyze data all assume that multi-dimensional data is +arranged in a matrix where each row is an observation, and each column is a +variable. Thus, the matrix defined by @example @group @@ -36,22 +37,19 @@ @end example @noindent -contains three observations from a two-dimensional distribution. -While this is the default data arrangement, most functions support -different arrangements. +contains three observations from a two-dimensional distribution. While this is +the default data arrangement, most functions support different arrangements. -It should be noted that the statistics functions don't test for data -containing NaN, NA, or Inf. These values need to be detected and dealt -with explicitly. See @ref{XREFisnan,,isnan}, @ref{XREFisna,,isna}, -@ref{XREFisinf,,isinf}, @ref{XREFisfinite,,isfinite}. +It should be noted that the statistics functions don't test for data containing +NaN, NA, or Inf. These values need to be detected and dealt with explicitly. +See @ref{XREFisnan,,isnan}, @ref{XREFisna,,isna}, @ref{XREFisinf,,isinf}, +@ref{XREFisfinite,,isfinite}. @menu * Descriptive Statistics:: * Basic Statistical Functions:: -* Statistical Plots:: * Correlation and Regression Analysis:: * Distributions:: -* Tests:: * Random Number Generation:: @end menu @@ -132,32 +130,6 @@ @DOCSTRING(runlength) -@DOCSTRING(probit) - -@DOCSTRING(logit) - -@DOCSTRING(cloglog) - -@DOCSTRING(crosstab) - -@node Statistical Plots -@section Statistical Plots - -@c Should hist be moved to here, or perhaps the qqplot and ppplot -@c functions should be moved to the Plotting Chapter? - -Octave can create Quantile Plots (QQ-Plots), and Probability Plots -(PP-Plots). These are simple graphical tests for determining if a -data set comes from a certain distribution. - -Note that Octave can also show histograms of data -using the @code{hist} function as described in -@ref{Two-Dimensional Plots}. - -@DOCSTRING(qqplot) - -@DOCSTRING(ppplot) - @node Correlation and Regression Analysis @section Correlation and Regression Analysis @@ -173,20 +145,16 @@ @DOCSTRING(kendall) -@c FIXME: Need discussion of ols & gls and references to them in optim.txi - - -@DOCSTRING(logistic_regression) - @node Distributions @section Distributions -Octave has functions for computing the Probability Density Function -(PDF), the Cumulative Distribution function (CDF), and the quantile -(the inverse of the CDF) for a large number of distributions. +Octave has functions for computing the Probability Density Function (PDF), the +Cumulative Distribution function (CDF), and the quantile (the inverse of the +CDF) for arbitrary user-defined distributions (discrete) and for experimental +data (empirical). -The following table summarizes the supported distributions (in -alphabetical order). +The following table summarizes the supported distributions (in alphabetical +order). @tex \vskip 6pt @@ -198,30 +166,8 @@ \noalign{\hrule height 0.6pt} & {\bf Distribution} && {\bf PDF} && {\bf CDF} && {\bf Quantile}&\cr \noalign{\hrule} -&Beta && betapdf && betacdf && betainv&\cr -&Binomial && binopdf && binocdf && binoinv&\cr -&Cauchy && cauchy\_pdf && cauchy\_cdf && cauchy\_inv&\cr -&Chi-Square && chi2pdf && chi2cdf && chi2inv&\cr &Univariate Discrete && discrete\_pdf && discrete\_cdf && discrete\_inv&\cr &Empirical && empirical\_pdf && empirical\_cdf && empirical\_inv&\cr -&Exponential && exppdf && expcdf && expinv&\cr -&F && fpdf && fcdf && finv&\cr -&Gamma && gampdf && gamcdf && gaminv&\cr -&Geometric && geopdf && geocdf && geoinv&\cr -&Hypergeometric && hygepdf && hygecdf && hygeinv&\cr -&Kolmogorov Smirnov && {\it Not Available} && kolmogorov\_&& {\it Not Available}&\cr -& && && smirnov\_cdf &&&\cr -&Laplace && laplace\_pdf && laplace\_cdf && laplace\_inv&\cr -&Logistic && logistic\_pdf && logistic\_cdf && logistic\_inv&\cr -&Log-Normal && lognpdf && logncdf && logninv&\cr -&Univariate Normal && normpdf && normcdf && norminv&\cr -&Pascal && nbinpdf && nbincdf && nbininv&\cr -&Poisson && poisspdf && poisscdf && poissinv&\cr -&Standard Normal && stdnormal\_pdf && stdnormal\_cdf && stdnormal\_inv&\cr -&t (Student) && tpdf && tcdf && tinv&\cr -&Uniform Discrete && unidpdf && unidcdf && unidinv&\cr -&Uniform && unifpdf && unifcdf && unifinv&\cr -&Weibull && wblpdf && wblcdf && wblinv&\cr \noalign{\hrule height 0.6pt} }}\hfill}} @end tex @@ -231,22 +177,6 @@ @tab PDF @tab CDF @tab Quantile -@item Beta Distribution - @tab @code{betapdf} - @tab @code{betacdf} - @tab @code{betainv} -@item Binomial Distribution - @tab @code{binopdf} - @tab @code{binocdf} - @tab @code{binoinv} -@item Cauchy Distribution - @tab @code{cauchy_pdf} - @tab @code{cauchy_cdf} - @tab @code{cauchy_inv} -@item Chi-Square Distribution - @tab @code{chi2pdf} - @tab @code{chi2cdf} - @tab @code{chi2inv} @item Univariate Discrete Distribution @tab @code{discrete_pdf} @tab @code{discrete_cdf} @@ -255,101 +185,9 @@ @tab @code{empirical_pdf} @tab @code{empirical_cdf} @tab @code{empirical_inv} -@item Exponential Distribution - @tab @code{exppdf} - @tab @code{expcdf} - @tab @code{expinv} -@item F Distribution - @tab @code{fpdf} - @tab @code{fcdf} - @tab @code{finv} -@item Gamma Distribution - @tab @code{gampdf} - @tab @code{gamcdf} - @tab @code{gaminv} -@item Geometric Distribution - @tab @code{geopdf} - @tab @code{geocdf} - @tab @code{geoinv} -@item Hypergeometric Distribution - @tab @code{hygepdf} - @tab @code{hygecdf} - @tab @code{hygeinv} -@item Kolmogorov Smirnov Distribution - @tab @emph{Not Available} - @tab @code{kolmogorov_smirnov_cdf} - @tab @emph{Not Available} -@item Laplace Distribution - @tab @code{laplace_pdf} - @tab @code{laplace_cdf} - @tab @code{laplace_inv} -@item Logistic Distribution - @tab @code{logistic_pdf} - @tab @code{logistic_cdf} - @tab @code{logistic_inv} -@item Log-Normal Distribution - @tab @code{lognpdf} - @tab @code{logncdf} - @tab @code{logninv} -@item Univariate Normal Distribution - @tab @code{normpdf} - @tab @code{normcdf} - @tab @code{norminv} -@item Pascal Distribution - @tab @code{nbinpdf} - @tab @code{nbincdf} - @tab @code{nbininv} -@item Poisson Distribution - @tab @code{poisspdf} - @tab @code{poisscdf} - @tab @code{poissinv} -@item Standard Normal Distribution - @tab @code{stdnormal_pdf} - @tab @code{stdnormal_cdf} - @tab @code{stdnormal_inv} -@item t (Student) Distribution - @tab @code{tpdf} - @tab @code{tcdf} - @tab @code{tinv} -@item Univariate Discrete Distribution - @tab @code{unidpdf} - @tab @code{unidcdf} - @tab @code{unidinv} -@item Uniform Distribution - @tab @code{unifpdf} - @tab @code{unifcdf} - @tab @code{unifinv} -@item Weibull Distribution - @tab @code{wblpdf} - @tab @code{wblcdf} - @tab @code{wblinv} @end multitable @end ifnottex -@DOCSTRING(betapdf) - -@DOCSTRING(betacdf) - -@DOCSTRING(betainv) - -@DOCSTRING(binopdf) - -@DOCSTRING(binocdf) - -@DOCSTRING(binoinv) - -@DOCSTRING(cauchy_pdf) - -@DOCSTRING(cauchy_cdf) - -@DOCSTRING(cauchy_inv) - -@DOCSTRING(chi2pdf) - -@DOCSTRING(chi2cdf) - -@DOCSTRING(chi2inv) - @DOCSTRING(discrete_pdf) @DOCSTRING(discrete_cdf) @@ -362,233 +200,15 @@ @DOCSTRING(empirical_inv) -@DOCSTRING(exppdf) - -@DOCSTRING(expcdf) - -@DOCSTRING(expinv) - -@DOCSTRING(fpdf) - -@DOCSTRING(fcdf) - -@DOCSTRING(finv) - -@DOCSTRING(gampdf) - -@DOCSTRING(gamcdf) - -@DOCSTRING(gaminv) - -@DOCSTRING(geopdf) - -@DOCSTRING(geocdf) - -@DOCSTRING(geoinv) - -@DOCSTRING(hygepdf) - -@DOCSTRING(hygecdf) - -@DOCSTRING(hygeinv) - -@DOCSTRING(kolmogorov_smirnov_cdf) - -@DOCSTRING(laplace_pdf) - -@DOCSTRING(laplace_cdf) - -@DOCSTRING(laplace_inv) - -@DOCSTRING(logistic_pdf) - -@DOCSTRING(logistic_cdf) - -@DOCSTRING(logistic_inv) - -@DOCSTRING(lognpdf) - -@DOCSTRING(logncdf) - -@DOCSTRING(logninv) - -@DOCSTRING(nbinpdf) - -@DOCSTRING(nbincdf) - -@DOCSTRING(nbininv) - -@DOCSTRING(normpdf) - -@DOCSTRING(normcdf) - -@DOCSTRING(norminv) - -@DOCSTRING(poisspdf) - -@DOCSTRING(poisscdf) - -@DOCSTRING(poissinv) - -@DOCSTRING(stdnormal_pdf) - -@DOCSTRING(stdnormal_cdf) - -@DOCSTRING(stdnormal_inv) - -@DOCSTRING(tpdf) - -@DOCSTRING(tcdf) - -@DOCSTRING(tinv) - -@DOCSTRING(unidpdf) - -@DOCSTRING(unidcdf) - -@DOCSTRING(unidinv) - -@DOCSTRING(unifpdf) - -@DOCSTRING(unifcdf) - -@DOCSTRING(unifinv) - -@DOCSTRING(wblpdf) - -@DOCSTRING(wblcdf) - -@DOCSTRING(wblinv) - -@node Tests -@section Tests - -Octave can perform many different statistical tests. The following -table summarizes the available tests. - -@tex -\vskip 6pt -{\hbox to \hsize {\hfill\vbox{\offinterlineskip \tabskip=0pt -\halign{ -\vrule height2.0ex depth1.ex width 0.6pt #\tabskip=0.3em & -# \hfil & \vrule # & # \hfil & # \vrule width 0.6pt \tabskip=0pt\cr -\noalign{\hrule height 0.6pt} -& @strong{Hypothesis} && {\bf Test Functions} &\cr -\noalign{\hrule} -& Equal mean values && anova, hotelling\_test2, t\_test\_2, &\cr -& && welch\_test, wilcoxon\_test, z\_test\_2 &\cr -& Equal medians && kruskal\_wallis\_test, sign\_test &\cr -& Equal variances && bartlett\_test, manova, var\_test &\cr -& Equal distributions && chisquare\_test\_homogeneity, &\cr -& && kolmogorov\_smirnov\_test\_2, u\_test &\cr -& Equal marginal frequencies && mcnemar\_test &\cr -& Equal success probabilities && prop\_test\_2 &\cr -& Independent observations && chisquare\_test\_independence, &\cr -& && run\_test &\cr -& Uncorrelated observations && cor\_test &\cr -& Given mean value && hotelling\_test, t\_test, z\_test &\cr -& Observations from distribution && kolmogorov\_smirnov\_test &\cr -& Regression && f\_test\_regression, t\_test\_regression &\cr -\noalign{\hrule height 0.6pt} -}}\hfill}} -@end tex -@ifnottex -@multitable @columnfractions .4 .5 -@headitem Hypothesis - @tab Test Functions -@item Equal mean values - @tab @code{anova}, @code{hotelling_test2}, @code{t_test_2}, - @code{welch_test}, @code{wilcoxon_test}, @code{z_test_2} -@item Equal medians - @tab @code{kruskal_wallis_test}, @code{sign_test} -@item Equal variances - @tab @code{bartlett_test}, @code{manova}, @code{var_test} -@item Equal distributions - @tab @code{chisquare_test_homogeneity}, @code{kolmogorov_smirnov_test_2}, - @code{u_test} -@item Equal marginal frequencies - @tab @code{mcnemar_test} -@item Equal success probabilities - @tab @code{prop_test_2} -@item Independent observations - @tab @code{chisquare_test_independence}, @code{run_test} -@item Uncorrelated observations - @tab @code{cor_test} -@item Given mean value - @tab @code{hotelling_test}, @code{t_test}, @code{z_test} -@item Observations from given distribution - @tab @code{kolmogorov_smirnov_test} -@item Regression - @tab @code{f_test_regression}, @code{t_test_regression} -@end multitable -@end ifnottex - -The tests return a p-value that describes the outcome of the test. -Assuming that the test hypothesis is true, the p-value is the probability -of obtaining a worse result than the observed one. So large p-values -corresponds to a successful test. Usually a test hypothesis is accepted -if the p-value exceeds 0.05. - -@DOCSTRING(anova) - -@DOCSTRING(bartlett_test) - -@DOCSTRING(chisquare_test_homogeneity) - -@DOCSTRING(chisquare_test_independence) - -@DOCSTRING(cor_test) - -@DOCSTRING(f_test_regression) - -@DOCSTRING(hotelling_test) - -@DOCSTRING(hotelling_test_2) - -@DOCSTRING(kolmogorov_smirnov_test) - -@DOCSTRING(kolmogorov_smirnov_test_2) - -@DOCSTRING(kruskal_wallis_test) - -@DOCSTRING(manova) - -@DOCSTRING(mcnemar_test) - -@DOCSTRING(prop_test_2) - -@DOCSTRING(run_test) - -@DOCSTRING(sign_test) - -@DOCSTRING(t_test) - -@DOCSTRING(t_test_2) - -@DOCSTRING(t_test_regression) - -@DOCSTRING(u_test) - -@DOCSTRING(var_test) - -@DOCSTRING(welch_test) - -@DOCSTRING(wilcoxon_test) - -@DOCSTRING(z_test) - -@DOCSTRING(z_test_2) - @node Random Number Generation @section Random Number Generation -Octave can generate random numbers from a large number of distributions. -The random number generators are based on the random number generators -described in @ref{Special Utility Matrices}. -@c Should rand, randn, rande, randp, and randg be moved to here? +Octave can generate random numbers from a large number of distributions. The +random number generators are based on the random number generators described in +@ref{Special Utility Matrices}. -The following table summarizes the available random number generators -(in alphabetical order). +The following table summarizes the available random number generators (in +alphabetical order). @tex \vskip 6pt @@ -599,103 +219,28 @@ \noalign{\hrule height 0.6pt} & {\bf Distribution} && {\bf Function} &\cr \noalign{\hrule} -& Beta Distribution && betarnd &\cr -& Binomial Distribution && binornd &\cr -& Cauchy Distribution && cauchy\_rnd &\cr -& Chi-Square Distribution && chi2rnd &\cr & Univariate Discrete Distribution && discrete\_rnd &\cr & Empirical Distribution && empirical\_rnd &\cr -& Exponential Distribution && exprnd &\cr -& F Distribution && frnd &\cr -& Gamma Distribution && gamrnd &\cr -& Geometric Distribution && geornd &\cr -& Hypergeometric Distribution && hygernd &\cr -& Laplace Distribution && laplace\_rnd &\cr -& Logistic Distribution && logistic\_rnd &\cr -& Log-Normal Distribution && lognrnd &\cr -& Pascal Distribution && nbinrnd &\cr -& Univariate Normal Distribution && normrnd &\cr -& Poisson Distribution && poissrnd &\cr -& Standard Normal Distribution && stdnormal\_rnd &\cr -& t (Student) Distribution && trnd &\cr -& Univariate Discrete Distribution && unidrnd &\cr -& Uniform Distribution && unifrnd &\cr -& Weibull Distribution && wblrnd &\cr -& Wiener Process && wienrnd &\cr +& Exponential Distribution && rande &\cr +& Gamma Distribution && randg &\cr +& Poisson Distribution && randp &\cr +& Standard Normal Distribution && randn &\cr +& Uniform Distribution && rand &\cr +& Uniform Distribution (integers) && randi &\cr \noalign{\hrule height 0.6pt} }}\hfill}} @end tex @ifnottex @multitable @columnfractions .4 .3 @headitem Distribution @tab Function -@item Beta Distribution @tab @code{betarnd} -@item Binomial Distribution @tab @code{binornd} -@item Cauchy Distribution @tab @code{cauchy_rnd} -@item Chi-Square Distribution @tab @code{chi2rnd} @item Univariate Discrete Distribution @tab @code{discrete_rnd} @item Empirical Distribution @tab @code{empirical_rnd} -@item Exponential Distribution @tab @code{exprnd} -@item F Distribution @tab @code{frnd} -@item Gamma Distribution @tab @code{gamrnd} -@item Geometric Distribution @tab @code{geornd} -@item Hypergeometric Distribution @tab @code{hygernd} -@item Laplace Distribution @tab @code{laplace_rnd} -@item Logistic Distribution @tab @code{logistic_rnd} -@item Log-Normal Distribution @tab @code{lognrnd} -@item Pascal Distribution @tab @code{nbinrnd} -@item Univariate Normal Distribution @tab @code{normrnd} -@item Poisson Distribution @tab @code{poissrnd} -@item Standard Normal Distribution @tab @code{stdnormal_rnd} -@item t (Student) Distribution @tab @code{trnd} -@item Univariate Discrete Distribution @tab @code{unidrnd} -@item Uniform Distribution @tab @code{unifrnd} -@item Weibull Distribution @tab @code{wblrnd} -@item Wiener Process @tab @code{wienrnd} +@item Exponential Distribution @tab @code{rande} +@item Gamma Distribution @tab @code{randg} +@item Poisson Distribution @tab @code{randp} +@item Standard Normal Distribution @tab @code{randn} +@item Uniform Distribution @tab @code{rand} +@item Uniform Distribution (integers) @tab @code{randi} @end multitable @end ifnottex -@DOCSTRING(betarnd) - -@DOCSTRING(binornd) - -@DOCSTRING(cauchy_rnd) - -@DOCSTRING(chi2rnd) - -@DOCSTRING(discrete_rnd) - -@DOCSTRING(empirical_rnd) - -@DOCSTRING(exprnd) - -@DOCSTRING(frnd) - -@DOCSTRING(gamrnd) - -@DOCSTRING(geornd) - -@DOCSTRING(hygernd) - -@DOCSTRING(laplace_rnd) - -@DOCSTRING(logistic_rnd) - -@DOCSTRING(lognrnd) - -@DOCSTRING(nbinrnd) - -@DOCSTRING(normrnd) - -@DOCSTRING(poissrnd) - -@DOCSTRING(stdnormal_rnd) - -@DOCSTRING(trnd) - -@DOCSTRING(unidrnd) - -@DOCSTRING(unifrnd) - -@DOCSTRING(wblrnd) - -@DOCSTRING(wienrnd)
--- a/scripts/module.mk Sun Jan 07 09:57:32 2018 -0800 +++ b/scripts/module.mk Sun Jan 07 17:13:23 2018 -0800 @@ -33,10 +33,7 @@ include %reldir%/specfun/module.mk include %reldir%/special-matrix/module.mk include %reldir%/startup/module.mk -include %reldir%/statistics/base/module.mk -include %reldir%/statistics/distributions/module.mk -include %reldir%/statistics/models/module.mk -include %reldir%/statistics/tests/module.mk +include %reldir%/statistics/module.mk include %reldir%/strings/module.mk include %reldir%/testfun/module.mk include %reldir%/time/module.mk
--- a/scripts/statistics/base/center.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,96 +0,0 @@ -## Copyright (C) 1995-2017 Kurt Hornik -## Copyright (C) 2009 VZLU Prague -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} center (@var{x}) -## @deftypefnx {} {} center (@var{x}, @var{dim}) -## Center data by subtracting its mean. -## -## If @var{x} is a vector, subtract its mean. -## -## If @var{x} is a matrix, do the above for each column. -## -## If the optional argument @var{dim} is given, operate along this dimension. -## -## Programming Note: @code{center} has obvious application for normalizing -## statistical data. It is also useful for improving the precision of general -## numerical calculations. Whenever there is a large value that is common -## to a batch of data, the mean can be subtracted off, the calculation -## performed, and then the mean added back to obtain the final answer. -## @seealso{zscore} -## @end deftypefn - -## Author: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: Center by subtracting means - -function retval = center (x, dim) - - if (nargin != 1 && nargin != 2) - print_usage (); - endif - - if (! (isnumeric (x) || islogical (x))) - error ("center: X must be a numeric vector or matrix"); - endif - - if (isinteger (x)) - x = double (x); - endif - - nd = ndims (x); - sz = size (x); - if (nargin != 2) - ## Find the first non-singleton dimension. - (dim = find (sz > 1, 1)) || (dim = 1); - else - if (! (isscalar (dim) && dim == fix (dim) && dim > 0)) - error ("center: DIM must be an integer and a valid dimension"); - endif - endif - - n = size (x, dim); - - if (n == 0) - retval = x; - else - ## FIXME: Use bsxfun, rather than broadcasting, until broadcasting - ## supports diagonal and sparse matrices (Bugs #41441, #35787). - retval = bsxfun (@minus, x, mean (x, dim)); - ## retval = x - mean (x, dim); # automatic broadcasting - endif - -endfunction - - -%!assert (center ([1,2,3]), [-1,0,1]) -%!assert (center (single ([1,2,3])), single ([-1,0,1])) -%!assert (center (int8 ([1,2,3])), [-1,0,1]) -%!assert (center (logical ([1, 0, 0, 1])), [0.5, -0.5, -0.5, 0.5]) -%!assert (center (ones (3,2,0,2)), zeros (3,2,0,2)) -%!assert (center (ones (3,2,0,2, "single")), zeros (3,2,0,2, "single")) -%!assert (center (magic (3)), [3,-4,1;-2,0,2;-1,4,-3]) -%!assert (center ([1 2 3; 6 5 4], 2), [-1 0 1; 1 0 -1]) -%!assert (center (1, 3), 0) - -## Test input validation -%!error center () -%!error center (1, 2, 3) -%!error <DIM must be an integer> center (1, ones (2,2)) -%!error <DIM must be an integer> center (1, 1.5) -%!error <DIM must be .* a valid dimension> center (1, 0)
--- a/scripts/statistics/base/cloglog.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,58 +0,0 @@ -## Copyright (C) 1995-2017 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} cloglog (@var{x}) -## Return the complementary log-log function of @var{x}. -## -## The complementary log-log function is defined as -## @tex -## $$ -## {\rm cloglog}(x) = - \log (- \log (x)) -## $$ -## @end tex -## @ifnottex -## -## @example -## cloglog (x) = - log (- log (@var{x})) -## @end example -## -## @end ifnottex -## @end deftypefn - -## Author: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: Complementary log-log function - -function y = cloglog (x) - - if (nargin != 1) - print_usage (); - endif - - y = - log (- log (x)); - -endfunction - - -%!assert (cloglog (0), -Inf) -%!assert (cloglog (1), Inf) -%!assert (cloglog (1/e), 0) - -## Test input validation -%!error cloglog () -%!error cloglog (1, 2)
--- a/scripts/statistics/base/corr.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,111 +0,0 @@ -## Copyright (C) 1996-2017 John W. Eaton -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} corr (@var{x}) -## @deftypefnx {} {} corr (@var{x}, @var{y}) -## Compute matrix of correlation coefficients. -## -## If each row of @var{x} and @var{y} is an observation and each column is -## a variable, then the @w{(@var{i}, @var{j})-th} entry of -## @code{corr (@var{x}, @var{y})} is the correlation between the -## @var{i}-th variable in @var{x} and the @var{j}-th variable in @var{y}. -## @tex -## $$ -## {\rm corr}(x,y) = {{\rm cov}(x,y) \over {\rm std}(x) \, {\rm std}(y)} -## $$ -## @end tex -## @ifnottex -## -## @example -## corr (@var{x},@var{y}) = cov (@var{x},@var{y}) / (std (@var{x}) * std (@var{y})) -## @end example -## -## @end ifnottex -## If called with one argument, compute @code{corr (@var{x}, @var{x})}, -## the correlation between the columns of @var{x}. -## @seealso{cov} -## @end deftypefn - -## Author: Kurt Hornik <hornik@wu-wien.ac.at> -## Created: March 1993 -## Adapted-By: jwe - -function retval = corr (x, y = []) - - if (nargin < 1 || nargin > 2) - print_usage (); - endif - - ## Input validation is done by cov.m. Don't repeat tests here - - ## Special case, scalar is always 100% correlated with itself - if (isscalar (x)) - if (isa (x, "single")) - retval = single (1); - else - retval = 1; - endif - return; - endif - - ## No check for division by zero error, which happens only when - ## there is a constant vector and should be rare. - if (nargin == 2) - c = cov (x, y); - s = std (x)' * std (y); - retval = c ./ s; - else - c = cov (x); - s = sqrt (diag (c)); - retval = c ./ (s * s'); - endif - -endfunction - - -%!test -%! x = rand (10); -%! cc1 = corr (x); -%! cc2 = corr (x, x); -%! assert (size (cc1) == [10, 10] && size (cc2) == [10, 10]); -%! assert (cc1, cc2, sqrt (eps)); - -%!test -%! x = [1:3]'; -%! y = [3:-1:1]'; -%! assert (corr (x, y), -1, 5*eps); -%! assert (corr (x, flipud (y)), 1, 5*eps); -%! assert (corr ([x, y]), [1 -1; -1 1], 5*eps); - -%!test -%! x = single ([1:3]'); -%! y = single ([3:-1:1]'); -%! assert (corr (x, y), single (-1), 5*eps); -%! assert (corr (x, flipud (y)), single (1), 5*eps); -%! assert (corr ([x, y]), single ([1 -1; -1 1]), 5*eps); - -%!assert (corr (5), 1) -%!assert (corr (single (5)), single (1)) - -## Test input validation -%!error corr () -%!error corr (1, 2, 3) -%!error corr ([1; 2], ["A", "B"]) -%!error corr (ones (2,2,2)) -%!error corr (ones (2,2), ones (2,2,2))
--- a/scripts/statistics/base/corrcoef.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,253 +0,0 @@ -## Copyright (C) 2016-2017 Guillaume Flandin -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {@var{r} =} corrcoef (@var{x}) -## @deftypefnx {} {@var{r} =} corrcoef (@var{x}, @var{y}) -## @deftypefnx {} {[@var{r}, @var{p}] =} corrcoef (@dots{}) -## @deftypefnx {} {[@var{r}, @var{p}, @var{lci}, @var{hci}] =} corrcoef (@dots{}) -## @deftypefnx {} {[@dots{}] =} corrcoef (@dots{}, @var{param}, @var{value}, @dots{}) -## Compute a matrix of correlation coefficients. -## -## @var{x} is an array where each column contains a variable and each row is -## an observation. -## -## If a second input @var{y} (of the same size as @var{x}) is given then -## calculate the correlation coefficients between @var{x} and @var{y}. -## -## @var{r} is a matrix of Pearson's product moment correlation coefficients for -## each pair of variables. -## -## @var{p} is a matrix of pair-wise p-values testing for the null hypothesis of -## a correlation coefficient of zero. -## -## @var{lci} and @var{hci} are matrices containing, respectively, the lower and -## higher bounds of the 95% confidence interval of each correlation -## coefficient. -## -## @var{param}, @var{value} are pairs of optional parameters and values. -## Valid options are: -## -## @table @asis -## @item @qcode{"alpha"} -## Confidence level used for the definition of the bounds of the confidence -## interval, @var{lci} and @var{hci}. Default is 0.05, i.e., 95% confidence -## interval. -## -## @item @qcode{"rows"} -## Determine processing of NaN values. Acceptable values are @qcode{"all"}, -## @qcode{"complete"}, and @qcode{"pairwise"}. Default is @qcode{"all"}. -## With @qcode{"complete"}, only the rows without NaN values are considered. -## With @qcode{"pairwise"}, the selection of NaN-free rows is made for each -## pair of variables. -## -## @end table -## -## @seealso{corr, cov, cor_test} -## @end deftypefn - -## FIXME: It would be good to add a definition of the calculation method -## for a Pearson product moment correlation to the documentation. - -function [r, p, lci, hci] = corrcoef (x, varargin) - - if (nargin == 0) - print_usage (); - endif - - alpha = 0.05; - rows = "all"; - - if (nargin > 1) - - ## Check for numeric y argument - if (isnumeric (varargin{1})) - x = [x(:), varargin{1}(:)]; - varargin(1) = []; - endif - - ## Check for Parameter/Value arguments - for i = 1:2:numel (varargin) - - if (! ischar (varargin{i})) - error ("corrcoef: parameter %d must be a string", i); - endif - parameter = varargin{i}; - if (numel (varargin) < i+1) - error ('corrcoef: parameter "%s" missing value', parameter); - endif - value = varargin{i+1}; - - switch (tolower (parameter)) - case "alpha" - if (isnumeric (value) && isscalar (value) - && value >= 0 && value <= 1) - alpha = value; - else - error ('corrcoef: "alpha" must be a number between 0 and 1'); - endif - - case "rows" - if (! ischar (value)) - error ('corrcoef: "rows" value must be a string'); - endif - value = tolower (value); - switch (value) - case {"all", "complete", "pairwise"} - rows = value; - otherwise - error ('corrcoef: "rows" must be "all", "complete", or "pairwise".'); - endswitch - - otherwise - error ('corrcoef: Unknown option "%s"', parameter); - - endswitch - endfor - endif - - if (strcmp (rows, "complete")) - x(any (isnan (x), 2), :) = []; - endif - - if (isempty (x) || isscalar (x)) - r = p = lci = hci = NaN; - return; - endif - - ## Flags for calculation - pairwise = strcmp (rows, "pairwise"); - calc_pval = nargout > 1; - - if (isrow (x)) - x = x(:); - endif - [m, n] = size (x); - r = eye (n); - if (calc_pval) - p = eye (n); - endif - if (strcmp (rows, "pairwise")) - mpw = m * ones (n); - endif - for i = 1:n - if (! pairwise && any (isnan (x(:,i)))) - r(i,i) = NaN; - if (nargout > 1) - p(i,i) = NaN; - endif - endif - for j = i+1:n - xi = x(:,i); - xj = x(:,j); - if (pairwise) - idx = any (isnan ([xi xj]), 2); - xi(idx) = xj(idx) = []; - mpw(i,j) = mpw(j,i) = m - nnz (idx); - endif - r(i,j) = r(j,i) = corr (xi, xj); - if (calc_pval) - T = cor_test (xi, xj, "!=", "pearson"); - p(i,j) = p(j,i) = T.pval; - endif - endfor - endfor - - if (nargout > 2) - if (pairwise) - m = mpw; - endif - CI = sqrt (2) * erfinv (1-alpha) ./ sqrt (m-3); - lci = tanh (atanh (r) - CI); - hci = tanh (atanh (r) + CI); - endif - -endfunction - - -%!test -%! x = rand (5); -%! r = corrcoef (x); -%! assert (size (r) == [5, 5]); - -%!test -%! x = [1 2 3]; -%! r = corrcoef (x); -%! assert (size (r) == [1, 1]); - -%!test -%! x = []; -%! r = corrcoef (x); -%! assert (isnan (r)); - -%!test -%! x = [NaN]; -%! r = corrcoef (x); -%! assert (isnan (r)); - -%!test -%! x = [1]; -%! r = corrcoef (x); -%! assert (isnan (r)); - -%!test -%! x = [NaN NaN]; -%! r = corrcoef (x); -%! assert (size(r) == [1, 1] && isnan (r)); - -%!test -%! x = rand (5); -%! [r, p] = corrcoef (x); -%! assert (size (r) == [5, 5] && size (p) == [5 5]); - -%!test -%! x = rand (5,1); -%! y = rand (5,1); -%! R1 = corrcoef (x, y); -%! R2 = corrcoef ([x, y]); -%! assert (R1, R2); - -%!test -%! x = [1;2;3]; -%! y = [1;2;3]; -%! r = corrcoef (x, y); -%! assert (r, ones (2,2)); - -%!test -%! x = [1;2;3]; -%! y = [3;2;1]; -%! r = corrcoef (x, y); -%! assert (r, [1, -1; -1, 1]); - -%!test -%! x = [1;2;3]; -%! y = [1;1;1]; -%! r = corrcoef (x, y); -%! assert (r, [1, NaN; NaN, 1]); - -%!test -%!error corrcoef () -%!error <parameter 1 must be a string> corrcoef (1, 2, 3) -%!error <parameter "alpha" missing value> corrcoef (1, 2, "alpha") -%!error <"alpha" must be a number> corrcoef (1,2, "alpha", "1") -%!error <"alpha" must be a number> corrcoef (1,2, "alpha", ones (2,2)) -%!error <"alpha" must be a number between 0 and 1> corrcoef (1,2, "alpha", -1) -%!error <"alpha" must be a number between 0 and 1> corrcoef (1,2, "alpha", 2) -%!error <"rows" must be "all"...> corrcoef (1,2, "rows", "foobar") -%!error <Unknown option "foobar"> corrcoef (1,2, "foobar", 1)
--- a/scripts/statistics/base/cov.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,175 +0,0 @@ -## Copyright (C) 1995-2017 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} cov (@var{x}) -## @deftypefnx {} {} cov (@var{x}, @var{opt}) -## @deftypefnx {} {} cov (@var{x}, @var{y}) -## @deftypefnx {} {} cov (@var{x}, @var{y}, @var{opt}) -## Compute the covariance matrix. -## -## If each row of @var{x} and @var{y} is an observation, and each column is -## a variable, then the @w{(@var{i}, @var{j})-th} entry of -## @code{cov (@var{x}, @var{y})} is the covariance between the @var{i}-th -## variable in @var{x} and the @var{j}-th variable in @var{y}. -## @tex -## $$ -## \sigma_{ij} = {1 \over N-1} \sum_{i=1}^N (x_i - \bar{x})(y_i - \bar{y}) -## $$ -## where $\bar{x}$ and $\bar{y}$ are the mean values of @var{x} and @var{y}. -## @end tex -## @ifnottex -## -## @example -## cov (@var{x}) = 1/(N-1) * SUM_i (@var{x}(i) - mean(@var{x})) * (@var{y}(i) - mean(@var{y})) -## @end example -## -## where @math{N} is the length of the @var{x} and @var{y} vectors. -## -## @end ifnottex -## -## If called with one argument, compute @code{cov (@var{x}, @var{x})}, the -## covariance between the columns of @var{x}. -## -## The argument @var{opt} determines the type of normalization to use. -## Valid values are -## -## @table @asis -## @item 0: -## normalize with @math{N-1}, provides the best unbiased estimator of the -## covariance [default] -## -## @item 1: -## normalize with @math{N}, this provides the second moment around the mean -## @end table -## -## Compatibility Note:: Octave always treats rows of @var{x} and @var{y} -## as multivariate random variables. -## For two inputs, however, @sc{matlab} treats @var{x} and @var{y} as two -## univariate distributions regardless of their shapes, and will calculate -## @code{cov ([@var{x}(:), @var{y}(:)])} whenever the number of elements in -## @var{x} and @var{y} are equal. This will result in a 2x2 matrix. -## Code relying on @sc{matlab}'s definition will need to be changed when -## running in Octave. -## @seealso{corr} -## @end deftypefn - -## Author: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: Compute covariances - -function c = cov (x, y = [], opt = 0) - - if (nargin < 1 || nargin > 3) - print_usage (); - endif - - if ( ! (isnumeric (x) || islogical (x)) - || ! (isnumeric (y) || islogical (y))) - error ("cov: X and Y must be numeric matrices or vectors"); - endif - - if (ndims (x) != 2 || ndims (y) != 2) - error ("cov: X and Y must be 2-D matrices or vectors"); - endif - - if (nargin == 2 && isscalar (y)) - opt = y; - endif - - if (opt != 0 && opt != 1) - error ("cov: normalization OPT must be 0 or 1"); - endif - - ## Special case, scalar has zero covariance - if (isscalar (x)) - if (isa (x, "single")) - c = single (0); - else - c = 0; - endif - return; - endif - - if (isrow (x)) - x = x.'; - endif - n = rows (x); - - if (nargin == 1 || isscalar (y)) - x = center (x, 1); - c = x' * x / (n - 1 + opt); - else - if (isrow (y)) - y = y.'; - endif - if (rows (y) != n) - error ("cov: X and Y must have the same number of observations"); - endif - x = center (x, 1); - y = center (y, 1); - c = x' * y / (n - 1 + opt); - endif - -endfunction - - -%!test -%! x = rand (10); -%! cx1 = cov (x); -%! cx2 = cov (x, x); -%! assert (size (cx1) == [10, 10] && size (cx2) == [10, 10]); -%! assert (cx1, cx2, 1e1*eps); - -%!test -%! x = [1:3]'; -%! y = [3:-1:1]'; -%! assert (cov (x, y), -1, 5*eps); -%! assert (cov (x, flipud (y)), 1, 5*eps); -%! assert (cov ([x, y]), [1 -1; -1 1], 5*eps); - -%!test -%! x = single ([1:3]'); -%! y = single ([3:-1:1]'); -%! assert (cov (x, y), single (-1), 5*eps); -%! assert (cov (x, flipud (y)), single (1), 5*eps); -%! assert (cov ([x, y]), single ([1 -1; -1 1]), 5*eps); - -%!test -%! x = [1:5]; -%! c = cov (x); -%! assert (isscalar (c)); -%! assert (c, 2.5); - -%!assert (cov (5), 0) -%!assert (cov (single (5)), single (0)) - -%!test -%! x = [1:5]; -%! c = cov (x, 0); -%! assert (c, 2.5); -%! c = cov (x, 1); -%! assert (c, 2); - -## Test input validation -%!error cov () -%!error cov (1, 2, 3, 4) -%!error cov ([1; 2], ["A", "B"]) -%!error cov (ones (2,2,2)) -%!error cov (ones (2,2), ones (2,2,2)) -%!error cov (1, 3) -%!error cov (ones (2,2), ones (3,2))
--- a/scripts/statistics/base/crosstab.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,64 +0,0 @@ -## Copyright (C) 1995-2017 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {@var{t} =} crosstab (@var{x}, @var{y}) -## Create a cross-tabulation (contingency table) @var{t} from data vectors. -## -## The inputs @var{x}, @var{y} must be vectors of equal length with a data -## type of numeric, logical, or char. -## -## Currently, only 1- and 2-dimensional tables are supported. -## @end deftypefn - -function t = crosstab (x, y) - - if (nargin != 2) - print_usage (); - endif - - if (! ( isvector (x) && isreal (x) - && isvector (y) && isreal (y) - && (numel (x) == numel (y)))) - error ("crosstab: X and Y must be real vectors of the same length"); - endif - - x = x(:); - y = y(:); - v = unique (x); - w = unique (y); - for i = 1 : length (v) - for j = 1 : length (w) - t(i,j) = sum ((x == v(i) | isnan (v(i)) * isnan (x)) & - (y == w(j) | isnan (w(j)) * isnan (y))); - endfor - endfor - -endfunction - - -## Test input validation -%!error crosstab () -%!error crosstab (1) -%!error crosstab (1, 2, 3) -%!error <X .* must be .* vector> crosstab (ones (2), [1 1]) -%!error <Y must be .* vector> crosstab ([1 1], ones (2)) -%!error <X .* must be real> crosstab ({true, true}, [1 1]) -%!error <Y must be real> crosstab ([1 1], {true, true}) -%!error <X and Y must be .* of the same length> crosstab ([1], [1 1]) -%!error <X and Y must be .* of the same length> crosstab ([1 1], [1])
--- a/scripts/statistics/base/histc.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,190 +0,0 @@ -## Copyright (C) 2009-2017 Søren Hauberg -## Copyright (C) 2009 VZLU Prague -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {@var{n} =} histc (@var{x}, @var{edges}) -## @deftypefnx {} {@var{n} =} histc (@var{x}, @var{edges}, @var{dim}) -## @deftypefnx {} {[@var{n}, @var{idx}] =} histc (@dots{}) -## Compute histogram counts. -## -## When @var{x} is a vector, the function counts the number of elements of -## @var{x} that fall in the histogram bins defined by @var{edges}. This -## must be a vector of monotonically increasing values that define the edges -## of the histogram bins. -## @tex -## $n(k)$ -## @end tex -## @ifnottex -## @code{@var{n}(k)} -## @end ifnottex -## contains the number of elements in @var{x} for which -## @tex -## $@var{edges}(k) <= @var{x} < @var{edges}(k+1)$. -## @end tex -## @ifnottex -## @code{@var{edges}(k) <= @var{x} < @var{edges}(k+1)}. -## @end ifnottex -## The final element of @var{n} contains the number of elements of @var{x} -## exactly equal to the last element of @var{edges}. -## -## When @var{x} is an @math{N}-dimensional array, the computation is carried -## out along dimension @var{dim}. If not specified @var{dim} defaults to the -## first non-singleton dimension. -## -## When a second output argument is requested an index matrix is also returned. -## The @var{idx} matrix has the same size as @var{x}. Each element of -## @var{idx} contains the index of the histogram bin in which the -## corresponding element of @var{x} was counted. -## @seealso{hist} -## @end deftypefn - -function [n, idx] = histc (x, edges, dim) - - if (nargin < 2 || nargin > 3) - print_usage (); - endif - - if (! isreal (x)) - error ("histc: X argument must be real-valued, not complex"); - endif - - num_edges = numel (edges); - if (num_edges == 0) - warning ("histc: empty EDGES specified\n"); - n = idx = []; - return; - endif - - if (! isreal (edges)) - error ("histc: EDGES must be real-valued, not complex"); - else - ## Make sure 'edges' is sorted - edges = edges(:); - if (! issorted (edges) || edges(1) > edges(end)) - warning ("histc: edge values not sorted on input"); - edges = sort (edges); - endif - endif - - nd = ndims (x); - sz = size (x); - if (nargin < 3) - ## Find the first non-singleton dimension. - (dim = find (sz > 1, 1)) || (dim = 1); - else - if (!(isscalar (dim) && dim == fix (dim)) - || !(1 <= dim && dim <= nd)) - error ("histc: DIM must be an integer and a valid dimension"); - endif - endif - - nsz = sz; - nsz(dim) = num_edges; - - ## the splitting point is 3 bins - - if (num_edges <= 3) - - ## This is the O(M*N) algorithm. - - ## Allocate the histogram - n = zeros (nsz); - - ## Allocate 'idx' - if (nargout > 1) - idx = zeros (sz); - endif - - ## Prepare indices - idx1 = cell (1, dim-1); - for k = 1:length (idx1) - idx1{k} = 1:sz(k); - endfor - idx2 = cell (length (sz) - dim); - for k = 1:length (idx2) - idx2{k} = 1:sz(k+dim); - endfor - - ## Compute the histograms - for k = 1:num_edges-1 - b = (edges(k) <= x & x < edges(k+1)); - n(idx1{:}, k, idx2{:}) = sum (b, dim); - if (nargout > 1) - idx(b) = k; - endif - endfor - b = (x == edges(end)); - n(idx1{:}, num_edges, idx2{:}) = sum (b, dim); - if (nargout > 1) - idx(b) = num_edges; - endif - - else - - ## This is the O(M*log(N) + N) algorithm. - - ## Look-up indices. - idx = lookup (edges, x); - ## Zero invalid ones (including NaNs). x < edges(1) are already zero. - idx(! (x <= edges(end))) = 0; - - iidx = idx; - - ## In case of matrix input, we adjust the indices. - if (! isvector (x)) - nl = prod (sz(1:dim-1)); - nn = sz(dim); - nu = prod (sz(dim+1:end)); - if (nl != 1) - iidx = (iidx-1) * nl; - iidx += reshape (kron (ones (1, nn*nu), 1:nl), sz); - endif - if (nu != 1) - ne =length (edges); - iidx += reshape (kron (nl*ne*(0:nu-1), ones (1, nl*nn)), sz); - endif - endif - - ## Select valid elements. - iidx = iidx(idx != 0); - - ## Call accumarray to sum the indexed elements. - n = accumarray (iidx(:), 1, nsz); - - endif - -endfunction - - -%!test -%! x = linspace (0, 10, 1001); -%! n = histc (x, 0:10); -%! assert (n, [repmat(100, 1, 10), 1]); - -%!test -%! x = repmat (linspace (0, 10, 1001), [2, 1, 3]); -%! n = histc (x, 0:10, 2); -%! assert (n, repmat ([repmat(100, 1, 10), 1], [2, 1, 3])); - -%!error histc () -%!error histc (1) -%!error histc (1, 2, 3, 4) -%!error histc ([1:10 1+i], 2) -%!warning <empty EDGES specified> histc (1:10, []); -%!error histc (1, 1, 3)
--- a/scripts/statistics/base/iqr.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,100 +0,0 @@ -## Copyright (C) 1995-2017 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} iqr (@var{x}) -## @deftypefnx {} {} iqr (@var{x}, @var{dim}) -## Return the interquartile range, i.e., the difference between the upper -## and lower quartile of the input data. -## -## If @var{x} is a matrix, do the above for first non-singleton dimension of -## @var{x}. -## -## If the optional argument @var{dim} is given, operate along this dimension. -## -## As a measure of dispersion, the interquartile range is less affected by -## outliers than either @code{range} or @code{std}. -## @seealso{range, std} -## @end deftypefn - -## Author KH <Kurt.Hornik@wu-wien.ac.at> -## Description: Interquartile range - -function y = iqr (x, dim) - - if (nargin != 1 && nargin != 2) - print_usage (); - endif - - if (! (isnumeric (x) || islogical (x))) - error ("iqr: X must be a numeric vector or matrix"); - endif - - nd = ndims (x); - sz = size (x); - nel = numel (x); - if (nargin != 2) - ## Find the first non-singleton dimension. - (dim = find (sz > 1, 1)) || (dim = 1); - else - if (!(isscalar (dim) && dim == fix (dim)) - || !(1 <= dim && dim <= nd)) - error ("iqr: DIM must be an integer and a valid dimension"); - endif - endif - - ## This code is a bit heavy, but is needed until empirical_inv - ## can take a matrix, rather than just a vector argument. - n = sz(dim); - sz(dim) = 1; - if (isa (x, "single")) - y = zeros (sz, "single"); - else - y = zeros (sz); - endif - stride = prod (sz(1:dim-1)); - for i = 1 : nel / n; - offset = i; - offset2 = 0; - while (offset > stride) - offset -= stride; - offset2 += 1; - endwhile - offset += offset2 * stride * n; - rng = [0 : n-1] * stride + offset; - - y(i) = diff (empirical_inv ([1/4, 3/4], x(rng))); - endfor - -endfunction - - -%!assert (iqr (1:101), 50) -%!assert (iqr (single (1:101)), single (50)) - -## FIXME: iqr throws horrible error when running across a dimension that is 1. -%!test -%! x = [1:100]'; -%! assert (iqr (x, 1), 50); -%! assert (iqr (x', 2), 50); - -%!error iqr () -%!error iqr (1, 2, 3) -%!error iqr (1) -%!error iqr (['A'; 'B']) -%!error iqr (1:10, 3)
--- a/scripts/statistics/base/kendall.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,153 +0,0 @@ -## Copyright (C) 1995-2017 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} kendall (@var{x}) -## @deftypefnx {} {} kendall (@var{x}, @var{y}) -## @cindex Kendall's Tau -## Compute Kendall's -## @tex -## $\tau$. -## @end tex -## @ifnottex -## @var{tau}. -## @end ifnottex -## -## For two data vectors @var{x}, @var{y} of common length @math{N}, Kendall's -## @tex -## $\tau$ -## @end tex -## @ifnottex -## @var{tau} -## @end ifnottex -## is the correlation of the signs of all rank differences of -## @var{x} and @var{y}; i.e., if both @var{x} and @var{y} have distinct -## entries, then -## -## @tex -## $$ \tau = {1 \over N(N-1)} \sum_{i,j} {\rm sign}(q_i-q_j) \, {\rm sign}(r_i-r_j) $$ -## @end tex -## @ifnottex -## -## @example -## @group -## 1 -## @var{tau} = ------- SUM sign (@var{q}(i) - @var{q}(j)) * sign (@var{r}(i) - @var{r}(j)) -## N (N-1) i,j -## @end group -## @end example -## -## @end ifnottex -## @noindent -## in which the -## @tex -## $q_i$ and $r_i$ -## @end tex -## @ifnottex -## @var{q}(i) and @var{r}(i) -## @end ifnottex -## are the ranks of @var{x} and @var{y}, respectively. -## -## If @var{x} and @var{y} are drawn from independent distributions, -## Kendall's -## @tex -## $\tau$ -## @end tex -## @ifnottex -## @var{tau} -## @end ifnottex -## is asymptotically normal with mean 0 and variance -## @tex -## ${2 (2N+5) \over 9N(N-1)}$. -## @end tex -## @ifnottex -## @code{(2 * (2N+5)) / (9 * N * (N-1))}. -## @end ifnottex -## -## @code{kendall (@var{x})} is equivalent to @code{kendall (@var{x}, -## @var{x})}. -## @seealso{ranks, spearman} -## @end deftypefn - -## Author: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: Kendall's rank correlation tau - -function tau = kendall (x, y = []) - - if (nargin < 1 || nargin > 2) - print_usage (); - endif - - if ( ! (isnumeric (x) || islogical (x)) - || ! (isnumeric (y) || islogical (y))) - error ("kendall: X and Y must be numeric matrices or vectors"); - endif - - if (ndims (x) != 2 || ndims (y) != 2) - error ("kendall: X and Y must be 2-D matrices or vectors"); - endif - - if (isrow (x)) - x = x.'; - endif - [n, c] = size (x); - - if (nargin == 2) - if (isrow (y)) - y = y.'; - endif - if (rows (y) != n) - error ("kendall: X and Y must have the same number of observations"); - else - x = [x, y]; - endif - endif - - if (isa (x, "single") || isa (y, "single")) - cls = "single"; - else - cls = "double"; - endif - r = ranks (x); - m = sign (kron (r, ones (n, 1, cls)) - kron (ones (n, 1, cls), r)); - tau = corr (m); - - if (nargin == 2) - tau = tau(1 : c, (c + 1) : columns (x)); - endif - -endfunction - - -%!test -%! x = [1:2:10]; -%! y = [100:10:149]; -%! assert (kendall (x,y), 1, 5*eps); -%! assert (kendall (x,fliplr (y)), -1, 5*eps); - -%!assert (kendall (logical (1)), 1) -%!assert (kendall (single (1)), single (1)) - -## Test input validation -%!error kendall () -%!error kendall (1, 2, 3) -%!error kendall (['A'; 'B']) -%!error kendall (ones (2,1), ['A'; 'B']) -%!error kendall (ones (2,2,2)) -%!error kendall (ones (2,2), ones (2,2,2)) -%!error kendall (ones (2,2), ones (3,2))
--- a/scripts/statistics/base/kurtosis.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,170 +0,0 @@ -## Copyright (C) 2013-2017 Julien Bect -## Copyright (C) 1996-2016 John W. Eaton -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} kurtosis (@var{x}) -## @deftypefnx {} {} kurtosis (@var{x}, @var{flag}) -## @deftypefnx {} {} kurtosis (@var{x}, @var{flag}, @var{dim}) -## Compute the sample kurtosis of the elements of @var{x}. -## -## The sample kurtosis is defined as -## @tex -## $$ -## \kappa_1 = {{{1\over N}\, -## \sum_{i=1}^N (x_i - \bar{x})^4} \over \sigma^4}, -## $$ -## where $N$ is the length of @var{x}, $\bar{x}$ its mean, and $\sigma$ -## its (uncorrected) standard deviation. -## @end tex -## @ifnottex -## -## @example -## @group -## mean ((@var{x} - mean (@var{x})).^4) -## k1 = ------------------------ -## std (@var{x}).^4 -## @end group -## @end example -## -## @end ifnottex -## -## @noindent -## The optional argument @var{flag} controls which normalization is used. -## If @var{flag} is equal to 1 (default value, used when @var{flag} is omitted -## or empty), return the sample kurtosis as defined above. If @var{flag} is -## equal to 0, return the @w{"bias-corrected"} kurtosis coefficient instead: -## @tex -## $$ -## \kappa_0 = 3 + {\scriptstyle N - 1 \over \scriptstyle (N - 2)(N - 3)} \, -## \left( (N + 1)\, \kappa_1 - 3 (N - 1) \right) -## $$ -## @end tex -## @ifnottex -## -## @example -## @group -## N - 1 -## k0 = 3 + -------------- * ((N + 1) * k1 - 3 * (N - 1)) -## (N - 2)(N - 3) -## @end group -## @end example -## -## where @math{N} is the length of the @var{x} vector. -## -## @end ifnottex -## The bias-corrected kurtosis coefficient is obtained by replacing the sample -## second and fourth central moments by their unbiased versions. It is an -## unbiased estimate of the population kurtosis for normal populations. -## -## If @var{x} is a matrix, or more generally a multi-dimensional array, return -## the kurtosis along the first non-singleton dimension. If the optional -## @var{dim} argument is given, operate along this dimension. -## -## @seealso{var, skewness, moment} -## @end deftypefn - -## Author: KH <Kurt.Hornik@wu-wien.ac.at> -## Created: 29 July 1994 -## Adapted-By: jwe - -function y = kurtosis (x, flag, dim) - - if (nargin < 1) || (nargin > 3) - print_usage (); - endif - - if (! (isnumeric (x) || islogical (x))) - error ("kurtosis: X must be a numeric vector or matrix"); - endif - - if (nargin < 2 || isempty (flag)) - flag = 1; # default: do not use the "bias corrected" version - else - if (! isscalar (flag) || (flag != 0 && flag != 1)) - error ("kurtosis: FLAG must be 0 or 1"); - endif - endif - - nd = ndims (x); - sz = size (x); - if (nargin < 3) - ## Find the first non-singleton dimension. - (dim = find (sz > 1, 1)) || (dim = 1); - else - if (! (isscalar (dim) && dim == fix (dim) && dim > 0)) - error ("kurtosis: DIM must be an integer and a valid dimension"); - endif - endif - - n = size (x, dim); - sz(dim) = 1; - - x = center (x, dim); # center also promotes integer, logical to double - v = var (x, 1, dim); # normalize with 1/N - y = sum (x .^ 4, dim); - idx = (v != 0); - y(idx) = y(idx) ./ (n * v(idx) .^ 2); - y(! idx) = NaN; - - ## Apply bias correction to the second and fourth central sample moment - if (flag == 0) - if (n > 3) - C = (n - 1) / ((n - 2) * (n - 3)); - y = 3 + C * ((n + 1) * y - 3 * (n - 1)); - else - y(:) = NaN; - endif - endif - -endfunction - - -%!test -%! x = [-1; 0; 0; 0; 1]; -%! y = [x, 2*x]; -%! assert (kurtosis (y), [2.5, 2.5], sqrt (eps)); - -%!assert (kurtosis ([-3, 0, 1]) == kurtosis ([-1, 0, 3])) -%!assert (kurtosis (ones (3, 5)), NaN (1, 5)) -%!assert (kurtosis (1, [], 3), NaN) - -%!assert (kurtosis ([1:5 10; 1:5 10], 0, 2), 5.4377317925288901 * [1; 1], 8 * eps) -%!assert (kurtosis ([1:5 10; 1:5 10], 1, 2), 2.9786509002956195 * [1; 1], 8 * eps) -%!assert (kurtosis ([1:5 10; 1:5 10], [], 2), 2.9786509002956195 * [1; 1], 8 * eps) - -## Test behavior on single input -%!assert (kurtosis (single ([1:5 10])), single (2.9786513), eps ("single")) -%!assert (kurtosis (single ([1 2]), 0), single (NaN)) - -## Verify no "divide-by-zero" warnings -%!test -%! warning ("on", "Octave:divide-by-zero", "local"); -%! lastwarn (""); # clear last warning -%! kurtosis (1); -%! assert (lastwarn (), ""); - -## Test input validation -%!error kurtosis () -%!error kurtosis (1, 2, 3) -%!error <X must be a numeric vector or matrix> kurtosis (['A'; 'B']) -%!error <FLAG must be 0 or 1> kurtosis (1, 2) -%!error <FLAG must be 0 or 1> kurtosis (1, [1 0]) -%!error <DIM must be an integer> kurtosis (1, [], ones (2,2)) -%!error <DIM must be an integer> kurtosis (1, [], 1.5) -%!error <DIM must be .* a valid dimension> kurtosis (1, [], 0)
--- a/scripts/statistics/base/logit.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,61 +0,0 @@ -## Copyright (C) 1995-2017 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} logit (@var{p}) -## Compute the logit for each value of @var{p} -## -## The logit is defined as -## @tex -## $$ -## {\rm logit}(p) = \log\Big({p \over 1-p}\Big) -## $$ -## @end tex -## @ifnottex -## -## @example -## logit (@var{p}) = log (@var{p} / (1-@var{p})) -## @end example -## -## @end ifnottex -## @seealso{probit, logistic_cdf} -## @end deftypefn - -## Author: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: Logit transformation - -function y = logit (p) - - if (nargin != 1) - print_usage (); - endif - - y = logistic_inv (p); - -endfunction - - -%!test -%! p = [0.01:0.01:0.99]; -%! assert (logit (p), log (p ./ (1-p)), 25*eps); - -%!assert (logit ([-1, 0, 0.5, 1, 2]), [NaN, -Inf, 0, +Inf, NaN]) - -## Test input validation -%!error logit () -%!error logit (1, 2)
--- a/scripts/statistics/base/mean.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,164 +0,0 @@ -## Copyright (C) 1995-2017 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} mean (@var{x}) -## @deftypefnx {} {} mean (@var{x}, @var{dim}) -## @deftypefnx {} {} mean (@var{x}, @var{opt}) -## @deftypefnx {} {} mean (@var{x}, @var{dim}, @var{opt}) -## Compute the mean of the elements of the vector @var{x}. -## -## The mean is defined as -## -## @tex -## $$ {\rm mean}(x) = \bar{x} = {1\over N} \sum_{i=1}^N x_i $$ -## where $N$ is the number of elements of @var{x}. -## -## @end tex -## @ifnottex -## -## @example -## mean (@var{x}) = SUM_i @var{x}(i) / N -## @end example -## -## where @math{N} is the length of the @var{x} vector. -## -## @end ifnottex -## If @var{x} is a matrix, compute the mean for each column and return them -## in a row vector. -## -## If the optional argument @var{dim} is given, operate along this dimension. -## -## The optional argument @var{opt} selects the type of mean to compute. -## The following options are recognized: -## -## @table @asis -## @item @qcode{"a"} -## Compute the (ordinary) arithmetic mean. [default] -## -## @item @qcode{"g"} -## Compute the geometric mean. -## -## @item @qcode{"h"} -## Compute the harmonic mean. -## @end table -## -## Both @var{dim} and @var{opt} are optional. If both are supplied, either -## may appear first. -## @seealso{median, mode} -## @end deftypefn - -## Author: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: Compute arithmetic, geometric, and harmonic mean - -function y = mean (x, opt1, opt2) - - if (nargin < 1 || nargin > 3) - print_usage (); - endif - - if (! (isnumeric (x) || islogical (x))) - error ("mean: X must be a numeric vector or matrix"); - endif - - need_dim = false; - - if (nargin == 1) - opt = "a"; - need_dim = true; - elseif (nargin == 2) - if (ischar (opt1)) - opt = opt1; - need_dim = true; - else - dim = opt1; - opt = "a"; - endif - elseif (nargin == 3) - if (ischar (opt1)) - opt = opt1; - dim = opt2; - elseif (ischar (opt2)) - opt = opt2; - dim = opt1; - else - error ("mean: OPT must be a string"); - endif - else - print_usage (); - endif - - nd = ndims (x); - sz = size (x); - if (need_dim) - ## Find the first non-singleton dimension. - (dim = find (sz > 1, 1)) || (dim = 1); - else - if (! (isscalar (dim) && dim == fix (dim) && dim > 0)) - error ("mean: DIM must be an integer and a valid dimension"); - endif - endif - - n = size (x, dim); - - if (strcmp (opt, "a")) - y = sum (x, dim) / n; - elseif (strcmp (opt, "g")) - if (all (x(:) >= 0)) - y = exp (sum (log (x), dim) ./ n); - else - error ("mean: X must not contain any negative values"); - endif - elseif (strcmp (opt, "h")) - y = n ./ sum (1 ./ x, dim); - else - error ("mean: option '%s' not recognized", opt); - endif - -endfunction - - -%!test -%! x = -10:10; -%! y = x'; -%! z = [y, y+10]; -%! assert (mean (x), 0); -%! assert (mean (y), 0); -%! assert (mean (z), [0, 10]); - -## Test small numbers -%!assert (mean (repmat (0.1,1,1000), "g"), 0.1, 20*eps) - -%!assert (mean (magic (3), 1), [5, 5, 5]) -%!assert (mean (magic (3), 2), [5; 5; 5]) -%!assert (mean ([2 8], "g"), 4) -%!assert (mean ([4 4 2], "h"), 3) -%!assert (mean (logical ([1 0 1 1])), 0.75) -%!assert (mean (single ([1 0 1 1])), single (0.75)) -%!assert (mean ([1 2], 3), [1 2]) - -## Test input validation -%!error mean () -%!error mean (1, 2, 3, 4) -%!error <X must be a numeric> mean ({1:5}) -%!error <OPT must be a string> mean (1, 2, 3) -%!error <DIM must be an integer> mean (1, ones (2,2)) -%!error <DIM must be an integer> mean (1, 1.5) -%!error <DIM must be .* a valid dimension> mean (1, 0) -%!error <X must not contain any negative values> mean ([1 -1], "g") -%!error <option 'b' not recognized> mean (1, "b")
--- a/scripts/statistics/base/meansq.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,92 +0,0 @@ -## Copyright (C) 1995-2017 Kurt Hornik -## Copyright (C) 2009 Jaroslav Hajek -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} meansq (@var{x}) -## @deftypefnx {} {} meansq (@var{x}, @var{dim}) -## Compute the mean square of the elements of the vector @var{x}. -## -## The mean square is defined as -## @tex -## $$ -## {\rm meansq} (x) = {\sum_{i=1}^N {x_i}^2 \over N} -## $$ -## where $N$ is the number of elements of @var{x}. -## -## @end tex -## @ifnottex -## -## @example -## @group -## meansq (@var{x}) = 1/N SUM_i @var{x}(i)^2 -## @end group -## @end example -## -## where @math{N} is the length of the @var{x} vector. -## -## @end ifnottex -## If @var{x} is a matrix, return a row vector containing the mean square -## of each column. -## -## If the optional argument @var{dim} is given, operate along this dimension. -## @seealso{var, std, moment} -## @end deftypefn - -## Author: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: Compute mean square - -function y = meansq (x, dim) - - if (nargin != 1 && nargin != 2) - print_usage (); - endif - - if (! (isnumeric (x) || islogical (x))) - error ("mean: X must be a numeric vector or matrix"); - endif - - nd = ndims (x); - sz = size (x); - if (nargin < 2) - ## Find the first non-singleton dimension. - (dim = find (sz > 1, 1)) || (dim = 1); - else - if (! (isscalar (dim) && dim == fix (dim) && dim > 0)) - error ("mean: DIM must be an integer and a valid dimension"); - endif - endif - - y = sumsq (x, dim) / size (x, dim); - -endfunction - - -%!assert (meansq (1:5), 11) -%!assert (meansq (single (1:5)), single (11)) -%!assert (meansq (magic (4)), [94.5, 92.5, 92.5, 94.5]) -%!assert (meansq (magic (4), 2), [109.5; 77.5; 77.5; 109.5]) -%!assert (meansq ([1 2], 3), [1 4]) - -## Test input validation -%!error meansq () -%!error meansq (1, 2, 3) -%!error <X must be a numeric> meansq (['A'; 'B']) -%!error <DIM must be an integer> meansq (1, ones (2,2)) -%!error <DIM must be an integer> meansq (1, 1.5) -%!error <DIM must be .* a valid dimension> meansq (1, 0)
--- a/scripts/statistics/base/median.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,141 +0,0 @@ -## Copyright (C) 1996-2017 John W. Eaton -## Copyright (C) 2009-2010 VZLU Prague -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} median (@var{x}) -## @deftypefnx {} {} median (@var{x}, @var{dim}) -## Compute the median value of the elements of the vector @var{x}. -## -## When the elements of @var{x} are sorted, say @code{@var{s} = sort (@var{x})}, -## the median is defined as -## @tex -## $$ -## {\rm median} (x) = -## \cases{s(\lceil N/2\rceil), & $N$ odd;\cr -## (s(N/2)+s(N/2+1))/2, & $N$ even.} -## $$ -## where $N$ is the number of elements of @var{x}. -## -## @end tex -## @ifnottex -## -## @example -## @group -## | @var{s}(ceil(N/2)) N odd -## median (@var{x}) = | -## | (@var{s}(N/2) + @var{s}(N/2+1))/2 N even -## @end group -## @end example -## -## @end ifnottex -## If @var{x} is of a discrete type such as integer or logical, then -## the case of even @math{N} rounds up (or toward @code{true}). -## -## If @var{x} is a matrix, compute the median value for each column and -## return them in a row vector. -## -## If the optional @var{dim} argument is given, operate along this dimension. -## @seealso{mean, mode} -## @end deftypefn - -## Author: jwe - -function retval = median (x, dim) - - if (nargin != 1 && nargin != 2) - print_usage (); - endif - - if (! (isnumeric (x) || islogical (x))) - error ("median: X must be a numeric vector or matrix"); - endif - - if (isempty (x)) - error ("median: X cannot be an empty matrix"); - endif - - nd = ndims (x); - sz = size (x); - if (nargin < 2) - ## Find the first non-singleton dimension. - (dim = find (sz > 1, 1)) || (dim = 1); - else - if (! (isscalar (dim) && dim == fix (dim) && dim > 0)) - error ("median: DIM must be an integer and a valid dimension"); - endif - endif - - n = size (x, dim); - k = floor ((n+1) / 2); - if (mod (n, 2) == 1) - retval = nth_element (x, k, dim); - else - retval = sum (nth_element (x, k:k+1, dim), dim, "native") / 2; - if (islogical (x)) - retval = logical (retval); - endif - endif - ## Inject NaNs where needed, to be consistent with Matlab. - if (isfloat (x)) - retval(any (isnan (x), dim)) = NaN; - endif - -endfunction - - -%!test -%! x = [1, 2, 3, 4, 5, 6]; -%! x2 = x'; -%! y = [1, 2, 3, 4, 5, 6, 7]; -%! y2 = y'; -%! -%! assert (median (x) == median (x2) && median (x) == 3.5); -%! assert (median (y) == median (y2) && median (y) == 4); -%! assert (median ([x2, 2*x2]), [3.5, 7]); -%! assert (median ([y2, 3*y2]), [4, 12]); - -%!assert (median (single ([1,2,3])), single (2)) -%!assert (median ([1,2,NaN;4,5,6;NaN,8,9]), [NaN, 5, NaN]) -%!assert (median ([1,2], 3), [1,2]) - -## Test multidimensional arrays -%!shared a, b, x, y -%! rand ("seed", 2); -%! a = rand (2,3,4,5); -%! b = rand (3,4,6,5); -%! x = sort (a, 4); -%! y = sort (b, 3); -%!assert <*35679> (median (a, 4), x(:, :, :, 3)) -%!assert <*35679> (median (b, 3), (y(:, :, 3, :) + y(:, :, 4, :))/2) - -## Test non-floating point types -%!assert (median ([true, false]), true) -%!assert (median (uint8 ([1, 3])), uint8 (2)) -%!assert (median (int8 ([1, 3, 4])), int8 (3)) -%!assert (median (single ([1, 3, 4])), single (3)) -%!assert (median (single ([1, 3, NaN])), single (NaN)) - -## Test input validation -%!error median () -%!error median (1, 2, 3) -%!error <X must be a numeric> median ({1:5}) -%!error <X cannot be an empty matrix> median ([]) -%!error <DIM must be an integer> median (1, ones (2,2)) -%!error <DIM must be an integer> median (1, 1.5) -%!error <DIM must be .* a valid dimension> median (1, 0)
--- a/scripts/statistics/base/mode.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,183 +0,0 @@ -## Copyright (C) 2007-2017 David Bateman -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} mode (@var{x}) -## @deftypefnx {} {} mode (@var{x}, @var{dim}) -## @deftypefnx {} {[@var{m}, @var{f}, @var{c}] =} mode (@dots{}) -## Compute the most frequently occurring value in a dataset (mode). -## -## @code{mode} determines the frequency of values along the first non-singleton -## dimension and returns the value with the highest frequency. If two, or -## more, values have the same frequency @code{mode} returns the smallest. -## -## If the optional argument @var{dim} is given, operate along this dimension. -## -## The return variable @var{f} is the number of occurrences of the mode in -## the dataset. -## -## The cell array @var{c} contains all of the elements with the maximum -## frequency. -## @seealso{mean, median} -## @end deftypefn - -function [m, f, c] = mode (x, dim) - - if (nargin < 1 || nargin > 2) - print_usage (); - endif - - if (! (isnumeric (x) || islogical (x))) - error ("mode: X must be a numeric vector or matrix"); - endif - - nd = ndims (x); - sz = size (x); - if (nargin < 2) - ## Find the first non-singleton dimension. - (dim = find (sz > 1, 1)) || (dim = 1); - else - if (! (isscalar (dim) && dim == fix (dim) && dim > 0)) - error ("mode: DIM must be an integer and a valid dimension"); - endif - endif - - if (dim > nd) - ## Special case of mode over non-existent dimension. - m = x; - f = ones (size (x)); - c = num2cell (x); - return; - endif - - sz2 = sz; - sz2(dim) = 1; - sz3 = ones (1, nd); - sz3(dim) = sz(dim); - - if (issparse (x)) - t2 = sparse (sz(1), sz(2)); - else - t2 = zeros (sz); - endif - - if (dim != 1) - perm = [dim, 1:dim-1, dim+1:nd]; - t2 = permute (t2, perm); - endif - - xs = sort (x, dim); - t = cat (dim, true (sz2), diff (xs, 1, dim) != 0); - - if (dim != 1) - t2(permute (t != 0, perm)) = diff ([find(permute (t, perm))(:); prod(sz)+1]); - f = max (ipermute (t2, perm), [], dim); - xs = permute (xs, perm); - else - t2(t) = diff ([find(t)(:); prod(sz)+1]); - f = max (t2, [], dim); - endif - - c = cell (sz2); - if (issparse (x)) - m = sparse (sz2(1), sz2(2)); - else - m = zeros (sz2, class (x)); - endif - for i = 1 : prod (sz2) - c{i} = xs(t2(:, i) == f(i), i); - m(i) = c{i}(1); - endfor - -endfunction - - -%!test -%! [m, f, c] = mode (toeplitz (1:5)); -%! assert (m, [1,2,2,2,1]); -%! assert (f, [1,2,2,2,1]); -%! assert (c, {[1;2;3;4;5],[2],[2;3],[2],[1;2;3;4;5]}); -%!test -%! [m, f, c] = mode (toeplitz (1:5), 2); -%! assert (m, [1;2;2;2;1]); -%! assert (f, [1;2;2;2;1]); -%! assert (c, {[1;2;3;4;5];[2];[2;3];[2];[1;2;3;4;5]}); -%!test -%! a = sprandn (32, 32, 0.05); -%! sp0 = sparse (0); -%! [m, f, c] = mode (a); -%! [m2, f2, c2] = mode (full (a)); -%! assert (m, sparse (m2)); -%! assert (f, sparse (f2)); -%! c_exp(1:length (a)) = { sp0 }; -%! assert (c ,c_exp); -%! assert (c2,c_exp); - -%!assert (mode ([2,3,1,2,3,4],1),[2,3,1,2,3,4]) -%!assert (mode ([2,3,1,2,3,4],2),2) -%!assert (mode ([2,3,1,2,3,4]),2) -%!assert (mode (single ([2,3,1,2,3,4])), single (2)) -%!assert (mode (int8 ([2,3,1,2,3,4])), int8 (2)) - -%!assert (mode ([2;3;1;2;3;4],1),2) -%!assert (mode ([2;3;1;2;3;4],2),[2;3;1;2;3;4]) -%!assert (mode ([2;3;1;2;3;4]),2) - -%!test -%! x = magic (3); -%! [m, f, c] = mode (x, 3); -%! assert (m, x); -%! assert (f, ones (3,3)); -%! assert (c, num2cell (x)); - -%!shared x -%! x(:,:,1) = toeplitz (1:3); -%! x(:,:,2) = circshift (toeplitz (1:3), 1); -%! x(:,:,3) = circshift (toeplitz (1:3), 2); -%!test -%! [m, f, c] = mode (x, 1); -%! assert (reshape (m, [3, 3]), [1 1 1; 2 2 2; 1 1 1]); -%! assert (reshape (f, [3, 3]), [1 1 1; 2 2 2; 1 1 1]); -%! c = reshape (c, [3, 3]); -%! assert (c{1}, [1; 2; 3]); -%! assert (c{2}, 2); -%! assert (c{3}, [1; 2; 3]); -%!test -%! [m, f, c] = mode (x, 2); -%! assert (reshape (m, [3, 3]), [1 1 2; 2 1 1; 1 2 1]); -%! assert (reshape (f, [3, 3]), [1 1 2; 2 1 1; 1 2 1]); -%! c = reshape (c, [3, 3]); -%! assert (c{1}, [1; 2; 3]); -%! assert (c{2}, 2); -%! assert (c{3}, [1; 2; 3]); -%!test -%! [m, f, c] = mode (x, 3); -%! assert (reshape (m, [3, 3]), [1 2 1; 1 2 1; 1 2 1]); -%! assert (reshape (f, [3, 3]), [1 2 1; 1 2 1; 1 2 1]); -%! c = reshape (c, [3, 3]); -%! assert (c{1}, [1; 2; 3]); -%! assert (c{2}, [1; 2; 3]); -%! assert (c{3}, [1; 2; 3]); - -## Test input validation -%!error mode () -%!error mode (1, 2, 3) -%!error <X must be a numeric> mode ({1 2 3}) -%!error <DIM must be an integer> mode (1, ones (2,2)) -%!error <DIM must be an integer> mode (1, 1.5) -%!error <DIM must be .* a valid dimension> mode (1, 0)
--- a/scripts/statistics/base/module.mk Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,44 +0,0 @@ -FCN_FILE_DIRS += scripts/statistics/base - -%canon_reldir%_FCN_FILES = \ - %reldir%/center.m \ - %reldir%/cloglog.m \ - %reldir%/corr.m \ - %reldir%/corrcoef.m \ - %reldir%/cov.m \ - %reldir%/crosstab.m \ - %reldir%/histc.m \ - %reldir%/iqr.m \ - %reldir%/kendall.m \ - %reldir%/kurtosis.m \ - %reldir%/logit.m \ - %reldir%/mean.m \ - %reldir%/meansq.m \ - %reldir%/median.m \ - %reldir%/mode.m \ - %reldir%/moment.m \ - %reldir%/ppplot.m \ - %reldir%/prctile.m \ - %reldir%/probit.m \ - %reldir%/qqplot.m \ - %reldir%/quantile.m \ - %reldir%/range.m \ - %reldir%/ranks.m \ - %reldir%/run_count.m \ - %reldir%/runlength.m \ - %reldir%/skewness.m \ - %reldir%/spearman.m \ - %reldir%/statistics.m \ - %reldir%/std.m \ - %reldir%/var.m \ - %reldir%/zscore.m - -%canon_reldir%dir = $(fcnfiledir)/statistics/base - -%canon_reldir%_DATA = $(%canon_reldir%_FCN_FILES) - -FCN_FILES += $(%canon_reldir%_FCN_FILES) - -PKG_ADD_FILES += %reldir%/PKG_ADD - -DIRSTAMP_FILES += %reldir%/$(octave_dirstamp)
--- a/scripts/statistics/base/moment.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,211 +0,0 @@ -## Copyright (C) 1995-2017 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} moment (@var{x}, @var{p}) -## @deftypefnx {} {} moment (@var{x}, @var{p}, @var{type}) -## @deftypefnx {} {} moment (@var{x}, @var{p}, @var{dim}) -## @deftypefnx {} {} moment (@var{x}, @var{p}, @var{type}, @var{dim}) -## @deftypefnx {} {} moment (@var{x}, @var{p}, @var{dim}, @var{type}) -## Compute the @var{p}-th central moment of the vector @var{x}: -## -## @tex -## $$ -## {\sum_{i=1}^N (x_i - \bar{x})^p \over N} -## $$ -## where $\bar{x}$ is the mean value of @var{x} and $N$ is the number of elements of @var{x}. -## -## -## @end tex -## @ifnottex -## -## @example -## @group -## 1/N SUM_i (@var{x}(i) - mean(@var{x}))^@var{p} -## @end group -## @end example -## -## where @math{N} is the length of the @var{x} vector. -## -## @end ifnottex -## -## If @var{x} is a matrix, return the row vector containing the @var{p}-th -## central moment of each column. -## -## If the optional argument @var{dim} is given, operate along this dimension. -## -## The optional string @var{type} specifies the type of moment to be computed. -## Valid options are: -## -## @table @asis -## @item @qcode{"c"} -## Central Moment (default). -## -## @item @qcode{"a"} -## @itemx @qcode{"ac"} -## Absolute Central Moment. The moment about the mean ignoring sign -## defined as -## @tex -## $$ -## {\sum_{i=1}^N {\left| x_i - \bar{x} \right|}^p \over N} -## $$ -## @end tex -## @ifnottex -## -## @example -## @group -## 1/N SUM_i (abs (@var{x}(i) - mean(@var{x})))^@var{p} -## @end group -## @end example -## -## @end ifnottex -## -## @item @qcode{"r"} -## Raw Moment. The moment about zero defined as -## -## @tex -## $$ -## {\rm moment} (x) = { \sum_{i=1}^N {x_i}^p \over N } -## $$ -## @end tex -## @ifnottex -## -## @example -## @group -## moment (@var{x}) = 1/N SUM_i @var{x}(i)^@var{p} -## @end group -## @end example -## -## @end ifnottex -## -## @item @nospell{@qcode{"ar"}} -## Absolute Raw Moment. The moment about zero ignoring sign defined as -## @tex -## $$ -## {\sum_{i=1}^N {\left| x_i \right|}^p \over N} -## $$ -## @end tex -## @ifnottex -## -## @example -## @group -## 1/N SUM_i ( abs (@var{x}(i)) )^@var{p} -## @end group -## @end example -## -## @end ifnottex -## @end table -## -## If both @var{type} and @var{dim} are given they may appear in any order. -## @seealso{var, skewness, kurtosis} -## @end deftypefn - -## Can easily be made to work for continuous distributions (using quad) -## as well, but how does the general case work? - -## Author: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: Compute moments - -function m = moment (x, p, opt1, opt2) - - if (nargin < 2 || nargin > 4) - print_usage (); - endif - - if (! (isnumeric (x) || islogical (x)) || isempty (x)) - error ("moment: X must be a non-empty numeric matrix or vector"); - endif - - if (! (isnumeric (p) && isscalar (p))) - error ("moment: P must be a numeric scalar"); - endif - - need_dim = false; - - if (nargin == 2) - type = ""; - need_dim = true; - elseif (nargin == 3) - if (ischar (opt1)) - type = opt1; - need_dim = true; - else - dim = opt1; - type = ""; - endif - elseif (nargin == 4) - if (ischar (opt1)) - type = opt1; - dim = opt2; - elseif (ischar (opt2)) - type = opt2; - dim = opt1; - else - error ("moment: TYPE must be a string"); - endif - endif - - nd = ndims (x); - sz = size (x); - if (need_dim) - ## Find the first non-singleton dimension. - (dim = find (sz > 1, 1)) || (dim = 1); - else - if (! (isscalar (dim) && dim == fix (dim) && dim > 0)) - error ("moment: DIM must be an integer and a valid dimension"); - endif - endif - - n = size (x, dim); - - if (! any (type == "r")) - x = center (x, dim); - endif - if (any (type == "a")) - x = abs (x); - endif - - m = sum (x .^ p, dim) / n; - -endfunction - - -%!shared x -%! x = rand (10); -%!assert (moment (x,1), mean (center (x)), eps) -%!assert (moment (x,2), meansq (center (x)), eps) -%!assert (moment (x,1,2), mean (center (x, 2), 2), eps) -%!assert (moment (x,1,"a"), mean (abs (center (x))), eps) -%!assert (moment (x,1,"r"), mean (x), eps) -%!assert (moment (x,1,"ar"), mean (abs (x)), eps) - -%!assert (moment (single ([1 2 3]), 1, "r"), single (2)) - -%!assert (moment (1, 2, 4), 0) - -## Test input validation -%!error moment () -%!error moment (1) -%!error moment (1, 2, 3, 4, 5) -%!error <X must be a non-empty numeric matrix> moment (['A'; 'B'], 2) -%!error <X must be a non-empty numeric matrix> moment (ones (2,0,3), 2) -%!error <P must be a numeric scalar> moment (1, true) -%!error <P must be a numeric scalar> moment (1, ones (2,2)) -%!error <TYPE must be a string> moment (1, 2, 3, 4) -%!error <DIM must be an integer and a valid dimension> moment (1, 2, ones (2,2)) -%!error <DIM must be an integer and a valid dimension> moment (1, 2, 1.5)
--- a/scripts/statistics/base/ppplot.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,91 +0,0 @@ -## Copyright (C) 1995-2017 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {[@var{p}, @var{y}] =} ppplot (@var{x}, @var{dist}, @var{params}) -## Perform a PP-plot (probability plot). -## -## If F is the CDF of the distribution @var{dist} with parameters -## @var{params} and @var{x} a sample vector of length @var{n}, the PP-plot -## graphs ordinate @var{y}(@var{i}) = F (@var{i}-th largest element of -## @var{x}) versus abscissa @var{p}(@var{i}) = (@var{i} - 0.5)/@var{n}. If -## the sample comes from F, the pairs will approximately follow a straight -## line. -## -## The default for @var{dist} is the standard normal distribution. -## -## The optional argument @var{params} contains a list of parameters of -## @var{dist}. -## -## For example, for a probability plot of the uniform distribution on [2,4] -## and @var{x}, use -## -## @example -## ppplot (x, "uniform", 2, 4) -## @end example -## -## @noindent -## @var{dist} can be any string for which a function @var{dist_cdf} that -## calculates the CDF of distribution @var{dist} exists. -## -## If no output is requested then the data are plotted immediately. -## @seealso{qqplot} -## @end deftypefn - -## Author: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: Perform a PP-plot (probability plot) - -function [p, y] = ppplot (x, dist, varargin) - - if (nargin < 1) - print_usage (); - endif - - if (! isvector (x)) - error ("ppplot: X must be a vector"); - endif - - s = sort (x); - n = length (x); - p = ((1 : n)' - 0.5) / n; - if (nargin == 1) - F = @stdnormal_cdf; - elseif (! ischar (dist)) - error ("ppplot: DIST must be a string"); - else - F = str2func ([dist "cdf"]); - endif - - if (nargin <= 2) - y = feval (F, s); - else - y = feval (F, s, varargin{:}); - endif - - if (nargout == 0) - plot (p, y); - axis ([0, 1, 0, 1]); - endif - -endfunction - - -## Test input validation -%!error ppplot () -%!error ppplot (ones (2,2)) -%!error <DIST must be a string> ppplot (1, 2)
--- a/scripts/statistics/base/prctile.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,186 +0,0 @@ -## Copyright (C) 2008-2017 Ben Abbott -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {@var{q} =} prctile (@var{x}) -## @deftypefnx {} {@var{q} =} prctile (@var{x}, @var{p}) -## @deftypefnx {} {@var{q} =} prctile (@var{x}, @var{p}, @var{dim}) -## For a sample @var{x}, compute the quantiles, @var{q}, corresponding -## to the cumulative probability values, @var{p}, in percent. -## -## If @var{x} is a matrix, compute the percentiles for each column and return -## them in a matrix, such that the i-th row of @var{q} contains the -## @var{p}(i)th percentiles of each column of @var{x}. -## -## If @var{p} is unspecified, return the quantiles for @code{[0 25 50 75 100]}. -## -## The optional argument @var{dim} determines the dimension along which the -## percentiles are calculated. If @var{dim} is omitted it defaults to the -## first non-singleton dimension. -## -## Programming Note: All non-numeric values (NaNs) of @var{x} are ignored. -## @seealso{quantile} -## @end deftypefn - -## Author: Ben Abbott <bpabbott@mac.com> -## Description: Matlab style prctile function. - -function q = prctile (x, p = [], dim) - - if (nargin < 1 || nargin > 3) - print_usage (); - endif - - if (! (isnumeric (x) || islogical (x))) - error ("prctile: X must be a numeric vector or matrix"); - endif - - if (isempty (p)) - p = [0, 25, 50, 75, 100]; - endif - - if (! (isnumeric (p) && isvector (p))) - error ("prctile: P must be a numeric vector"); - endif - - nd = ndims (x); - sz = size (x); - if (nargin < 3) - ## Find the first non-singleton dimension. - (dim = find (sz > 1, 1)) || (dim = 1); - else - if (!(isscalar (dim) && dim == fix (dim)) - || !(1 <= dim && dim <= nd)) - error ("prctile: DIM must be an integer and a valid dimension"); - endif - endif - - ## Convert from percent to decimal. - p /= 100; - - q = quantile (x, p, dim); - -endfunction - - -%!test -%! pct = 50; -%! q = prctile (1:4, pct); -%! qa = 2.5; -%! assert (q, qa); -%! q = prctile (1:4, pct, 1); -%! qa = [1, 2, 3, 4]; -%! assert (q, qa); -%! q = prctile (1:4, pct, 2); -%! qa = 2.5; -%! assert (q, qa); - -%!test -%! pct = [50 75]; -%! q = prctile (1:4, pct); -%! qa = [2.5 3.5]; -%! assert (q, qa); -%! q = prctile (1:4, pct, 1); -%! qa = [1, 2, 3, 4; 1, 2, 3, 4]; -%! assert (q, qa); -%! q = prctile (1:4, pct, 2); -%! qa = [2.5 3.5]; -%! assert (q, qa); - -%!test -%! pct = 50; -%! x = [0.1126, 0.1148, 0.0521, 0.2364, 0.1393 -%! 0.1718, 0.7273, 0.2041, 0.4531, 0.1585 -%! 0.2795, 0.7978, 0.3296, 0.5567, 0.7307 -%! 0.4288, 0.8753, 0.6477, 0.6287, 0.8165 -%! 0.9331, 0.9312, 0.9635, 0.7796, 0.8461]; -%! tol = 0.0001; -%! q = prctile (x, pct, 1); -%! qa = [0.2795, 0.7978, 0.3296, 0.5567, 0.7307]; -%! assert (q, qa, tol); -%! q = prctile (x, pct, 2); -%! qa = [0.1148; 0.2041; 0.5567; 0.6477; 0.9312]; -%! assert (q, qa, tol); - -%!test -%! pct = 50; -%! tol = 0.0001; -%! x = [0.1126, 0.1148, 0.0521, 0.2364, 0.1393 -%! 0.1718, 0.7273, 0.2041, 0.4531, 0.1585 -%! 0.2795, 0.7978, 0.3296, 0.5567, 0.7307 -%! 0.4288, 0.8753, 0.6477, 0.6287, 0.8165 -%! 0.9331, 0.9312, 0.9635, 0.7796, 0.8461]; -%! x(5,5) = Inf; -%! q = prctile (x, pct, 1); -%! qa = [0.2795, 0.7978, 0.3296, 0.5567, 0.7307]; -%! assert (q, qa, tol); -%! x(5,5) = -Inf; -%! q = prctile (x, pct, 1); -%! qa = [0.2795, 0.7978, 0.3296, 0.5567, 0.1585]; -%! assert (q, qa, tol); -%! x(1,1) = Inf; -%! q = prctile (x, pct, 1); -%! qa = [0.4288, 0.7978, 0.3296, 0.5567, 0.1585]; -%! assert (q, qa, tol); - -%!test -%! pct = 50; -%! tol = 0.0001; -%! x = [0.1126, 0.1148, 0.0521, 0.2364, 0.1393 -%! 0.1718, 0.7273, 0.2041, 0.4531, 0.1585 -%! 0.2795, 0.7978, 0.3296, 0.5567, 0.7307 -%! 0.4288, 0.8753, 0.6477, 0.6287, 0.8165 -%! 0.9331, 0.9312, 0.9635, 0.7796, 0.8461]; -%! x(3,3) = Inf; -%! q = prctile (x, pct, 1); -%! qa = [0.2795, 0.7978, 0.6477, 0.5567, 0.7307]; -%! assert (q, qa, tol); -%! q = prctile (x, pct, 2); -%! qa = [0.1148; 0.2041; 0.7307; 0.6477; 0.9312]; -%! assert (q, qa, tol); - -%!test -%! pct = 50; -%! tol = 0.0001; -%! x = [0.1126, 0.1148, 0.0521, 0.2364, 0.1393 -%! 0.1718, 0.7273, 0.2041, 0.4531, 0.1585 -%! 0.2795, 0.7978, 0.3296, 0.5567, 0.7307 -%! 0.4288, 0.8753, 0.6477, 0.6287, 0.8165 -%! 0.9331, 0.9312, 0.9635, 0.7796, 0.8461]; -%! x(5,5) = NaN; -%! q = prctile (x, pct, 2); -%! qa = [0.1148; 0.2041; 0.5567; 0.6477; 0.9322]; -%! assert (q, qa, tol); -%! x(1,1) = NaN; -%! q = prctile (x, pct, 2); -%! qa = [0.1270; 0.2041; 0.5567; 0.6477; 0.9322]; -%! assert (q, qa, tol); -%! x(3,3) = NaN; -%! q = prctile (x, pct, 2); -%! qa = [0.1270; 0.2041; 0.6437; 0.6477; 0.9322]; -%! assert (q, qa, tol); - -## Test input validation -%!error prctile () -%!error prctile (1, 2, 3, 4) -%!error prctile (['A'; 'B'], 10) -%!error prctile (1:10, [true, false]) -%!error prctile (1:10, ones (2,2)) -%!error prctile (1, 1, 1.5) -%!error prctile (1, 1, 0) -%!error prctile (1, 1, 3)
--- a/scripts/statistics/base/probit.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,45 +0,0 @@ -## Copyright (C) 1995-2017 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} probit (@var{p}) -## Return the probit (the quantile of the standard normal distribution) for -## each element of @var{p}. -## @seealso{logit} -## @end deftypefn - -## Written by KH <Kurt.Hornik@wu-wien.ac.at> on 1995/02/04 -## Description: Probit transformation - -function y = probit (p) - - - if (nargin != 1) - print_usage (); - endif - - y = stdnormal_inv (p); - -endfunction - - -%!assert (probit ([-1, 0, 0.5, 1, 2]), [NaN, -Inf, 0, Inf, NaN]) - -## Test input validation -%!error probit () -%!error probit (1, 2)
--- a/scripts/statistics/base/qqplot.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,119 +0,0 @@ -## Copyright (C) 1995-2017 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {[@var{q}, @var{s}] =} qqplot (@var{x}) -## @deftypefnx {} {[@var{q}, @var{s}] =} qqplot (@var{x}, @var{y}) -## @deftypefnx {} {[@var{q}, @var{s}] =} qqplot (@var{x}, @var{dist}) -## @deftypefnx {} {[@var{q}, @var{s}] =} qqplot (@var{x}, @var{y}, @var{params}) -## @deftypefnx {} {} qqplot (@dots{}) -## Perform a QQ-plot (quantile plot). -## -## If F is the CDF of the distribution @var{dist} with parameters -## @var{params} and G its inverse, and @var{x} a sample vector of length -## @var{n}, the QQ-plot graphs ordinate @var{s}(@var{i}) = @var{i}-th -## largest element of x versus abscissa @var{q}(@var{i}f) = G((@var{i} - -## 0.5)/@var{n}). -## -## If the sample comes from F, except for a transformation of location -## and scale, the pairs will approximately follow a straight line. -## -## If the second argument is a vector @var{y} the empirical CDF of @var{y} -## is used as @var{dist}. -## -## The default for @var{dist} is the standard normal distribution. The -## optional argument @var{params} contains a list of parameters of -## @var{dist}. For example, for a quantile plot of the uniform -## distribution on [2,4] and @var{x}, use -## -## @example -## qqplot (x, "unif", 2, 4) -## @end example -## -## @noindent -## @var{dist} can be any string for which a function @var{distinv} or -## @var{dist_inv} exists that calculates the inverse CDF of distribution -## @var{dist}. -## -## If no output arguments are given, the data are plotted directly. -## @seealso{ppplot} -## @end deftypefn - -## Author: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: Perform a QQ-plot (quantile plot) - -function [qout, sout] = qqplot (x, dist, varargin) - - if (nargin < 1) - print_usage (); - endif - - if (! (isnumeric (x) && isvector (x))) - error ("qqplot: X must be a numeric vector"); - endif - - if (nargin == 1) - f = @stdnormal_inv; - else - if (isnumeric (dist)) - f = @(y) empirical_inv (y, dist); - elseif (ischar (dist) && (exist (invname = [dist "inv"]) - || exist (invname = [dist "_inv"]))) - f = str2func (invname); - else - error ("qqplot: no inverse CDF found for distribution DIST"); - endif - endif; - - s = sort (x); - n = length (x); - t = ((1 : n)' - .5) / n; - if (nargin <= 2) - q = f (t); - q_label = func2str (f); - else - q = f (t, varargin{:}); - if (nargin == 3) - q_label = sprintf ("%s with parameter %g", func2str (f), varargin{1}); - else - q_label = sprintf ("%s with parameters %g", func2str (f), varargin{1}); - param_str = sprintf (", %g", varargin{2:end}); - q_label = [q_label param_str]; - endif - endif - - if (nargout == 0) - plot (q, s, "-x"); - q_label = strrep (q_label, '_inv', '\_inv'); - if (q_label(1) == '@') - q_label = q_label(6:end); # Strip "@(y) " from anon. function - endif - xlabel (q_label); - ylabel ("sample points"); - else - qout = q; - sout = s; - endif - -endfunction - -## Test input validation -%!error qqplot () -%!error <X must be a numeric> qqplot ({1}) -%!error <X must be a .* vector> qqplot (ones (2,2)) -%!error <no inverse CDF found> qqplot (1, "foobar")
--- a/scripts/statistics/base/quantile.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,490 +0,0 @@ -## Copyright (C) 2008-2017 Ben Abbott and Jaroslav Hajek -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {@var{q} =} quantile (@var{x}) -## @deftypefnx {} {@var{q} =} quantile (@var{x}, @var{p}) -## @deftypefnx {} {@var{q} =} quantile (@var{x}, @var{p}, @var{dim}) -## @deftypefnx {} {@var{q} =} quantile (@var{x}, @var{p}, @var{dim}, @var{method}) -## For a sample, @var{x}, calculate the quantiles, @var{q}, corresponding to -## the cumulative probability values in @var{p}. All non-numeric values (NaNs) -## of @var{x} are ignored. -## -## If @var{x} is a matrix, compute the quantiles for each column and -## return them in a matrix, such that the i-th row of @var{q} contains -## the @var{p}(i)th quantiles of each column of @var{x}. -## -## If @var{p} is unspecified, return the quantiles for -## @code{[0.00 0.25 0.50 0.75 1.00]}. -## The optional argument @var{dim} determines the dimension along which -## the quantiles are calculated. If @var{dim} is omitted it defaults to -## the first non-singleton dimension. -## -## The methods available to calculate sample quantiles are the nine methods -## used by R (@url{http://www.r-project.org/}). The default value is -## @w{@var{method} = 5}. -## -## Discontinuous sample quantile methods 1, 2, and 3 -## -## @enumerate 1 -## @item Method 1: Inverse of empirical distribution function. -## -## @item Method 2: Similar to method 1 but with averaging at discontinuities. -## -## @item Method 3: SAS definition: nearest even order statistic. -## @end enumerate -## -## Continuous sample quantile methods 4 through 9, where -## @tex -## $p(k)$ -## @end tex -## @ifnottex -## @var{p}(k) -## @end ifnottex -## is the linear -## interpolation function respecting each method's representative cdf. -## -## @enumerate 4 -## @item Method 4: -## @tex -## $p(k) = k / N$. -## @end tex -## @ifnottex -## @var{p}(k) = k / N. -## @end ifnottex -## That is, linear interpolation of the empirical cdf, where @math{N} is the -## length of @var{P}. -## -## @item Method 5: -## @tex -## $p(k) = (k - 0.5) / N$. -## @end tex -## @ifnottex -## @var{p}(k) = (k - 0.5) / N. -## @end ifnottex -## That is, a piecewise linear function where the knots are the values midway -## through the steps of the empirical cdf. -## -## @item Method 6: -## @tex -## $p(k) = k / (N + 1)$. -## @end tex -## @ifnottex -## @var{p}(k) = k / (N + 1). -## @end ifnottex -## -## @item Method 7: -## @tex -## $p(k) = (k - 1) / (N - 1)$. -## @end tex -## @ifnottex -## @var{p}(k) = (k - 1) / (N - 1). -## @end ifnottex -## -## @item Method 8: -## @tex -## $p(k) = (k - 1/3) / (N + 1/3)$. -## @end tex -## @ifnottex -## @var{p}(k) = (k - 1/3) / (N + 1/3). -## @end ifnottex -## The resulting quantile estimates are approximately median-unbiased -## regardless of the distribution of @var{x}. -## -## @item Method 9: -## @tex -## $p(k) = (k - 3/8) / (N + 1/4)$. -## @end tex -## @ifnottex -## @var{p}(k) = (k - 3/8) / (N + 1/4). -## @end ifnottex -## The resulting quantile estimates are approximately unbiased for the -## expected order statistics if @var{x} is normally distributed. -## @end enumerate -## -## @nospell{Hyndman and Fan} (1996) recommend method 8. Maxima, S, and R -## (versions prior to 2.0.0) use 7 as their default. Minitab and SPSS -## use method 6. @sc{matlab} uses method 5. -## -## References: -## -## @itemize @bullet -## @item @nospell{Becker, R. A., Chambers, J. M. and Wilks, A. R.} (1988) -## The New S Language. @nospell{Wadsworth & Brooks/Cole}. -## -## @item @nospell{Hyndman, R. J. and Fan, Y.} (1996) Sample quantiles in -## statistical packages, American Statistician, 50, 361--365. -## -## @item R: A Language and Environment for Statistical Computing; -## @url{http://cran.r-project.org/doc/manuals/fullrefman.pdf}. -## @end itemize -## -## Examples: -## @c Set example in small font to prevent overfull line -## -## @smallexample -## @group -## x = randi (1000, [10, 1]); # Create empirical data in range 1-1000 -## q = quantile (x, [0, 1]); # Return minimum, maximum of distribution -## q = quantile (x, [0.25 0.5 0.75]); # Return quartiles of distribution -## @end group -## @end smallexample -## @seealso{prctile} -## @end deftypefn - -## Author: Ben Abbott <bpabbott@mac.com> -## Description: Matlab style quantile function of a discrete/continuous -## distribution. - -function q = quantile (x, p = [], dim, method = 5) - - if (nargin < 1 || nargin > 4) - print_usage (); - endif - - if (! (isnumeric (x) || islogical (x)) || isempty (x)) - error ("quantile: X must be a non-empty numeric vector or matrix"); - endif - - if (isempty (p)) - p = [0.00 0.25, 0.50, 0.75, 1.00]; - endif - - if (! (isnumeric (p) && isvector (p))) - error ("quantile: P must be a numeric vector"); - endif - - if (nargin < 3) - ## Find the first non-singleton dimension. - (dim = find (size (x) > 1, 1)) || (dim = 1); - else - if (!(isscalar (dim) && dim == fix (dim)) - || !(1 <= dim && dim <= ndims (x))) - error ("quantile: DIM must be an integer and a valid dimension"); - endif - endif - - ## Set the permutation vector. - perm = 1:ndims (x); - perm(1) = dim; - perm(dim) = 1; - - ## Permute dim to the 1st index. - x = permute (x, perm); - - ## Save the size of the permuted x N-d array. - sx = size (x); - - ## Reshape to a 2-d array. - x = reshape (x, [sx(1), prod(sx(2:end))]); - - ## Calculate the quantiles. - q = __quantile__ (x, p, method); - - ## Return the shape to the original N-d array. - q = reshape (q, [numel(p), sx(2:end)]); - - ## Permute the 1st index back to dim. - q = ipermute (q, perm); - -endfunction - - -%!test -%! p = 0.50; -%! q = quantile (1:4, p); -%! qa = 2.5; -%! assert (q, qa); -%! q = quantile (1:4, p, 1); -%! qa = [1, 2, 3, 4]; -%! assert (q, qa); -%! q = quantile (1:4, p, 2); -%! qa = 2.5; -%! assert (q, qa); - -%!test -%! p = [0.50 0.75]; -%! q = quantile (1:4, p); -%! qa = [2.5 3.5]; -%! assert (q, qa); -%! q = quantile (1:4, p, 1); -%! qa = [1, 2, 3, 4; 1, 2, 3, 4]; -%! assert (q, qa); -%! q = quantile (1:4, p, 2); -%! qa = [2.5 3.5]; -%! assert (q, qa); - -%!test -%! p = 0.5; -%! x = sort (rand (11)); -%! q = quantile (x, p); -%! assert (q, x(6,:)); -%! x = x.'; -%! q = quantile (x, p, 2); -%! assert (q, x(:,6)); - -%!test -%! p = [0.00, 0.25, 0.50, 0.75, 1.00]; -%! x = [1; 2; 3; 4]; -%! a = [1.0000 1.0000 2.0000 3.0000 4.0000 -%! 1.0000 1.5000 2.5000 3.5000 4.0000 -%! 1.0000 1.0000 2.0000 3.0000 4.0000 -%! 1.0000 1.0000 2.0000 3.0000 4.0000 -%! 1.0000 1.5000 2.5000 3.5000 4.0000 -%! 1.0000 1.2500 2.5000 3.7500 4.0000 -%! 1.0000 1.7500 2.5000 3.2500 4.0000 -%! 1.0000 1.4167 2.5000 3.5833 4.0000 -%! 1.0000 1.4375 2.5000 3.5625 4.0000]; -%! for m = 1:9 -%! q = quantile (x, p, 1, m).'; -%! assert (q, a(m,:), 0.0001); -%! endfor - -%!test -%! p = [0.00, 0.25, 0.50, 0.75, 1.00]; -%! x = [1; 2; 3; 4; 5]; -%! a = [1.0000 2.0000 3.0000 4.0000 5.0000 -%! 1.0000 2.0000 3.0000 4.0000 5.0000 -%! 1.0000 1.0000 2.0000 4.0000 5.0000 -%! 1.0000 1.2500 2.5000 3.7500 5.0000 -%! 1.0000 1.7500 3.0000 4.2500 5.0000 -%! 1.0000 1.5000 3.0000 4.5000 5.0000 -%! 1.0000 2.0000 3.0000 4.0000 5.0000 -%! 1.0000 1.6667 3.0000 4.3333 5.0000 -%! 1.0000 1.6875 3.0000 4.3125 5.0000]; -%! for m = 1:9 -%! q = quantile (x, p, 1, m).'; -%! assert (q, a(m,:), 0.0001); -%! endfor - -%!test -%! p = [0.00, 0.25, 0.50, 0.75, 1.00]; -%! x = [1; 2; 5; 9]; -%! a = [1.0000 1.0000 2.0000 5.0000 9.0000 -%! 1.0000 1.5000 3.5000 7.0000 9.0000 -%! 1.0000 1.0000 2.0000 5.0000 9.0000 -%! 1.0000 1.0000 2.0000 5.0000 9.0000 -%! 1.0000 1.5000 3.5000 7.0000 9.0000 -%! 1.0000 1.2500 3.5000 8.0000 9.0000 -%! 1.0000 1.7500 3.5000 6.0000 9.0000 -%! 1.0000 1.4167 3.5000 7.3333 9.0000 -%! 1.0000 1.4375 3.5000 7.2500 9.0000]; -%! for m = 1:9 -%! q = quantile (x, p, 1, m).'; -%! assert (q, a(m,:), 0.0001); -%! endfor - -%!test -%! p = [0.00, 0.25, 0.50, 0.75, 1.00]; -%! x = [1; 2; 5; 9; 11]; -%! a = [1.0000 2.0000 5.0000 9.0000 11.0000 -%! 1.0000 2.0000 5.0000 9.0000 11.0000 -%! 1.0000 1.0000 2.0000 9.0000 11.0000 -%! 1.0000 1.2500 3.5000 8.0000 11.0000 -%! 1.0000 1.7500 5.0000 9.5000 11.0000 -%! 1.0000 1.5000 5.0000 10.0000 11.0000 -%! 1.0000 2.0000 5.0000 9.0000 11.0000 -%! 1.0000 1.6667 5.0000 9.6667 11.0000 -%! 1.0000 1.6875 5.0000 9.6250 11.0000]; -%! for m = 1:9 -%! q = quantile (x, p, 1, m).'; -%! assert (q, a(m,:), 0.0001); -%! endfor - -%!test -%! p = [0.00, 0.25, 0.50, 0.75, 1.00]; -%! x = [16; 11; 15; 12; 15; 8; 11; 12; 6; 10]; -%! a = [6.0000 10.0000 11.0000 15.0000 16.0000 -%! 6.0000 10.0000 11.5000 15.0000 16.0000 -%! 6.0000 8.0000 11.0000 15.0000 16.0000 -%! 6.0000 9.0000 11.0000 13.5000 16.0000 -%! 6.0000 10.0000 11.5000 15.0000 16.0000 -%! 6.0000 9.5000 11.5000 15.0000 16.0000 -%! 6.0000 10.2500 11.5000 14.2500 16.0000 -%! 6.0000 9.8333 11.5000 15.0000 16.0000 -%! 6.0000 9.8750 11.5000 15.0000 16.0000]; -%! for m = 1:9 -%! q = quantile (x, p, 1, m).'; -%! assert (q, a(m,:), 0.0001); -%! endfor - -%!test -%! p = [0.00, 0.25, 0.50, 0.75, 1.00]; -%! x = [-0.58851; 0.40048; 0.49527; -2.551500; -0.52057; ... -%! -0.17841; 0.057322; -0.62523; 0.042906; 0.12337]; -%! a = [-2.551474 -0.588505 -0.178409 0.123366 0.495271 -%! -2.551474 -0.588505 -0.067751 0.123366 0.495271 -%! -2.551474 -0.625231 -0.178409 0.123366 0.495271 -%! -2.551474 -0.606868 -0.178409 0.090344 0.495271 -%! -2.551474 -0.588505 -0.067751 0.123366 0.495271 -%! -2.551474 -0.597687 -0.067751 0.192645 0.495271 -%! -2.551474 -0.571522 -0.067751 0.106855 0.495271 -%! -2.551474 -0.591566 -0.067751 0.146459 0.495271 -%! -2.551474 -0.590801 -0.067751 0.140686 0.495271]; -%! for m = 1:9 -%! q = quantile (x, p, 1, m).'; -%! assert (q, a(m,:), 0.0001); -%! endfor - -%!test -%! p = 0.5; -%! x = [0.112600, 0.114800, 0.052100, 0.236400, 0.139300 -%! 0.171800, 0.727300, 0.204100, 0.453100, 0.158500 -%! 0.279500, 0.797800, 0.329600, 0.556700, 0.730700 -%! 0.428800, 0.875300, 0.647700, 0.628700, 0.816500 -%! 0.933100, 0.931200, 0.963500, 0.779600, 0.846100]; -%! tol = 0.00001; -%! x(5,5) = NaN; -%! assert (quantile (x, p, 1), [0.27950, 0.79780, 0.32960, 0.55670, 0.44460], tol); -%! x(1,1) = NaN; -%! assert (quantile (x, p, 1), [0.35415, 0.79780, 0.32960, 0.55670, 0.44460], tol); -%! x(3,3) = NaN; -%! assert (quantile (x, p, 1), [0.35415, 0.79780, 0.42590, 0.55670, 0.44460], tol); - -%!test -%! sx = [2, 3, 4]; -%! x = rand (sx); -%! dim = 2; -%! p = 0.5; -%! yobs = quantile (x, p, dim); -%! yexp = median (x, dim); -%! assert (yobs, yexp); - -%!assert <*45455> (quantile ([1 3 2], 0.5, 1), [1 3 2]) - -## Test input validation -%!error quantile () -%!error quantile (1, 2, 3, 4, 5) -%!error quantile (['A'; 'B'], 10) -%!error quantile (1:10, [true, false]) -%!error quantile (1:10, ones (2,2)) -%!error quantile (1, 1, 1.5) -%!error quantile (1, 1, 0) -%!error quantile (1, 1, 3) -%!error quantile ((1:5)', 0.5, 1, 0) -%!error quantile ((1:5)', 0.5, 1, 10) - -## For the cumulative probability values in @var{p}, compute the -## quantiles, @var{q} (the inverse of the cdf), for the sample, @var{x}. -## -## The optional input, @var{method}, refers to nine methods available in R -## (http://www.r-project.org/). The default is @var{method} = 7. -## @seealso{prctile, quantile, statistics} - -## Author: Ben Abbott <bpabbott@mac.com> -## Vectorized version: Jaroslav Hajek <highegg@gmail.com> -## Description: Quantile function of empirical samples - -function inv = __quantile__ (x, p, method = 5) - - if (nargin < 2 || nargin > 3) - print_usage (); - endif - - if (isinteger (x) || islogical (x)) - x = double (x); - endif - - ## set shape of quantiles to column vector. - p = p(:); - - ## Save length and set shape of samples. - x = sort (x, 1); - m = sum (! isnan (x)); - [xr, xc] = size (x); - - ## Initialize output values. - inv = Inf (class (x)) * (-(p < 0) + (p > 1)); - inv = repmat (inv, 1, xc); - - ## Do the work. - if (any (k = find ((p >= 0) & (p <= 1)))) - n = length (k); - p = p(k); - ## Special case of 1 row. - if (xr == 1) - inv(k,:) = repmat (x, n, 1); - return; - endif - - ## The column-distribution indices. - pcd = kron (ones (n, 1), xr*(0:xc-1)); - mm = kron (ones (n, 1), m); - switch (method) - case {1, 2, 3} - switch (method) - case 1 - p = max (ceil (kron (p, m)), 1); - inv(k,:) = x(p + pcd); - - case 2 - p = kron (p, m); - p_lr = max (ceil (p), 1); - p_rl = min (floor (p + 1), mm); - inv(k,:) = (x(p_lr + pcd) + x(p_rl + pcd))/2; - - case 3 - ## Used by SAS, method PCTLDEF=2. - ## http://support.sas.com/onlinedoc/913/getDoc/en/statug.hlp/stdize_sect14.htm - t = max (kron (p, m), 1); - t = roundb (t); - inv(k,:) = x(t + pcd); - endswitch - - otherwise - switch (method) - case 4 - p = kron (p, m); - - case 5 - ## Used by Matlab. - p = kron (p, m) + 0.5; - - case 6 - ## Used by Minitab and SPSS. - p = kron (p, m+1); - - case 7 - ## Used by S and R. - p = kron (p, m-1) + 1; - - case 8 - ## Median unbiased. - p = kron (p, m+1/3) + 1/3; - - case 9 - ## Approximately unbiased respecting order statistics. - p = kron (p, m+0.25) + 0.375; - - otherwise - error ("quantile: Unknown METHOD, '%d'", method); - endswitch - - ## Duplicate single values. - imm1 = (mm(1,:) == 1); - x(2,imm1) = x(1,imm1); - - ## Interval indices. - pi = max (min (floor (p), mm-1), 1); - pr = max (min (p - pi, 1), 0); - pi += pcd; - inv(k,:) = (1-pr) .* x(pi) + pr .* x(pi+1); - endswitch - endif - -endfunction
--- a/scripts/statistics/base/range.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,63 +0,0 @@ -## Copyright (C) 1995-2017 Kurt Hornik -## Copyright (C) 2009 Jaroslav Hajek -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} range (@var{x}) -## @deftypefnx {} {} range (@var{x}, @var{dim}) -## Return the range, i.e., the difference between the maximum and the minimum -## of the input data. -## -## If @var{x} is a vector, the range is calculated over the elements of -## @var{x}. If @var{x} is a matrix, the range is calculated over each column -## of @var{x}. -## -## If the optional argument @var{dim} is given, operate along this dimension. -## -## The range is a quickly computed measure of the dispersion of a data set, but -## is less accurate than @code{iqr} if there are outlying data points. -## @seealso{iqr, std} -## @end deftypefn - -## Author: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: Compute range - -function y = range (x, dim) - - if (nargin < 1 || nargin > 2) - print_usage (); - endif - - if (nargin == 1) - y = max (x) - min (x); - else - y = max (x, [], dim) - min (x, [], dim); - endif - -endfunction - - -%!assert (range (1:10), 9) -%!assert (range (single (1:10)), single (9)) -%!assert (range (magic (3)), [5, 8, 5]) -%!assert (range (magic (3), 2), [7; 4; 7]) -%!assert (range (2), 0) - -## Test input validation -%!error range () -%!error range (1, 2, 3)
--- a/scripts/statistics/base/ranks.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,104 +0,0 @@ -## Copyright (C) 1995-2017 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} ranks (@var{x}, @var{dim}) -## Return the ranks of @var{x} along the first non-singleton dimension -## adjusted for ties. -## -## If the optional argument @var{dim} is given, operate along this dimension. -## @seealso{spearman, kendall} -## @end deftypefn - -## Author: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: Compute ranks - -## This code was rather ugly, since it didn't use sort due to the -## fact of how to deal with ties. Now it does use sort and its -## even uglier! At least it handles NDArrays. - -function y = ranks (x, dim) - - if (nargin != 1 && nargin != 2) - print_usage (); - endif - - if (! (isnumeric (x) || islogical (x))) - error ("ranks: X must be a numeric vector or matrix"); - endif - - nd = ndims (x); - sz = size (x); - if (nargin != 2) - ## Find the first non-singleton dimension. - (dim = find (sz > 1, 1)) || (dim = 1); - else - if (!(isscalar (dim) && dim == fix (dim)) - || !(1 <= dim && dim <= nd)) - error ("ranks: DIM must be an integer and a valid dimension"); - endif - endif - - if (sz(dim) == 1) - y = ones (sz); - else - ## The algorithm works only on dim = 1, so permute if necesary. - if (dim != 1) - perm = [1 : nd]; - perm(1) = dim; - perm(dim) = 1; - x = permute (x, perm); - endif - sz = size (x); - infvec = -Inf ([1, sz(2 : end)]); - [xs, xi] = sort (x); - eq_el = find (diff ([xs; infvec]) == 0); - if (isempty (eq_el)) - [eq_el, y] = sort (xi); - else - runs = setdiff (eq_el, eq_el+1); - len = diff (find (diff ([Inf; eq_el; -Inf]) != 1)) + 1; - [eq_el, y] = sort (xi); - for i = 1 : length (runs) - y (xi (runs (i) + [0:(len(i)-1)]) + floor (runs (i) ./ sz(1)) - * sz(1)) = eq_el(runs(i)) + (len(i) - 1) / 2; - endfor - endif - if (dim != 1) - y = permute (y, perm); - endif - endif - -endfunction - - -%!assert (ranks (1:2:10), 1:5) -%!assert (ranks (10:-2:1), 5:-1:1) -%!assert (ranks ([2, 1, 2, 4]), [2.5, 1, 2.5, 4]) -%!assert (ranks (ones (1, 5)), 3*ones (1, 5)) -%!assert (ranks (1e6*ones (1, 5)), 3*ones (1, 5)) -%!assert (ranks (rand (1, 5), 1), ones (1, 5)) - -## Test input validation -%!error ranks () -%!error ranks (1, 2, 3) -%!error ranks ({1, 2}) -%!error ranks (['A'; 'B']) -%!error ranks (1, 1.5) -%!error ranks (1, 0) -%!error ranks (1, 3)
--- a/scripts/statistics/base/run_count.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,112 +0,0 @@ -## Copyright (C) 1995-2017 Friedrich Leisch -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} run_count (@var{x}, @var{n}) -## @deftypefnx {} {} run_count (@var{x}, @var{n}, @var{dim}) -## Count the upward runs along the first non-singleton dimension of @var{x} -## of length 1, 2, @dots{}, @var{n}-1 and greater than or equal to @var{n}. -## -## If the optional argument @var{dim} is given then operate along this -## dimension. -## @seealso{runlength} -## @end deftypefn - -## Author: FL <Friedrich.Leisch@ci.tuwien.ac.at> -## Description: Count upward runs - -function retval = run_count (x, n, dim) - - if (nargin != 2 && nargin != 3) - print_usage (); - endif - - if (! (isnumeric (x) || islogical (x))) - error ("run_count: X must be a numeric vector or matrix"); - endif - - if (!(isscalar (n) && n == fix (n) && n > 0)) - error ("run_count: N must be a positive integer"); - endif - - nd = ndims (x); - sz = size (x); - if (nargin != 3) - ## Find the first non-singleton dimension. - (dim = find (sz > 1, 1)) || (dim = 1); - else - if (!(isscalar (dim) && dim == fix (dim)) - || !(1 <= dim && dim <= nd)) - error ("run_count: DIM must be an integer and a valid dimension"); - endif - endif - - ## Algorithm works on rows. Permute array if necessary, ipermute back at end - if (dim != 1) - perm = [1 : nd]; - perm(1) = dim; - perm(dim) = 1; - x = permute (x, perm); - endif - - sz = size (x); - idx = cell (); - for i = 1 : nd - idx{i} = 1 : sz(i); - endfor - c = sz(1); - tmp = zeros ([c + 1, sz(2 : end)]); - infvec = Inf ([1, sz(2 : end)]); - - ind = find (diff ([infvec; x; -infvec]) < 0); - tmp(ind(2:end) - 1) = diff (ind); - tmp = tmp(idx{:}); - - sz(1) = n; - retval = zeros (sz); - for k = 1 : (n-1) - idx{1} = k; - retval(idx{:}) = sum (tmp == k); - endfor - idx{1} = n; - retval(idx{:}) = sum (tmp >= n); - - if (dim != 1) - retval = ipermute (retval, perm); - endif - -endfunction - - -%!assert (run_count (magic (3), 4), [1,0,1;1,0,1;0,1,0;0,0,0]) -%!assert (run_count (magic (3), 4, 2), [1,0,1;1,0,1;0,1,0;0,0,0]') -%!assert (run_count (5:-1:1, 5), [5, 0, 0, 0, 0]) -%!assert (run_count (ones (3), 4), [0,0,0;0,0,0;1,1,1;0,0,0]) - -## Test input validation -%!error run_count () -%!error run_count (1) -%!error run_count (1, 2, 3, 4) -%!error run_count ({1, 2}, 3) -%!error run_count (['A'; 'A'; 'B'], 3) -%!error run_count (1:5, ones (2,2)) -%!error run_count (1:5, 1.5) -%!error run_count (1:5, -2) -%!error run_count (1:5, 3, ones (2,2)) -%!error run_count (1:5, 3, 1.5) -%!error run_count (1:5, 3, 0)
--- a/scripts/statistics/base/runlength.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,72 +0,0 @@ -## Copyright (C) 2005-2017 Paul Kienzle -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {count =} runlength (@var{x}) -## @deftypefnx {} {[count, value] =} runlength (@var{x}) -## Find the lengths of all sequences of common values. -## -## @var{count} is a vector with the lengths of each repeated value. -## -## The optional output @var{value} contains the value that was repeated in -## the sequence. -## -## @example -## @group -## runlength ([2, 2, 0, 4, 4, 4, 0, 1, 1, 1, 1]) -## @result{} [2, 1, 3, 1, 4] -## @end group -## @end example -## @seealso{run_count} -## @end deftypefn - -function [count, value] = runlength (x) - - if (nargin != 1) - print_usage (); - endif - - if (! (isnumeric (x) || islogical (x)) || ! isvector (x)) - error ("runlength: X must be a numeric vector"); - endif - - if (iscolumn (x)) - x = x.'; - endif - - idx = [find(x(1:end-1) != x(2:end)), length(x)]; - count = diff ([0 idx]); - if (nargout == 2) - value = x(idx); - endif - -endfunction - - -%!assert (runlength ([2 2 0 4 4 4 0 1 1 1 1]), [2 1 3 1 4]) -%!assert (runlength ([2 2 0 4 4 4 0 1 1 1 1]'), [2 1 3 1 4]) -%!test -%! [c, v] = runlength ([2 2 0 4 4 4 0 1 1 1 1]); -%! assert (c, [2 1 3 1 4]); -%! assert (v, [2 0 4 0 1]); - -## Test input validation -%!error runlength () -%!error runlength (1, 2) -%!error runlength (['A'; 'B']) -%!error runlength (ones (2,2))
--- a/scripts/statistics/base/skewness.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,169 +0,0 @@ -## Copyright (C) 2013-2017 Julien Bect -## Copyright (C) 1996-2016 John W. Eaton -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} skewness (@var{x}) -## @deftypefnx {} {} skewness (@var{x}, @var{flag}) -## @deftypefnx {} {} skewness (@var{x}, @var{flag}, @var{dim}) -## Compute the sample skewness of the elements of @var{x}. -## -## The sample skewness is defined as -## @tex -## $$ -## {\rm skewness} (@var{x}) = {{{1\over N}\, -## \sum_{i=1}^N (x_i - \bar{x})^3} \over \sigma^3}, -## $$ -## where $N$ is the length of @var{x}, $\bar{x}$ its mean and $\sigma$ -## its (uncorrected) standard deviation. -## @end tex -## @ifnottex -## -## @example -## @group -## mean ((@var{x} - mean (@var{x})).^3) -## skewness (@var{X}) = ------------------------. -## std (@var{x}).^3 -## @end group -## @end example -## -## @end ifnottex -## -## @noindent -## The optional argument @var{flag} controls which normalization is used. -## If @var{flag} is equal to 1 (default value, used when @var{flag} is omitted -## or empty), return the sample skewness as defined above. If @var{flag} is -## equal to 0, return the adjusted skewness coefficient instead: -## @tex -## $$ -## {\rm skewness} (@var{x}) = {\sqrt{N (N - 1)} \over N - 2} \times \, -## {{{1 \over N} \sum_{i=1}^N (x_i - \bar{x})^3} \over \sigma^3} -## $$ -## @end tex -## @ifnottex -## -## @example -## @group -## sqrt (N*(N-1)) mean ((@var{x} - mean (@var{x})).^3) -## skewness (@var{X}, 0) = -------------- * ------------------------. -## (N - 2) std (@var{x}).^3 -## @end group -## @end example -## -## where @math{N} is the length of the @var{x} vector. -## -## @end ifnottex -## The adjusted skewness coefficient is obtained by replacing the sample second -## and third central moments by their bias-corrected versions. -## -## If @var{x} is a matrix, or more generally a multi-dimensional array, return -## the skewness along the first non-singleton dimension. If the optional -## @var{dim} argument is given, operate along this dimension. -## -## @seealso{var, kurtosis, moment} -## @end deftypefn - -## Author: KH <Kurt.Hornik@wu-wien.ac.at> -## Created: 29 July 1994 -## Adapted-By: jwe - -function y = skewness (x, flag, dim) - - if (nargin < 1) || (nargin > 3) - print_usage (); - endif - - if (! (isnumeric (x) || islogical (x))) - error ("skewness: X must be a numeric vector or matrix"); - endif - - if (nargin < 2 || isempty (flag)) - flag = 1; # default: do not use the "bias corrected" version - elseif (! isscalar (flag) || (flag != 0 && flag != 1)) - error ("skewness: FLAG must be 0 or 1"); - endif - - nd = ndims (x); - sz = size (x); - if (nargin < 3) - ## Find the first non-singleton dimension. - (dim = find (sz > 1, 1)) || (dim = 1); - else - if (! (isscalar (dim) && dim == fix (dim) && dim > 0)) - error ("skewness: DIM must be an integer and a valid dimension"); - endif - endif - - n = size (x, dim); - sz(dim) = 1; - - x = center (x, dim); # center also promotes integer, logical to double - s = std (x, 1, dim); # Normalize with 1/N - y = sum (x .^ 3, dim); - idx = (s != 0); - y(idx) ./= (n * s(idx) .^ 3); - y(! idx) = NaN; - - ## Apply bias correction to the second and third central sample moment - if (flag == 0) - if (n > 2) - y *= sqrt (n * (n - 1)) / (n - 2); - else - y(:) = NaN; - endif - endif - -endfunction - - -%!assert (skewness ([-1, 0, 1]), 0) -%!assert (skewness ([-2, 0, 1]) < 0) -%!assert (skewness ([-1, 0, 2]) > 0) -%!assert (skewness ([-3, 0, 1]) == -1 * skewness ([-1, 0, 3])) -%!assert (skewness (ones (3, 5)), NaN (1, 5)) -%!assert (skewness (1, [], 3), NaN) - -%!test -%! x = [0; 0; 0; 1]; -%! y = [x, 2*x]; -%! assert (skewness (y), 1.154700538379251 * [1 1], 5*eps); - -%!assert (skewness ([1:5 10; 1:5 10], 0, 2), 1.439590274527954 * [1; 1], eps) -%!assert (skewness ([1:5 10; 1:5 10], 1, 2), 1.051328089232020 * [1; 1], 2*eps) -%!assert (skewness ([1:5 10; 1:5 10], [], 2), 1.051328089232020 * [1; 1], 2*eps) - -## Test behavior on single input -%!assert (skewness (single ([1:5 10])), single (1.0513283), eps ("single")) -%!assert (skewness (single ([1 2]), 0), single (NaN)) - -## Verify no "divide-by-zero" warnings -%!test -%! warning ("on", "Octave:divide-by-zero", "local"); -%! lastwarn (""); # clear last warning -%! skewness (1); -%! assert (lastwarn (), ""); - -## Test input validation -%!error skewness () -%!error skewness (1, 2, 3) -%!error <X must be a numeric vector or matrix> skewness (['A'; 'B']) -%!error <FLAG must be 0 or 1> skewness (1, 2) -%!error <FLAG must be 0 or 1> skewness (1, [1 0]) -%!error <DIM must be an integer> skewness (1, [], ones (2,2)) -%!error <DIM must be an integer> skewness (1, [], 1.5) -%!error <DIM must be .* a valid dimension> skewness (1, [], 0)
--- a/scripts/statistics/base/spearman.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,119 +0,0 @@ -## Copyright (C) 1995-2017 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} spearman (@var{x}) -## @deftypefnx {} {} spearman (@var{x}, @var{y}) -## @cindex Spearman's Rho -## Compute Spearman's rank correlation coefficient -## @tex -## $\rho$. -## @end tex -## @ifnottex -## @var{rho}. -## @end ifnottex -## -## For two data vectors @var{x} and @var{y}, Spearman's -## @tex -## $\rho$ -## @end tex -## @ifnottex -## @var{rho} -## @end ifnottex -## is the correlation coefficient of the ranks of @var{x} and @var{y}. -## -## If @var{x} and @var{y} are drawn from independent distributions, -## @tex -## $\rho$ -## @end tex -## @ifnottex -## @var{rho} -## @end ifnottex -## has zero mean and variance -## @tex -## $1 / (N - 1)$, -## @end tex -## @ifnottex -## @code{1 / (N - 1)}, -## @end ifnottex -## where @math{N} is the length of the @var{x} and @var{y} vectors, and is -## asymptotically normally distributed. -## -## @code{spearman (@var{x})} is equivalent to -## @code{spearman (@var{x}, @var{x})}. -## @seealso{ranks, kendall} -## @end deftypefn - -## Author: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: Spearman's rank correlation rho - -function rho = spearman (x, y = []) - - if (nargin < 1 || nargin > 2) - print_usage (); - endif - - if ( ! (isnumeric (x) || islogical (x)) - || ! (isnumeric (y) || islogical (y))) - error ("spearman: X and Y must be numeric matrices or vectors"); - endif - - if (ndims (x) != 2 || ndims (y) != 2) - error ("spearman: X and Y must be 2-D matrices or vectors"); - endif - - if (isrow (x)) - x = x.'; - endif - - if (nargin == 1) - rho = corr (ranks (x)); - else - if (isrow (y)) - y = y.'; - endif - if (rows (x) != rows (y)) - error ("spearman: X and Y must have the same number of observations"); - endif - rho = corr (ranks (x), ranks (y)); - endif - - ## Restore class cleared by ranks - if (isa (x, "single") || isa (y, "single")) - rho = single (rho); - endif - -endfunction - - -%!test -%! x = 1:10; -%! y = exp (x); -%! assert (spearman (x,y), 1, 5*eps); -%! assert (spearman (x,-y), -1, 5*eps); - -%!assert (spearman ([1 2 3], [-1 1 -2]), -0.5, 5*eps) - -## Test input validation -%!error spearman () -%!error spearman (1, 2, 3) -%!error spearman (['A'; 'B']) -%!error spearman (ones (1,2), {1, 2}) -%!error spearman (ones (2,2,2)) -%!error spearman (ones (2,2), ones (2,2,2)) -%!error spearman (ones (2,2), ones (3,2))
--- a/scripts/statistics/base/statistics.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,99 +0,0 @@ -## Copyright (C) 1995-2017 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} statistics (@var{x}) -## @deftypefnx {} {} statistics (@var{x}, @var{dim}) -## Return a vector with the minimum, first quartile, median, third quartile, -## maximum, mean, standard deviation, skewness, and kurtosis of the elements of -## the vector @var{x}. -## -## If @var{x} is a matrix, calculate statistics over the first non-singleton -## dimension. -## -## If the optional argument @var{dim} is given, operate along this dimension. -## @seealso{min, max, median, mean, std, skewness, kurtosis} -## @end deftypefn - -## Author: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: Compute basic statistics - -function stats = statistics (x, dim) - - if (nargin != 1 && nargin != 2) - print_usage (); - endif - - if (! (isnumeric (x) || islogical (x))) - error ("statistics: X must be a numeric vector or matrix"); - endif - - nd = ndims (x); - sz = size (x); - if (nargin != 2) - ## Find the first non-singleton dimension. - (dim = find (sz > 1, 1)) || (dim = 1); - else - if (!(isscalar (dim) && dim == fix (dim)) - || !(1 <= dim && dim <= nd)) - error ("statistics: DIM must be an integer and a valid dimension"); - endif - endif - - if (sz(dim) < 2) - error ("statistics: dimension of X is too small (<2)"); - endif - - emp_inv = quantile (x, [0.25; 0.5; 0.75], dim, 7); - - stats = cat (dim, min (x, [], dim), emp_inv, max (x, [], dim), mean (x, dim), - std (x, [], dim), skewness (x, [], dim), kurtosis (x, [], dim)); - -endfunction - - -%!test -%! x = rand (7,5); -%! s = statistics (x); -%! assert (min (x), s(1,:), eps); -%! assert (median (x), s(3,:), eps); -%! assert (max (x), s(5,:), eps); -%! assert (mean (x), s(6,:), eps); -%! assert (std (x), s(7,:), eps); -%! assert (skewness (x), s(8,:), eps); -%! assert (kurtosis (x), s(9,:), eps); - -%! x = rand (7,5); -%! s = statistics (x, 2); -%! assert (min (x, [], 2), s(:,1), eps); -%! assert (median (x, 2), s(:,3), eps); -%! assert (max (x, [], 2), s(:,5), eps); -%! assert (mean (x, 2), s(:,6), eps); -%! assert (std (x, [], 2), s(:,7), eps); -%! assert (skewness (x, [], 2), s(:,8), eps); -%! assert (kurtosis (x, [], 2), s(:,9), eps); - -## Test input validation -%!error statistics () -%!error statistics (1, 2, 3) -%!error statistics (['A'; 'B']) -%!error statistics (1, ones (2,2)) -%!error statistics (1, 1.5) -%!error statistics (1, 0) -%!error statistics (1, 3) -%!error statistics (1)
--- a/scripts/statistics/base/std.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,130 +0,0 @@ -## Copyright (C) 1996-2017 John W. Eaton -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} std (@var{x}) -## @deftypefnx {} {} std (@var{x}, @var{opt}) -## @deftypefnx {} {} std (@var{x}, @var{opt}, @var{dim}) -## Compute the standard deviation of the elements of the vector @var{x}. -## -## The standard deviation is defined as -## @tex -## $$ -## {\rm std} (x) = \sigma = \sqrt{{\sum_{i=1}^N (x_i - \bar{x})^2 \over N - 1}} -## $$ -## where $\bar{x}$ is the mean value of @var{x} and $N$ is the number of elements of @var{x}. -## @end tex -## @ifnottex -## -## @example -## @group -## std (@var{x}) = sqrt ( 1/(N-1) SUM_i (@var{x}(i) - mean(@var{x}))^2 ) -## @end group -## @end example -## -## @noindent -## where @math{N} is the number of elements of the @var{x} vector. -## @end ifnottex -## -## If @var{x} is a matrix, compute the standard deviation for each column and -## return them in a row vector. -## -## The argument @var{opt} determines the type of normalization to use. -## Valid values are -## -## @table @asis -## @item 0: -## normalize with @math{N-1}, provides the square root of the best unbiased -## estimator of the variance [default] -## -## @item 1: -## normalize with @math{N}, this provides the square root of the second -## moment around the mean -## @end table -## -## If the optional argument @var{dim} is given, operate along this dimension. -## @seealso{var, range, iqr, mean, median} -## @end deftypefn - -## Author: jwe - -function retval = std (x, opt = 0, dim) - - if (nargin < 1 || nargin > 3) - print_usage (); - endif - - if (! (isnumeric (x) || islogical (x))) - error ("std: X must be a numeric vector or matrix"); - endif - - if (isempty (opt)) - opt = 0; - elseif (! isscalar (opt) || (opt != 0 && opt != 1)) - error ("std: normalization OPT must be 0 or 1"); - endif - - nd = ndims (x); - sz = size (x); - if (nargin < 3) - ## Find the first non-singleton dimension. - (dim = find (sz > 1, 1)) || (dim = 1); - else - if (! (isscalar (dim) && dim == fix (dim) && dim > 0)) - error ("std: DIM must be an integer and a valid dimension"); - endif - endif - - n = size (x, dim); - if (n == 1 || isempty (x)) - if (isa (x, "single")) - retval = zeros (sz, "single"); - else - retval = zeros (sz); - endif - else - retval = sqrt (sumsq (center (x, dim), dim) / (n - 1 + opt)); - endif - -endfunction - - -%!test -%! x = ones (10, 2); -%! y = [1, 3]; -%! assert (std (x), [0, 0]); -%! assert (std (y), sqrt (2), sqrt (eps)); -%! assert (std (x, 0, 2), zeros (10, 1)); - -%!assert (std (ones (3, 1, 2), 0, 2), zeros (3, 1, 2)) -%!assert (std ([1 2], 0), sqrt (2)/2, 5*eps) -%!assert (std ([1 2], 1), 0.5, 5*eps) -%!assert (std (1), 0) -%!assert (std (single (1)), single (0)) -%!assert (std ([]), []) -%!assert (std (ones (1,3,0,2)), ones (1,3,0,2)) -%!assert (std ([1 2 3], [], 3), [0 0 0]) - -## Test input validation -%!error std () -%!error std (1, 2, 3, 4) -%!error <X must be a numeric> std (['A'; 'B']) -%!error <OPT must be 0 or 1> std (1, 2) -%!error <DIM must be an integer> std (1, [], ones (2,2)) -%!error <DIM must be an integer> std (1, [], 1.5) -%!error <DIM must be .* a valid dimension> std (1, [], 0)
--- a/scripts/statistics/base/var.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,130 +0,0 @@ -## Copyright (C) 1995-2017 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} var (@var{x}) -## @deftypefnx {} {} var (@var{x}, @var{opt}) -## @deftypefnx {} {} var (@var{x}, @var{opt}, @var{dim}) -## Compute the variance of the elements of the vector @var{x}. -## -## The variance is defined as -## @tex -## $$ -## {\rm var} (x) = \sigma^2 = {\sum_{i=1}^N (x_i - \bar{x})^2 \over N - 1} -## $$ -## where $\bar{x}$ is the mean value of @var{x} and $N$ is the number of -## elements of @var{x}. -## -## @end tex -## @ifnottex -## -## @example -## @group -## var (@var{x}) = 1/(N-1) SUM_i (@var{x}(i) - mean(@var{x}))^2 -## @end group -## @end example -## -## where @math{N} is the length of the @var{x} vector. -## -## @end ifnottex -## If @var{x} is a matrix, compute the variance for each column and return -## them in a row vector. -## -## The argument @var{opt} determines the type of normalization to use. -## Valid values are -## -## @table @asis -## @item 0: -## normalize with @math{N-1}, provides the best unbiased estimator of the -## variance [default] -## -## @item 1: -## normalizes with @math{N}, this provides the second moment around the mean -## @end table -## -## If @math{N} is equal to 1 the value of @var{opt} is ignored and -## normalization by @math{N} is used. -## -## If the optional argument @var{dim} is given, operate along this dimension. -## @seealso{cov, std, skewness, kurtosis, moment} -## @end deftypefn - -## Author: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: Compute variance - -function retval = var (x, opt = 0, dim) - - if (nargin < 1 || nargin > 3) - print_usage (); - endif - - if (! (isnumeric (x) || islogical (x))) - error ("var: X must be a numeric vector or matrix"); - endif - - if (isempty (opt)) - opt = 0; - elseif (opt != 0 && opt != 1) - error ("var: normalization OPT must be 0 or 1"); - endif - - nd = ndims (x); - sz = size (x); - if (nargin < 3) - ## Find the first non-singleton dimension. - (dim = find (sz > 1, 1)) || (dim = 1); - else - if (! (isscalar (dim) && dim == fix (dim) && dim > 0)) - error ("var: DIM must be an integer and a valid dimension"); - endif - endif - - n = size (x, dim); - if (n == 1) - if (isa (x, "single")) - retval = zeros (sz, "single"); - else - retval = zeros (sz); - endif - elseif (numel (x) > 0) - retval = sumsq (center (x, dim), dim) / (n - 1 + opt); - else - error ("var: X must not be empty"); - endif - -endfunction - - -%!assert (var (13), 0) -%!assert (var (single (13)), single (0)) -%!assert (var ([1,2,3]), 1) -%!assert (var ([1,2,3], 1), 2/3, eps) -%!assert (var ([1,2,3], [], 1), [0,0,0]) -%!assert (var ([1,2,3], [], 3), [0,0,0]) - -## Test input validation -%!error var () -%!error var (1,2,3,4) -%!error <X must be a numeric> var (['A'; 'B']) -%!error <OPT must be 0 or 1> var (1, -1) -%!error <FLAG must be 0 or 1> skewness (1, 2) -%!error <FLAG must be 0 or 1> skewness (1, [1 0]) -%!error <DIM must be an integer> var (1, [], ones (2,2)) -%!error <DIM must be an integer> var (1, [], 1.5) -%!error <DIM must be .* a valid dimension> var (1, [], 0) -%!error <X must not be empty> var ([], 1)
--- a/scripts/statistics/base/zscore.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,108 +0,0 @@ -## Copyright (C) 1995-2017 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {@var{z} =} zscore (@var{x}) -## @deftypefnx {} {@var{z} =} zscore (@var{x}, @var{opt}) -## @deftypefnx {} {@var{z} =} zscore (@var{x}, @var{opt}, @var{dim}) -## @deftypefnx {} {[@var{z}, @var{mu}, @var{sigma}] =} zscore (@dots{}) -## Compute the Z score of @var{x} -## -## If @var{x} is a vector, subtract its mean and divide by its standard -## deviation. If the standard deviation is zero, divide by 1 instead. -## -## The optional parameter @var{opt} determines the normalization to use when -## computing the standard deviation and has the same definition as the -## corresponding parameter for @code{std}. -## -## If @var{x} is a matrix, calculate along the first non-singleton dimension. -## If the third optional argument @var{dim} is given, operate along this -## dimension. -## -## The optional outputs @var{mu} and @var{sigma} contain the mean and standard -## deviation. -## -## @seealso{mean, std, center} -## @end deftypefn - -## Author: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: Subtract mean and divide by standard deviation - -function [z, mu, sigma] = zscore (x, opt, dim) - - if (nargin < 1 || nargin > 3 ) - print_usage (); - endif - - if (! (isnumeric (x) || islogical (x))) - error ("zscore: X must be a numeric vector or matrix"); - endif - - if (nargin < 2) - opt = 0; - else - if (opt != 0 && opt != 1 || ! isscalar (opt)) - error ("zscore: OPT must be empty, 0, or 1"); - endif - endif - - nd = ndims (x); - sz = size (x); - if (nargin < 3) - ## Find the first non-singleton dimension. - (dim = find (sz > 1, 1)) || (dim = 1); - else - if (!(isscalar (dim) && dim == fix (dim)) - || !(1 <= dim && dim <= nd)) - error ("zscore: DIM must be an integer and a valid dimension"); - endif - endif - - n = sz(dim); - if (n == 0) - z = x; - else - - if (isinteger (x)) - x = double (x); - endif - - mu = mean (x, dim); - sigma = std (x, opt, dim); - s = sigma; - s(s==0) = 1; - z = (x - mu) ./ s; - endif - -endfunction - - -%!assert (zscore ([1,2,3]), [-1,0,1]) -%!assert (zscore (single ([1,2,3])), single ([-1,0,1])) -%!assert (zscore (int8 ([1,2,3])), [-1,0,1]) -%!assert (zscore (ones (3,2,2,2)), zeros (3,2,2,2)) -%!assert (zscore ([2,0,-2;0,2,0;-2,-2,2]), [1,0,-1;0,1,0;-1,-1,1]) - -## Test input validation -%!error zscore () -%!error zscore (1, 2, 3) -%!error zscore (['A'; 'B']) -%!error zscore (1, ones (2,2)) -%!error zscore (1, 1.5) -%!error zscore (1, 1, 0) -%!error zscore (1, 3)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/scripts/statistics/center.m Sun Jan 07 17:13:23 2018 -0800 @@ -0,0 +1,96 @@ +## Copyright (C) 1995-2017 Kurt Hornik +## Copyright (C) 2009 VZLU Prague +## +## This file is part of Octave. +## +## Octave is free software: you can redistribute it and/or modify it +## under the terms of the GNU General Public License as published by +## the Free Software Foundation, either version 3 of the License, or +## (at your option) any later version. +## +## Octave is distributed in the hope that it will be useful, but +## WITHOUT ANY WARRANTY; without even the implied warranty of +## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +## GNU General Public License for more details. +## +## You should have received a copy of the GNU General Public License +## along with Octave; see the file COPYING. If not, see +## <https://www.gnu.org/licenses/>. + +## -*- texinfo -*- +## @deftypefn {} {} center (@var{x}) +## @deftypefnx {} {} center (@var{x}, @var{dim}) +## Center data by subtracting its mean. +## +## If @var{x} is a vector, subtract its mean. +## +## If @var{x} is a matrix, do the above for each column. +## +## If the optional argument @var{dim} is given, operate along this dimension. +## +## Programming Note: @code{center} has obvious application for normalizing +## statistical data. It is also useful for improving the precision of general +## numerical calculations. Whenever there is a large value that is common +## to a batch of data, the mean can be subtracted off, the calculation +## performed, and then the mean added back to obtain the final answer. +## @seealso{zscore} +## @end deftypefn + +## Author: KH <Kurt.Hornik@wu-wien.ac.at> +## Description: Center by subtracting means + +function retval = center (x, dim) + + if (nargin != 1 && nargin != 2) + print_usage (); + endif + + if (! (isnumeric (x) || islogical (x))) + error ("center: X must be a numeric vector or matrix"); + endif + + if (isinteger (x)) + x = double (x); + endif + + nd = ndims (x); + sz = size (x); + if (nargin != 2) + ## Find the first non-singleton dimension. + (dim = find (sz > 1, 1)) || (dim = 1); + else + if (! (isscalar (dim) && dim == fix (dim) && dim > 0)) + error ("center: DIM must be an integer and a valid dimension"); + endif + endif + + n = size (x, dim); + + if (n == 0) + retval = x; + else + ## FIXME: Use bsxfun, rather than broadcasting, until broadcasting + ## supports diagonal and sparse matrices (Bugs #41441, #35787). + retval = bsxfun (@minus, x, mean (x, dim)); + ## retval = x - mean (x, dim); # automatic broadcasting + endif + +endfunction + + +%!assert (center ([1,2,3]), [-1,0,1]) +%!assert (center (single ([1,2,3])), single ([-1,0,1])) +%!assert (center (int8 ([1,2,3])), [-1,0,1]) +%!assert (center (logical ([1, 0, 0, 1])), [0.5, -0.5, -0.5, 0.5]) +%!assert (center (ones (3,2,0,2)), zeros (3,2,0,2)) +%!assert (center (ones (3,2,0,2, "single")), zeros (3,2,0,2, "single")) +%!assert (center (magic (3)), [3,-4,1;-2,0,2;-1,4,-3]) +%!assert (center ([1 2 3; 6 5 4], 2), [-1 0 1; 1 0 -1]) +%!assert (center (1, 3), 0) + +## Test input validation +%!error center () +%!error center (1, 2, 3) +%!error <DIM must be an integer> center (1, ones (2,2)) +%!error <DIM must be an integer> center (1, 1.5) +%!error <DIM must be .* a valid dimension> center (1, 0)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/scripts/statistics/corr.m Sun Jan 07 17:13:23 2018 -0800 @@ -0,0 +1,111 @@ +## Copyright (C) 1996-2017 John W. Eaton +## +## This file is part of Octave. +## +## Octave is free software: you can redistribute it and/or modify it +## under the terms of the GNU General Public License as published by +## the Free Software Foundation, either version 3 of the License, or +## (at your option) any later version. +## +## Octave is distributed in the hope that it will be useful, but +## WITHOUT ANY WARRANTY; without even the implied warranty of +## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +## GNU General Public License for more details. +## +## You should have received a copy of the GNU General Public License +## along with Octave; see the file COPYING. If not, see +## <https://www.gnu.org/licenses/>. + +## -*- texinfo -*- +## @deftypefn {} {} corr (@var{x}) +## @deftypefnx {} {} corr (@var{x}, @var{y}) +## Compute matrix of correlation coefficients. +## +## If each row of @var{x} and @var{y} is an observation and each column is +## a variable, then the @w{(@var{i}, @var{j})-th} entry of +## @code{corr (@var{x}, @var{y})} is the correlation between the +## @var{i}-th variable in @var{x} and the @var{j}-th variable in @var{y}. +## @tex +## $$ +## {\rm corr}(x,y) = {{\rm cov}(x,y) \over {\rm std}(x) \, {\rm std}(y)} +## $$ +## @end tex +## @ifnottex +## +## @example +## corr (@var{x},@var{y}) = cov (@var{x},@var{y}) / (std (@var{x}) * std (@var{y})) +## @end example +## +## @end ifnottex +## If called with one argument, compute @code{corr (@var{x}, @var{x})}, +## the correlation between the columns of @var{x}. +## @seealso{cov} +## @end deftypefn + +## Author: Kurt Hornik <hornik@wu-wien.ac.at> +## Created: March 1993 +## Adapted-By: jwe + +function retval = corr (x, y = []) + + if (nargin < 1 || nargin > 2) + print_usage (); + endif + + ## Input validation is done by cov.m. Don't repeat tests here + + ## Special case, scalar is always 100% correlated with itself + if (isscalar (x)) + if (isa (x, "single")) + retval = single (1); + else + retval = 1; + endif + return; + endif + + ## No check for division by zero error, which happens only when + ## there is a constant vector and should be rare. + if (nargin == 2) + c = cov (x, y); + s = std (x)' * std (y); + retval = c ./ s; + else + c = cov (x); + s = sqrt (diag (c)); + retval = c ./ (s * s'); + endif + +endfunction + + +%!test +%! x = rand (10); +%! cc1 = corr (x); +%! cc2 = corr (x, x); +%! assert (size (cc1) == [10, 10] && size (cc2) == [10, 10]); +%! assert (cc1, cc2, sqrt (eps)); + +%!test +%! x = [1:3]'; +%! y = [3:-1:1]'; +%! assert (corr (x, y), -1, 5*eps); +%! assert (corr (x, flipud (y)), 1, 5*eps); +%! assert (corr ([x, y]), [1 -1; -1 1], 5*eps); + +%!test +%! x = single ([1:3]'); +%! y = single ([3:-1:1]'); +%! assert (corr (x, y), single (-1), 5*eps); +%! assert (corr (x, flipud (y)), single (1), 5*eps); +%! assert (corr ([x, y]), single ([1 -1; -1 1]), 5*eps); + +%!assert (corr (5), 1) +%!assert (corr (single (5)), single (1)) + +## Test input validation +%!error corr () +%!error corr (1, 2, 3) +%!error corr ([1; 2], ["A", "B"]) +%!error corr (ones (2,2,2)) +%!error corr (ones (2,2), ones (2,2,2))
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/scripts/statistics/corrcoef.m Sun Jan 07 17:13:23 2018 -0800 @@ -0,0 +1,295 @@ +## Copyright (C) 2016-2017 Guillaume Flandin +## +## This file is part of Octave. +## +## Octave is free software: you can redistribute it and/or modify it +## under the terms of the GNU General Public License as published by +## the Free Software Foundation, either version 3 of the License, or +## (at your option) any later version. +## your option) any later version. +## +## Octave is distributed in the hope that it will be useful, but +## WITHOUT ANY WARRANTY; without even the implied warranty of +## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +## GNU General Public License for more details. +## +## You should have received a copy of the GNU General Public License +## along with Octave; see the file COPYING. If not, see +## <https://www.gnu.org/licenses/>. + +## -*- texinfo -*- +## @deftypefn {} {@var{r} =} corrcoef (@var{x}) +## @deftypefnx {} {@var{r} =} corrcoef (@var{x}, @var{y}) +## @deftypefnx {} {[@var{r}, @var{p}] =} corrcoef (@dots{}) +## @deftypefnx {} {[@var{r}, @var{p}, @var{lci}, @var{hci}] =} corrcoef (@dots{}) +## @deftypefnx {} {[@dots{}] =} corrcoef (@dots{}, @var{param}, @var{value}, @dots{}) +## Compute a matrix of correlation coefficients. +## +## @var{x} is an array where each column contains a variable and each row is +## an observation. +## +## If a second input @var{y} (of the same size as @var{x}) is given then +## calculate the correlation coefficients between @var{x} and @var{y}. +## +## @var{r} is a matrix of Pearson's product moment correlation coefficients for +## each pair of variables. +## +## @var{p} is a matrix of pair-wise p-values testing for the null hypothesis of +## a correlation coefficient of zero. +## +## @var{lci} and @var{hci} are matrices containing, respectively, the lower and +## higher bounds of the 95% confidence interval of each correlation +## coefficient. +## +## @var{param}, @var{value} are pairs of optional parameters and values. +## Valid options are: +## +## @table @asis +## @item @qcode{"alpha"} +## Confidence level used for the definition of the bounds of the confidence +## interval, @var{lci} and @var{hci}. Default is 0.05, i.e., 95% confidence +## interval. +## +## @item @qcode{"rows"} +## Determine processing of NaN values. Acceptable values are @qcode{"all"}, +## @qcode{"complete"}, and @qcode{"pairwise"}. Default is @qcode{"all"}. +## With @qcode{"complete"}, only the rows without NaN values are considered. +## With @qcode{"pairwise"}, the selection of NaN-free rows is made for each +## pair of variables. +## +## @end table +## +## @seealso{corr, cov} +## @end deftypefn + +## FIXME: It would be good to add a definition of the calculation method +## for a Pearson product moment correlation to the documentation. + +function [r, p, lci, hci] = corrcoef (x, varargin) + + if (nargin == 0) + print_usage (); + endif + + alpha = 0.05; + rows = "all"; + + if (nargin > 1) + + ## Check for numeric y argument + if (isnumeric (varargin{1})) + x = [x(:), varargin{1}(:)]; + varargin(1) = []; + endif + + ## Check for Parameter/Value arguments + for i = 1:2:numel (varargin) + + if (! ischar (varargin{i})) + error ("corrcoef: parameter %d must be a string", i); + endif + parameter = varargin{i}; + if (numel (varargin) < i+1) + error ('corrcoef: parameter "%s" missing value', parameter); + endif + value = varargin{i+1}; + + switch (tolower (parameter)) + case "alpha" + if (isnumeric (value) && isscalar (value) + && value >= 0 && value <= 1) + alpha = value; + else + error ('corrcoef: "alpha" must be a number between 0 and 1'); + endif + + case "rows" + if (! ischar (value)) + error ('corrcoef: "rows" value must be a string'); + endif + value = tolower (value); + switch (value) + case {"all", "complete", "pairwise"} + rows = value; + otherwise + error ('corrcoef: "rows" must be "all", "complete", or "pairwise".'); + endswitch + + otherwise + error ('corrcoef: Unknown option "%s"', parameter); + + endswitch + endfor + endif + + if (strcmp (rows, "complete")) + x(any (isnan (x), 2), :) = []; + endif + + if (isempty (x) || isscalar (x)) + r = p = lci = hci = NaN; + return; + endif + + ## Flags for calculation + pairwise = strcmp (rows, "pairwise"); + calc_pval = nargout > 1; + + if (isrow (x)) + x = x(:); + endif + [m, n] = size (x); + r = eye (n); + if (calc_pval) + p = eye (n); + endif + if (strcmp (rows, "pairwise")) + mpw = m * ones (n); + endif + for i = 1:n + if (! pairwise && any (isnan (x(:,i)))) + r(i,i) = NaN; + if (nargout > 1) + p(i,i) = NaN; + endif + endif + for j = i+1:n + xi = x(:,i); + xj = x(:,j); + if (pairwise) + idx = any (isnan ([xi xj]), 2); + xi(idx) = xj(idx) = []; + mpw(i,j) = mpw(j,i) = m - nnz (idx); + endif + r(i,j) = r(j,i) = corr (xi, xj); + if (calc_pval) + df = m - 2; + stat = sqrt (df) * r(i,j) / sqrt (1 - r(i,j)^2); + cdf = tcdf (stat, df); + p(i,j) = p(j,i) = 2 * min (cdf, 1 - cdf); + endif + endfor + endfor + + if (nargout > 2) + if (pairwise) + m = mpw; + endif + CI = sqrt (2) * erfinv (1-alpha) ./ sqrt (m-3); + lci = tanh (atanh (r) - CI); + hci = tanh (atanh (r) + CI); + endif + +endfunction + + +## Compute cumulative distribution function for T distribution. +function cdf = tcdf (x, n) + + if (iscomplex (x)) + error ("tcdf: X must not be complex"); + endif + + if (isa (x, "single")) + cdf = zeros (size (x), "single"); + else + cdf = zeros (size (x)); + endif + + k = ! isinf (x) & (n > 0); + + xx = x .^ 2; + x_big_abs = (xx > n); + + ## deal with the case "abs(x) big" + kk = k & x_big_abs; + cdf(kk) = betainc (n ./ (n + xx(kk)), n/2, 1/2) / 2; + + ## deal with the case "abs(x) small" + kk = k & ! x_big_abs; + cdf(kk) = 0.5 * (1 - betainc (xx(kk) ./ (n + xx(kk)), 1/2, n/2)); + + k &= (x > 0); + if (any (k(:))) + cdf(k) = 1 - cdf(k); + endif + + k = isnan (x) | !(n > 0); + cdf(k) = NaN; + + k = (x == Inf) & (n > 0); + cdf(k) = 1; + +endfunction + + +%!test +%! x = rand (5); +%! r = corrcoef (x); +%! assert (size (r) == [5, 5]); + +%!test +%! x = [1 2 3]; +%! r = corrcoef (x); +%! assert (size (r) == [1, 1]); + +%!test +%! x = []; +%! r = corrcoef (x); +%! assert (isnan (r)); + +%!test +%! x = [NaN]; +%! r = corrcoef (x); +%! assert (isnan (r)); + +%!test +%! x = [1]; +%! r = corrcoef (x); +%! assert (isnan (r)); + +%!test +%! x = [NaN NaN]; +%! r = corrcoef (x); +%! assert (size(r) == [1, 1] && isnan (r)); + +%!test +%! x = rand (5); +%! [r, p] = corrcoef (x); +%! assert (size (r) == [5, 5] && size (p) == [5 5]); + +%!test +%! x = rand (5,1); +%! y = rand (5,1); +%! R1 = corrcoef (x, y); +%! R2 = corrcoef ([x, y]); +%! assert (R1, R2); + +%!test +%! x = [1;2;3]; +%! y = [1;2;3]; +%! r = corrcoef (x, y); +%! assert (r, ones (2,2)); + +%!test +%! x = [1;2;3]; +%! y = [3;2;1]; +%! r = corrcoef (x, y); +%! assert (r, [1, -1; -1, 1]); + +%!test +%! x = [1;2;3]; +%! y = [1;1;1]; +%! r = corrcoef (x, y); +%! assert (r, [1, NaN; NaN, 1]); + +%!test +%!error corrcoef () +%!error <parameter 1 must be a string> corrcoef (1, 2, 3) +%!error <parameter "alpha" missing value> corrcoef (1, 2, "alpha") +%!error <"alpha" must be a number> corrcoef (1,2, "alpha", "1") +%!error <"alpha" must be a number> corrcoef (1,2, "alpha", ones (2,2)) +%!error <"alpha" must be a number between 0 and 1> corrcoef (1,2, "alpha", -1) +%!error <"alpha" must be a number between 0 and 1> corrcoef (1,2, "alpha", 2) +%!error <"rows" must be "all"...> corrcoef (1,2, "rows", "foobar") +%!error <Unknown option "foobar"> corrcoef (1,2, "foobar", 1)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/scripts/statistics/cov.m Sun Jan 07 17:13:23 2018 -0800 @@ -0,0 +1,175 @@ +## Copyright (C) 1995-2017 Kurt Hornik +## +## This file is part of Octave. +## +## Octave is free software: you can redistribute it and/or modify it +## under the terms of the GNU General Public License as published by +## the Free Software Foundation, either version 3 of the License, or +## (at your option) any later version. +## +## Octave is distributed in the hope that it will be useful, but +## WITHOUT ANY WARRANTY; without even the implied warranty of +## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +## GNU General Public License for more details. +## +## You should have received a copy of the GNU General Public License +## along with Octave; see the file COPYING. If not, see +## <https://www.gnu.org/licenses/>. + +## -*- texinfo -*- +## @deftypefn {} {} cov (@var{x}) +## @deftypefnx {} {} cov (@var{x}, @var{opt}) +## @deftypefnx {} {} cov (@var{x}, @var{y}) +## @deftypefnx {} {} cov (@var{x}, @var{y}, @var{opt}) +## Compute the covariance matrix. +## +## If each row of @var{x} and @var{y} is an observation, and each column is +## a variable, then the @w{(@var{i}, @var{j})-th} entry of +## @code{cov (@var{x}, @var{y})} is the covariance between the @var{i}-th +## variable in @var{x} and the @var{j}-th variable in @var{y}. +## @tex +## $$ +## \sigma_{ij} = {1 \over N-1} \sum_{i=1}^N (x_i - \bar{x})(y_i - \bar{y}) +## $$ +## where $\bar{x}$ and $\bar{y}$ are the mean values of @var{x} and @var{y}. +## @end tex +## @ifnottex +## +## @example +## cov (@var{x}) = 1/(N-1) * SUM_i (@var{x}(i) - mean(@var{x})) * (@var{y}(i) - mean(@var{y})) +## @end example +## +## where @math{N} is the length of the @var{x} and @var{y} vectors. +## +## @end ifnottex +## +## If called with one argument, compute @code{cov (@var{x}, @var{x})}, the +## covariance between the columns of @var{x}. +## +## The argument @var{opt} determines the type of normalization to use. +## Valid values are +## +## @table @asis +## @item 0: +## normalize with @math{N-1}, provides the best unbiased estimator of the +## covariance [default] +## +## @item 1: +## normalize with @math{N}, this provides the second moment around the mean +## @end table +## +## Compatibility Note:: Octave always treats rows of @var{x} and @var{y} +## as multivariate random variables. +## For two inputs, however, @sc{matlab} treats @var{x} and @var{y} as two +## univariate distributions regardless of their shapes, and will calculate +## @code{cov ([@var{x}(:), @var{y}(:)])} whenever the number of elements in +## @var{x} and @var{y} are equal. This will result in a 2x2 matrix. +## Code relying on @sc{matlab}'s definition will need to be changed when +## running in Octave. +## @seealso{corr} +## @end deftypefn + +## Author: KH <Kurt.Hornik@wu-wien.ac.at> +## Description: Compute covariances + +function c = cov (x, y = [], opt = 0) + + if (nargin < 1 || nargin > 3) + print_usage (); + endif + + if ( ! (isnumeric (x) || islogical (x)) + || ! (isnumeric (y) || islogical (y))) + error ("cov: X and Y must be numeric matrices or vectors"); + endif + + if (ndims (x) != 2 || ndims (y) != 2) + error ("cov: X and Y must be 2-D matrices or vectors"); + endif + + if (nargin == 2 && isscalar (y)) + opt = y; + endif + + if (opt != 0 && opt != 1) + error ("cov: normalization OPT must be 0 or 1"); + endif + + ## Special case, scalar has zero covariance + if (isscalar (x)) + if (isa (x, "single")) + c = single (0); + else + c = 0; + endif + return; + endif + + if (isrow (x)) + x = x.'; + endif + n = rows (x); + + if (nargin == 1 || isscalar (y)) + x = center (x, 1); + c = x' * x / (n - 1 + opt); + else + if (isrow (y)) + y = y.'; + endif + if (rows (y) != n) + error ("cov: X and Y must have the same number of observations"); + endif + x = center (x, 1); + y = center (y, 1); + c = x' * y / (n - 1 + opt); + endif + +endfunction + + +%!test +%! x = rand (10); +%! cx1 = cov (x); +%! cx2 = cov (x, x); +%! assert (size (cx1) == [10, 10] && size (cx2) == [10, 10]); +%! assert (cx1, cx2, 1e1*eps); + +%!test +%! x = [1:3]'; +%! y = [3:-1:1]'; +%! assert (cov (x, y), -1, 5*eps); +%! assert (cov (x, flipud (y)), 1, 5*eps); +%! assert (cov ([x, y]), [1 -1; -1 1], 5*eps); + +%!test +%! x = single ([1:3]'); +%! y = single ([3:-1:1]'); +%! assert (cov (x, y), single (-1), 5*eps); +%! assert (cov (x, flipud (y)), single (1), 5*eps); +%! assert (cov ([x, y]), single ([1 -1; -1 1]), 5*eps); + +%!test +%! x = [1:5]; +%! c = cov (x); +%! assert (isscalar (c)); +%! assert (c, 2.5); + +%!assert (cov (5), 0) +%!assert (cov (single (5)), single (0)) + +%!test +%! x = [1:5]; +%! c = cov (x, 0); +%! assert (c, 2.5); +%! c = cov (x, 1); +%! assert (c, 2); + +## Test input validation +%!error cov () +%!error cov (1, 2, 3, 4) +%!error cov ([1; 2], ["A", "B"]) +%!error cov (ones (2,2,2)) +%!error cov (ones (2,2), ones (2,2,2)) +%!error cov (1, 3) +%!error cov (ones (2,2), ones (3,2))
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/scripts/statistics/discrete_cdf.m Sun Jan 07 17:13:23 2018 -0800 @@ -0,0 +1,80 @@ +## Copyright (C) 2012 Rik Wehbring +## Copyright (C) 2010-2016 David Bateman +## +## This file is part of Octave. +## +## Octave is free software: you can redistribute it and/or modify it +## under the terms of the GNU General Public License as published by +## the Free Software Foundation, either version 3 of the License, or +## (at your option) any later version. +## +## Octave is distributed in the hope that it will be useful, but +## WITHOUT ANY WARRANTY; without even the implied warranty of +## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +## GNU General Public License for more details. +## +## You should have received a copy of the GNU General Public License +## along with Octave; see the file COPYING. If not, see +## <https://www.gnu.org/licenses/>. + +## -*- texinfo -*- +## @deftypefn {} {} discrete_cdf (@var{x}, @var{v}, @var{p}) +## For each element of @var{x}, compute the cumulative distribution function +## (CDF) at @var{x} of a univariate discrete distribution which assumes the +## values in @var{v} with probabilities @var{p}. +## @end deftypefn + +function cdf = discrete_cdf (x, v, p) + + if (nargin != 3) + print_usage (); + endif + + if (! isvector (v)) + error ("discrete_cdf: V must be a vector"); + elseif (any (isnan (v))) + error ("discrete_cdf: V must not have any NaN elements"); + elseif (! isvector (p) || (length (p) != length (v))) + error ("discrete_cdf: P must be a vector with length (V) elements"); + elseif (! (all (p >= 0) && any (p))) + error ("discrete_cdf: P must be a nonzero, non-negative vector"); + endif + + p = p(:) / sum (p); # Reshape and normalize probability vector + + if (isa (x, "single") || isa (v, "single") || isa (p, "single")); + cdf = NaN (size (x), "single"); + else + cdf = NaN (size (x)); + endif + + k = ! isnan (x); + [vs, vi] = sort (v); + cdf(k) = [0 ; cumsum(p(vi))](lookup (vs, x(k)) + 1); + +endfunction + + +%!shared x,v,p,y +%! x = [-1 0.1 1.1 1.9 3]; +%! v = 0.1:0.2:1.9; +%! p = 1/length(v) * ones (1, length(v)); +%! y = [0 0.1 0.6 1 1]; +%!assert (discrete_cdf ([x, NaN], v, p), [y, NaN], eps) + +## Test class of input preserved +%!assert (discrete_cdf (single ([x, NaN]), v, p), single ([y, NaN]), 2*eps ("single")) +%!assert (discrete_cdf ([x, NaN], single (v), p), single ([y, NaN]), 2*eps ("single")) +%!assert (discrete_cdf ([x, NaN], v, single (p)), single ([y, NaN]), 2*eps ("single")) + +## Test input validation +%!error discrete_cdf () +%!error discrete_cdf (1) +%!error discrete_cdf (1,2) +%!error discrete_cdf (1,2,3,4) +%!error discrete_cdf (1, ones (2), ones (2,1)) +%!error discrete_cdf (1, [1 ; NaN], ones (2,1)) +%!error discrete_cdf (1, ones (2,1), ones (1,1)) +%!error discrete_cdf (1, ones (2,1), [1 -1]) +%!error discrete_cdf (1, ones (2,1), [1 NaN]) +%!error discrete_cdf (1, ones (2,1), [0 0])
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/scripts/statistics/discrete_inv.m Sun Jan 07 17:13:23 2018 -0800 @@ -0,0 +1,94 @@ +## Copyright (C) 2012 Rik Wehbring +## Copyright (C) 1996-2016 Kurt Hornik +## +## This file is part of Octave. +## +## Octave is free software: you can redistribute it and/or modify it +## under the terms of the GNU General Public License as published by +## the Free Software Foundation, either version 3 of the License, or +## (at your option) any later version. +## +## Octave is distributed in the hope that it will be useful, but +## WITHOUT ANY WARRANTY; without even the implied warranty of +## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +## GNU General Public License for more details. +## +## You should have received a copy of the GNU General Public License +## along with Octave; see the file COPYING. If not, see +## <https://www.gnu.org/licenses/>. + +## -*- texinfo -*- +## @deftypefn {} {} discrete_inv (@var{x}, @var{v}, @var{p}) +## For each element of @var{x}, compute the quantile (the inverse of the CDF) +## at @var{x} of the univariate distribution which assumes the values in +## @var{v} with probabilities @var{p}. +## @end deftypefn + +## Author: KH <Kurt.Hornik@wu-wien.ac.at> +## Description: Quantile function of a discrete distribution + +function inv = discrete_inv (x, v, p) + + if (nargin != 3) + print_usage (); + endif + + if (! isvector (v)) + error ("discrete_inv: V must be a vector"); + elseif (! isvector (p) || (length (p) != length (v))) + error ("discrete_inv: P must be a vector with length (V) elements"); + elseif (any (isnan (p))) + error ("discrete_rnd: P must not have any NaN elements"); + elseif (! (all (p >= 0) && any (p))) + error ("discrete_inv: P must be a nonzero, non-negative vector"); + endif + + if (isa (x, "single") || isa (v, "single") || isa (p, "single")); + inv = NaN (size (x), "single"); + else + inv = NaN (size (x)); + endif + + ## FIXME: This isn't elegant. But cumsum and lookup together produce + ## different results when called with a single or a double. + if (isa (p, "single")); + p = double (p); + endif + + [v, idx] = sort (v); + p = cumsum (p(idx)(:)) / sum (p); # Reshape and normalize probability vector + + k = (x == 0); + inv(k) = v(1); + + k = (x == 1); + inv(k) = v(end); + + k = (x > 0) & (x < 1); + inv(k) = v(length (p) - lookup (sort (p, "descend"), x(k)) + 1); + +endfunction + + +%!shared x,v,p,y +%! x = [-1 0 0.1 0.5 1 2]; +%! v = 0.1:0.2:1.9; +%! p = 1/length(v) * ones (1, length(v)); +%! y = [NaN v(1) v(1) v(end/2) v(end) NaN]; +%!assert (discrete_inv ([x, NaN], v, p), [y, NaN], eps) + +## Test class of input preserved +%!assert (discrete_inv (single ([x, NaN]), v, p), single ([y, NaN]), eps ("single")) +%!assert (discrete_inv ([x, NaN], single (v), p), single ([y, NaN]), eps ("single")) +%!assert (discrete_inv ([x, NaN], v, single (p)), single ([y, NaN]), eps ("single")) + +## Test input validation +%!error discrete_inv () +%!error discrete_inv (1) +%!error discrete_inv (1,2) +%!error discrete_inv (1,2,3,4) +%!error discrete_inv (1, ones (2), ones (2,1)) +%!error discrete_inv (1, ones (2,1), ones (1,1)) +%!error discrete_inv (1, ones (2,1), [1 NaN]) +%!error discrete_inv (1, ones (2,1), [1 -1]) +%!error discrete_inv (1, ones (2,1), [0 0])
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/scripts/statistics/discrete_pdf.m Sun Jan 07 17:13:23 2018 -0800 @@ -0,0 +1,84 @@ +## Copyright (C) 2012 Rik Wehbring +## Copyright (C) 1996-2016 Kurt Hornik +## +## This file is part of Octave. +## +## Octave is free software: you can redistribute it and/or modify it +## under the terms of the GNU General Public License as published by +## the Free Software Foundation, either version 3 of the License, or +## (at your option) any later version. +## +## Octave is distributed in the hope that it will be useful, but +## WITHOUT ANY WARRANTY; without even the implied warranty of +## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +## GNU General Public License for more details. +## +## You should have received a copy of the GNU General Public License +## along with Octave; see the file COPYING. If not, see +## <https://www.gnu.org/licenses/>. + +## -*- texinfo -*- +## @deftypefn {} {} discrete_pdf (@var{x}, @var{v}, @var{p}) +## For each element of @var{x}, compute the probability density function (PDF) +## at @var{x} of a univariate discrete distribution which assumes the values +## in @var{v} with probabilities @var{p}. +## @end deftypefn + +## Author: KH <Kurt.Hornik@wu-wien.ac.at> +## Description: PDF of a discrete distribution + +function pdf = discrete_pdf (x, v, p) + + if (nargin != 3) + print_usage (); + endif + + if (! isvector (v)) + error ("discrete_pdf: V must be a vector"); + elseif (any (isnan (v))) + error ("discrete_pdf: V must not have any NaN elements"); + elseif (! isvector (p) || (length (p) != length (v))) + error ("discrete_pdf: P must be a vector with length (V) elements"); + elseif (! (all (p >= 0) && any (p))) + error ("discrete_pdf: P must be a nonzero, non-negative vector"); + endif + + ## Reshape and normalize probability vector. Values not in table get 0 prob. + p = [0 ; p(:)/sum(p)]; + + if (isa (x, "single") || isa (v, "single") || isa (p, "single")) + pdf = NaN (size (x), "single"); + else + pdf = NaN (size (x)); + endif + + k = ! isnan (x); + [vs, vi] = sort (v(:)); + pdf(k) = p([0 ; vi](lookup (vs, x(k), 'm') + 1) + 1); + +endfunction + + +%!shared x,v,p,y +%! x = [-1 0.1 1.1 1.9 3]; +%! v = 0.1:0.2:1.9; +%! p = 1/length (v) * ones (1, length (v)); +%! y = [0 0.1 0.1 0.1 0]; +%!assert (discrete_pdf ([x, NaN], v, p), [y, NaN], 5*eps) + +## Test class of input preserved +%!assert (discrete_pdf (single ([x, NaN]), v, p), single ([y, NaN]), 5*eps ("single")) +%!assert (discrete_pdf ([x, NaN], single (v), p), single ([y, NaN]), 5*eps ("single")) +%!assert (discrete_pdf ([x, NaN], v, single (p)), single ([y, NaN]), 5*eps ("single")) + +## Test input validation +%!error discrete_pdf () +%!error discrete_pdf (1) +%!error discrete_pdf (1,2) +%!error discrete_pdf (1,2,3,4) +%!error discrete_pdf (1, ones (2), ones (2,1)) +%!error discrete_pdf (1, [1 ; NaN], ones (2,1)) +%!error discrete_pdf (1, ones (2,1), ones (1,1)) +%!error discrete_pdf (1, ones (2,1), [1 -1]) +%!error discrete_pdf (1, ones (2,1), [1 NaN]) +%!error discrete_pdf (1, ones (2,1), [0 0])
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/scripts/statistics/discrete_rnd.m Sun Jan 07 17:13:23 2018 -0800 @@ -0,0 +1,103 @@ +## Copyright (C) 2012 Rik Wehbring +## Copyright (C) 1996-2016 Kurt Hornik +## +## This file is part of Octave. +## +## Octave is free software: you can redistribute it and/or modify it +## under the terms of the GNU General Public License as published by +## the Free Software Foundation, either version 3 of the License, or +## (at your option) any later version. +## +## Octave is distributed in the hope that it will be useful, but +## WITHOUT ANY WARRANTY; without even the implied warranty of +## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +## GNU General Public License for more details. +## +## You should have received a copy of the GNU General Public License +## along with Octave; see the file COPYING. If not, see +## <https://www.gnu.org/licenses/>. + +## -*- texinfo -*- +## @deftypefn {} {} discrete_rnd (@var{v}, @var{p}) +## @deftypefnx {} {} discrete_rnd (@var{v}, @var{p}, @var{r}) +## @deftypefnx {} {} discrete_rnd (@var{v}, @var{p}, @var{r}, @var{c}, @dots{}) +## @deftypefnx {} {} discrete_rnd (@var{v}, @var{p}, [@var{sz}]) +## Return a matrix of random samples from the univariate distribution which +## assumes the values in @var{v} with probabilities @var{p}. +## +## When called with a single size argument, return a square matrix with +## the dimension specified. When called with more than one scalar argument the +## first two arguments are taken as the number of rows and columns and any +## further arguments specify additional matrix dimensions. The size may also +## be specified with a vector of dimensions @var{sz}. +## +## If no size arguments are given then the result matrix is the common size of +## @var{v} and @var{p}. +## @end deftypefn + +## Author: KH <Kurt.Hornik@wu-wien.ac.at> +## Description: Random deviates from a discrete distribution + +function rnd = discrete_rnd (v, p, varargin) + + if (nargin < 2) + print_usage (); + endif + + if (! isvector (v)) + error ("discrete_rnd: V must be a vector"); + elseif (! isvector (p) || (length (p) != length (v))) + error ("discrete_rnd: P must be a vector with length (V) elements"); + elseif (any (isnan (p))) + error ("discrete_rnd: P must not have any NaN elements"); + elseif (! (all (p >= 0) && any (p))) + error ("discrete_rnd: P must be a nonzero, non-negative vector"); + endif + + if (nargin == 2) + sz = size (v); + elseif (nargin == 3) + if (isscalar (varargin{1}) && varargin{1} >= 0) + sz = [varargin{1}, varargin{1}]; + elseif (isrow (varargin{1}) && all (varargin{1} >= 0)) + sz = varargin{1}; + else + error ("discrete_rnd: dimension vector must be row vector of non-negative integers"); + endif + elseif (nargin > 3) + if (any (cellfun (@(x) (! isscalar (x) || x < 0), varargin))) + error ("discrete_rnd: dimensions must be non-negative integers"); + endif + sz = [varargin{:}]; + endif + + rnd = v(lookup (cumsum (p(1:end-1)) / sum (p), rand (sz)) + 1); + rnd = reshape (rnd, sz); + +endfunction + + +%!assert (size (discrete_rnd (1:2, 1:2, 3)), [3, 3]) +%!assert (size (discrete_rnd (1:2, 1:2, [4 1])), [4, 1]) +%!assert (size (discrete_rnd (1:2, 1:2, 4, 1)), [4, 1]) + +## Test class of input preserved +%!assert (class (discrete_rnd (1:2, 1:2)), "double") +%!assert (class (discrete_rnd (single (1:2), 1:2)), "single") +## FIXME: Maybe this should work, maybe it shouldn't. +#%!assert(class (discrete_rnd (1:2, single(1:2))), "single") + +## Test input validation +%!error discrete_rnd () +%!error discrete_rnd (1) +%!error discrete_rnd (1:2,1:2, -1) +%!error discrete_rnd (1:2,1:2, ones (2)) +%!error discrete_rnd (1:2,1:2, [2 -1 2]) +%!error discrete_rnd (1:2,1:2, 1, ones (2)) +%!error discrete_rnd (1:2,1:2, 1, -1) +## test v,p verification +%!error discrete_rnd (1, ones (2), ones (2,1)) +%!error discrete_rnd (1, ones (2,1), ones (1,1)) +%!error discrete_rnd (1, ones (2,1), [1 -1]) +%!error discrete_rnd (1, ones (2,1), [1 NaN]) +%!error discrete_rnd (1, ones (2,1), [0 0])
--- a/scripts/statistics/distributions/betacdf.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,92 +0,0 @@ -## Copyright (C) 2012 Rik Wehbring -## Copyright (C) 1995-2016 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} betacdf (@var{x}, @var{a}, @var{b}) -## For each element of @var{x}, compute the cumulative distribution function -## (CDF) at @var{x} of the Beta distribution with parameters @var{a} and -## @var{b}. -## @end deftypefn - -## Author: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: CDF of the Beta distribution - -function cdf = betacdf (x, a, b) - - if (nargin != 3) - print_usage (); - endif - - if (! isscalar (a) || ! isscalar (b)) - [retval, x, a, b] = common_size (x, a, b); - if (retval > 0) - error ("betacdf: X, A, and B must be of common size or scalars"); - endif - endif - - if (iscomplex (x) || iscomplex (a) || iscomplex (b)) - error ("betacdf: X, A, and B must not be complex"); - endif - - if (isa (x, "single") || isa (a, "single") || isa (b, "single")) - cdf = zeros (size (x), "single"); - else - cdf = zeros (size (x)); - endif - - k = isnan (x) | !(a > 0) | !(b > 0); - cdf(k) = NaN; - - k = (x >= 1) & (a > 0) & (b > 0); - cdf(k) = 1; - - k = (x > 0) & (x < 1) & (a > 0) & (b > 0); - if (isscalar (a) && isscalar (b)) - cdf(k) = betainc (x(k), a, b); - else - cdf(k) = betainc (x(k), a(k), b(k)); - endif - -endfunction - - -%!shared x,y -%! x = [-1 0 0.5 1 2]; -%! y = [0 0 0.75 1 1]; -%!assert (betacdf (x, ones (1,5), 2*ones (1,5)), y) -%!assert (betacdf (x, 1, 2*ones (1,5)), y) -%!assert (betacdf (x, ones (1,5), 2), y) -%!assert (betacdf (x, [0 1 NaN 1 1], 2), [NaN 0 NaN 1 1]) -%!assert (betacdf (x, 1, 2*[0 1 NaN 1 1]), [NaN 0 NaN 1 1]) -%!assert (betacdf ([x(1:2) NaN x(4:5)], 1, 2), [y(1:2) NaN y(4:5)]) - -## Test class of input preserved -%!assert (betacdf ([x, NaN], 1, 2), [y, NaN]) -%!assert (betacdf (single ([x, NaN]), 1, 2), single ([y, NaN])) -%!assert (betacdf ([x, NaN], single (1), 2), single ([y, NaN])) -%!assert (betacdf ([x, NaN], 1, single (2)), single ([y, NaN])) - -## Test input validation -%!error betacdf () -%!error betacdf (1) -%!error betacdf (1,2) -%!error betacdf (1,2,3,4) -%!error betacdf (ones (3), ones (2), ones (2)) -%!error betacdf (ones (2), ones (3), ones (2)) -%!error betacdf (ones (2), ones (2), ones (3))
--- a/scripts/statistics/distributions/betainv.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,136 +0,0 @@ -## Copyright (C) 2012 Rik Wehbring -## Copyright (C) 1995-2016 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} betainv (@var{x}, @var{a}, @var{b}) -## For each element of @var{x}, compute the quantile (the inverse of the CDF) -## at @var{x} of the Beta distribution with parameters @var{a} and @var{b}. -## @end deftypefn - -## Author: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: Quantile function of the Beta distribution - -function inv = betainv (x, a, b) - - if (nargin != 3) - print_usage (); - endif - - if (! isscalar (a) || ! isscalar (b)) - [retval, x, a, b] = common_size (x, a, b); - if (retval > 0) - error ("betainv: X, A, and B must be of common size or scalars"); - endif - endif - - if (iscomplex (x) || iscomplex (a) || iscomplex (b)) - error ("betainv: X, A, and B must not be complex"); - endif - - if (isa (x, "single") || isa (a, "single") || isa (b, "single")) - inv = zeros (size (x), "single"); - else - inv = zeros (size (x)); - endif - - k = (x < 0) | (x > 1) | !(a > 0) | !(b > 0) | isnan (x); - inv(k) = NaN; - - k = (x == 1) & (a > 0) & (b > 0); - inv(k) = 1; - - k = find ((x > 0) & (x < 1) & (a > 0) & (b > 0)); - if (! isempty (k)) - if (! isscalar (a) || ! isscalar (b)) - a = a(k); - b = b(k); - y = a ./ (a + b); - else - y = a / (a + b) * ones (size (k)); - endif - x = x(k); - - if (isa (y, "single")) - myeps = eps ("single"); - else - myeps = eps; - endif - - l = find (y < myeps); - if (any (l)) - y(l) = sqrt (myeps) * ones (length (l), 1); - endif - l = find (y > 1 - myeps); - if (any (l)) - y(l) = 1 - sqrt (myeps) * ones (length (l), 1); - endif - - y_new = y; - loopcnt = 0; - do - y_old = y_new; - h = (betacdf (y_old, a, b) - x) ./ betapdf (y_old, a, b); - y_new = y_old - h; - ind = find (y_new <= myeps); - if (any (ind)) - y_new(ind) = y_old(ind) / 10; - endif - ind = find (y_new >= 1 - myeps); - if (any (ind)) - y_new(ind) = 1 - (1 - y_old(ind)) / 10; - endif - h = y_old - y_new; - until (max (abs (h)) < sqrt (myeps) || ++loopcnt == 40) - - if (loopcnt == 40) - warning ("betainv: calculation failed to converge for some values"); - endif - - inv(k) = y_new; - endif - -endfunction - - -%!shared x -%! x = [-1 0 0.75 1 2]; -%!assert (betainv (x, ones (1,5), 2*ones (1,5)), [NaN 0 0.5 1 NaN]) -%!assert (betainv (x, 1, 2*ones (1,5)), [NaN 0 0.5 1 NaN]) -%!assert (betainv (x, ones (1,5), 2), [NaN 0 0.5 1 NaN]) -%!assert (betainv (x, [1 0 NaN 1 1], 2), [NaN NaN NaN 1 NaN]) -%!assert (betainv (x, 1, 2*[1 0 NaN 1 1]), [NaN NaN NaN 1 NaN]) -%!assert (betainv ([x(1:2) NaN x(4:5)], 1, 2), [NaN 0 NaN 1 NaN]) - -## Test class of input preserved -%!assert (betainv ([x, NaN], 1, 2), [NaN 0 0.5 1 NaN NaN]) -%!assert (betainv (single ([x, NaN]), 1, 2), single ([NaN 0 0.5 1 NaN NaN])) -%!assert (betainv ([x, NaN], single (1), 2), single ([NaN 0 0.5 1 NaN NaN])) -%!assert (betainv ([x, NaN], 1, single (2)), single ([NaN 0 0.5 1 NaN NaN])) - -## Test input validation -%!error betainv () -%!error betainv (1) -%!error betainv (1,2) -%!error betainv (1,2,3,4) -%!error betainv (ones (3), ones (2), ones (2)) -%!error betainv (ones (2), ones (3), ones (2)) -%!error betainv (ones (2), ones (2), ones (3)) -%!error betainv (i, 2, 2) -%!error betainv (2, i, 2) -%!error betainv (2, 2, i)
--- a/scripts/statistics/distributions/betapdf.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,129 +0,0 @@ -## Copyright (C) 2012 Rik Wehbring -## Copyright (C) 1995-2016 Kurt Hornik -## Copyright (C) 2010 Christos Dimitrakakis -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} betapdf (@var{x}, @var{a}, @var{b}) -## For each element of @var{x}, compute the probability density function (PDF) -## at @var{x} of the Beta distribution with parameters @var{a} and @var{b}. -## @end deftypefn - -## Author: KH <Kurt.Hornik@wu-wien.ac.at>, CD <christos.dimitrakakis@gmail.com> -## Description: PDF of the Beta distribution - -function pdf = betapdf (x, a, b) - - if (nargin != 3) - print_usage (); - endif - - if (! isscalar (a) || ! isscalar (b)) - [retval, x, a, b] = common_size (x, a, b); - if (retval > 0) - error ("betapdf: X, A, and B must be of common size or scalars"); - endif - endif - - if (iscomplex (x) || iscomplex (a) || iscomplex (b)) - error ("betapdf: X, A, and B must not be complex"); - endif - - if (isa (x, "single") || isa (a, "single") || isa (b, "single")); - pdf = zeros (size (x), "single"); - else - pdf = zeros (size (x)); - endif - - k = !(a > 0) | !(b > 0) | isnan (x); - pdf(k) = NaN; - - k = (x > 0) & (x < 1) & (a > 0) & (b > 0) & ((a != 1) | (b != 1)); - if (isscalar (a) && isscalar (b)) - pdf(k) = exp ((a - 1) * log (x(k)) - + (b - 1) * log (1 - x(k)) - + gammaln (a + b) - gammaln (a) - gammaln (b)); - else - pdf(k) = exp ((a(k) - 1) .* log (x(k)) - + (b(k) - 1) .* log (1 - x(k)) - + gammaln (a(k) + b(k)) - gammaln (a(k)) - gammaln (b(k))); - endif - - ## Most important special cases when the density is finite. - k = (x == 0) & (a == 1) & (b > 0) & (b != 1); - if (isscalar (a) && isscalar (b)) - pdf(k) = exp (gammaln (a + b) - gammaln (a) - gammaln (b)); - else - pdf(k) = exp (gammaln (a(k) + b(k)) - gammaln (a(k)) - gammaln (b(k))); - endif - - k = (x == 1) & (b == 1) & (a > 0) & (a != 1); - if (isscalar (a) && isscalar (b)) - pdf(k) = exp (gammaln (a + b) - gammaln (a) - gammaln (b)); - else - pdf(k) = exp (gammaln (a(k) + b(k)) - gammaln (a(k)) - gammaln (b(k))); - endif - - k = (x >= 0) & (x <= 1) & (a == 1) & (b == 1); - pdf(k) = 1; - - ## Other special case when the density at the boundary is infinite. - k = (x == 0) & (a < 1); - pdf(k) = Inf; - - k = (x == 1) & (b < 1); - pdf(k) = Inf; - -endfunction - - -%!shared x,y -%! x = [-1 0 0.5 1 2]; -%! y = [0 2 1 0 0]; -%!assert (betapdf (x, ones (1,5), 2*ones (1,5)), y) -%!assert (betapdf (x, 1, 2*ones (1,5)), y) -%!assert (betapdf (x, ones (1,5), 2), y) -%!assert (betapdf (x, [0 NaN 1 1 1], 2), [NaN NaN y(3:5)]) -%!assert (betapdf (x, 1, 2*[0 NaN 1 1 1]), [NaN NaN y(3:5)]) -%!assert (betapdf ([x, NaN], 1, 2), [y, NaN]) - -## Test class of input preserved -%!assert (betapdf (single ([x, NaN]), 1, 2), single ([y, NaN])) -%!assert (betapdf ([x, NaN], single (1), 2), single ([y, NaN])) -%!assert (betapdf ([x, NaN], 1, single (2)), single ([y, NaN])) - -## Beta (1/2,1/2) == arcsine distribution -%!test -%! x = rand (10,1); -%! y = 1./(pi * sqrt (x.*(1-x))); -%! assert (betapdf (x, 1/2, 1/2), y, 50*eps); - -## Test large input values to betapdf -%!assert (betapdf (0.5, 1000, 1000), 35.678, 1e-3) - -## Test input validation -%!error betapdf () -%!error betapdf (1) -%!error betapdf (1,2) -%!error betapdf (1,2,3,4) -%!error betapdf (ones (3), ones (2), ones (2)) -%!error betapdf (ones (2), ones (3), ones (2)) -%!error betapdf (ones (2), ones (2), ones (3)) -%!error betapdf (i, 2, 2) -%!error betapdf (2, i, 2) -%!error betapdf (2, 2, i)
--- a/scripts/statistics/distributions/betarnd.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,133 +0,0 @@ -## Copyright (C) 2012 Rik Wehbring -## Copyright (C) 1995-2016 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} betarnd (@var{a}, @var{b}) -## @deftypefnx {} {} betarnd (@var{a}, @var{b}, @var{r}) -## @deftypefnx {} {} betarnd (@var{a}, @var{b}, @var{r}, @var{c}, @dots{}) -## @deftypefnx {} {} betarnd (@var{a}, @var{b}, [@var{sz}]) -## Return a matrix of random samples from the Beta distribution with parameters -## @var{a} and @var{b}. -## -## When called with a single size argument, return a square matrix with -## the dimension specified. When called with more than one scalar argument the -## first two arguments are taken as the number of rows and columns and any -## further arguments specify additional matrix dimensions. The size may also -## be specified with a vector of dimensions @var{sz}. -## -## If no size arguments are given then the result matrix is the common size of -## @var{a} and @var{b}. -## @end deftypefn - -## Author: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: Random deviates from the Beta distribution - -function rnd = betarnd (a, b, varargin) - - if (nargin < 2) - print_usage (); - endif - - if (! isscalar (a) || ! isscalar (b)) - [retval, a, b] = common_size (a, b); - if (retval > 0) - error ("betarnd: A and B must be of common size or scalars"); - endif - endif - - if (iscomplex (a) || iscomplex (b)) - error ("betarnd: A and B must not be complex"); - endif - - if (nargin == 2) - sz = size (a); - elseif (nargin == 3) - if (isscalar (varargin{1}) && varargin{1} >= 0) - sz = [varargin{1}, varargin{1}]; - elseif (isrow (varargin{1}) && all (varargin{1} >= 0)) - sz = varargin{1}; - else - error ("betarnd: dimension vector must be row vector of non-negative integers"); - endif - elseif (nargin > 3) - if (any (cellfun (@(x) (! isscalar (x) || x < 0), varargin))) - error ("betarnd: dimensions must be non-negative integers"); - endif - sz = [varargin{:}]; - endif - - if (! isscalar (a) && ! isequal (size (a), sz)) - error ("betarnd: A and B must be scalar or of size SZ"); - endif - - if (isa (a, "single") || isa (b, "single")) - cls = "single"; - else - cls = "double"; - endif - - if (isscalar (a) && isscalar (b)) - if ((a > 0) && (a < Inf) && (b > 0) && (b < Inf)) - r = randg (a, sz, cls); - rnd = r ./ (r + randg (b, sz, cls)); - else - rnd = NaN (sz, cls); - endif - else - rnd = NaN (sz, cls); - - k = (a > 0) & (a < Inf) & (b > 0) & (b < Inf); - r = randg (a(k), cls); - rnd(k) = r ./ (r + randg (b(k), cls)); - endif - -endfunction - - -%!assert (size (betarnd (1,2)), [1, 1]) -%!assert (size (betarnd (ones (2,1), 2)), [2, 1]) -%!assert (size (betarnd (ones (2,2), 2)), [2, 2]) -%!assert (size (betarnd (1, 2*ones (2,1))), [2, 1]) -%!assert (size (betarnd (1, 2*ones (2,2))), [2, 2]) -%!assert (size (betarnd (1, 2, 3)), [3, 3]) -%!assert (size (betarnd (1, 2, [4 1])), [4, 1]) -%!assert (size (betarnd (1, 2, 4, 1)), [4, 1]) - -## Test class of input preserved -%!assert (class (betarnd (1, 2)), "double") -%!assert (class (betarnd (single (1), 2)), "single") -%!assert (class (betarnd (single ([1 1]), 2)), "single") -%!assert (class (betarnd (1, single (2))), "single") -%!assert (class (betarnd (1, single ([2 2]))), "single") - -## Test input validation -%!error betarnd () -%!error betarnd (1) -%!error betarnd (ones (3), ones (2)) -%!error betarnd (ones (2), ones (3)) -%!error betarnd (i, 2) -%!error betarnd (2, i) -%!error betarnd (1,2, -1) -%!error betarnd (1,2, ones (2)) -%!error binornd (1,2, [2 -1 2]) -%!error betarnd (1,2, 1, ones (2)) -%!error betarnd (1,2, 1, -1) -%!error betarnd (ones (2,2), 2, 3) -%!error betarnd (ones (2,2), 2, [3, 2]) -%!error betarnd (ones (2,2), 2, 2, 3)
--- a/scripts/statistics/distributions/binocdf.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,97 +0,0 @@ -## Copyright (C) 2012 Rik Wehbring -## Copyright (C) 1995-2016 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} binocdf (@var{x}, @var{n}, @var{p}) -## For each element of @var{x}, compute the cumulative distribution function -## (CDF) at @var{x} of the binomial distribution with parameters @var{n} and -## @var{p}, where @var{n} is the number of trials and @var{p} is the -## probability of success. -## @end deftypefn - -## Author: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: CDF of the binomial distribution - -function cdf = binocdf (x, n, p) - - if (nargin != 3) - print_usage (); - endif - - if (! isscalar (n) || ! isscalar (p)) - [retval, x, n, p] = common_size (x, n, p); - if (retval > 0) - error ("binocdf: X, N, and P must be of common size or scalars"); - endif - endif - - if (iscomplex (x) || iscomplex (n) || iscomplex (p)) - error ("binocdf: X, N, and P must not be complex"); - endif - - if (isa (x, "single") || isa (n, "single") || isa (p, "single")); - cdf = zeros (size (x), "single"); - else - cdf = zeros (size (x)); - endif - - k = isnan (x) | !(n >= 0) | (n != fix (n)) | !(p >= 0) | !(p <= 1); - cdf(k) = NaN; - - k = (x >= n) & (n >= 0) & (n == fix (n) & (p >= 0) & (p <= 1)); - cdf(k) = 1; - - k = (x >= 0) & (x < n) & (n == fix (n)) & (p >= 0) & (p <= 1); - tmp = floor (x(k)); - if (isscalar (n) && isscalar (p)) - cdf(k) = betainc (1 - p, n - tmp, tmp + 1); - else - cdf(k) = betainc (1 .- p(k), n(k) - tmp, tmp + 1); - endif - -endfunction - - -%!shared x,y -%! x = [-1 0 1 2 3]; -%! y = [0 1/4 3/4 1 1]; -%!assert (binocdf (x, 2*ones (1,5), 0.5*ones (1,5)), y) -%!assert (binocdf (x, 2, 0.5*ones (1,5)), y) -%!assert (binocdf (x, 2*ones (1,5), 0.5), y) -%!assert (binocdf (x, 2*[0 -1 NaN 1.1 1], 0.5), [0 NaN NaN NaN 1]) -%!assert (binocdf (x, 2, 0.5*[0 -1 NaN 3 1]), [0 NaN NaN NaN 1]) -%!assert (binocdf ([x(1:2) NaN x(4:5)], 2, 0.5), [y(1:2) NaN y(4:5)]) - -## Test class of input preserved -%!assert (binocdf ([x, NaN], 2, 0.5), [y, NaN]) -%!assert (binocdf (single ([x, NaN]), 2, 0.5), single ([y, NaN])) -%!assert (binocdf ([x, NaN], single (2), 0.5), single ([y, NaN])) -%!assert (binocdf ([x, NaN], 2, single (0.5)), single ([y, NaN])) - -## Test input validation -%!error binocdf () -%!error binocdf (1) -%!error binocdf (1,2) -%!error binocdf (1,2,3,4) -%!error binocdf (ones (3), ones (2), ones (2)) -%!error binocdf (ones (2), ones (3), ones (2)) -%!error binocdf (ones (2), ones (2), ones (3)) -%!error binocdf (i, 2, 2) -%!error binocdf (2, i, 2) -%!error binocdf (2, 2, i)
--- a/scripts/statistics/distributions/binoinv.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,198 +0,0 @@ -## Copyright (C) 2016-2017 Lachlan Andrew -## Copyright (C) 2012-2016 Rik Wehbring -## Copyright (C) 1995-2012 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} binoinv (@var{x}, @var{n}, @var{p}) -## For each element of @var{x}, compute the quantile (the inverse of the CDF) -## at @var{x} of the binomial distribution with parameters -## @var{n} and @var{p}, where @var{n} is the number of trials and -## @var{p} is the probability of success. -## @end deftypefn - -function inv = binoinv (x, n, p) - - if (nargin != 3) - print_usage (); - endif - - if (! isscalar (n) || ! isscalar (p)) - [retval, x, n, p] = common_size (x, n, p); - if (retval > 0) - error ("binoinv: X, N, and P must be of common size or scalars"); - endif - endif - - if (iscomplex (x) || iscomplex (n) || iscomplex (p)) - error ("binoinv: X, N, and P must not be complex"); - endif - - if (isa (x, "single") || isa (n, "single") || isa (p, "single")); - inv = zeros (size (x), "single"); - else - inv = zeros (size (x)); - endif - - k = (!(x >= 0) | !(x <= 1) | !(n >= 0) | (n != fix (n)) | - !(p >= 0) | !(p <= 1)); - inv(k) = NaN; - - k = find ((x >= 0) & (x <= 1) & (n >= 0) & (n == fix (n) - & (p >= 0) & (p <= 1))); - if (! isempty (k)) - x = x(k); - if (isscalar (n) && isscalar (p)) - [inv(k), unfinished] = scalar_binoinv (x(:), n, p); - k = k(unfinished); - if (! isempty (k)) - inv(k) = bin_search_binoinv (x(k), n, p); - endif - else - [inv(k), unfinished] = vector_binoinv (x(:), n(:), p(:)); - k = k(unfinished); - if (! isempty (k)) - inv(k) = bin_search_binoinv (x(k), n(k), p(k)); - endif - endif - endif - -endfunction - -## Core algorithm to calculate the inverse binomial, for n and p real scalars -## and y a column vector, and for which the output is not NaN or Inf. -## Compute CDF in batches of doubling size until CDF > x, or answer > 500 -## Return the locations of unfinished cases in k. -function [m, k] = scalar_binoinv (x, n, p) - - k = 1:length (x); - m = zeros (size (x)); - prev_limit = 0; - limit = 10; - cdf = 0; - v = 0; - do - cdf = binocdf (prev_limit:limit-1, n, p); - r = bsxfun (@le, x(k), cdf); - [v, m(k)] = max (r, [], 2); # find first instance of x <= cdf - m(k) += prev_limit - 1; - k = k(v == 0); - - prev_limit = limit; - limit += limit; - until (isempty (k) || limit >= 1000) - -endfunction - -## Core algorithm to calculate the inverse binomial, for n, p, and y column -## vectors, and for which the output is not NaN or Inf. -## Compute CDF in batches of doubling size until CDF > x, or answer > 500 -## Return the locations of unfinished cases in k. -## Calculates CDF by summing PDF, which is faster than calls to binocdf. -function [m, k] = vector_binoinv (x, n, p) - - k = 1:length(x); - m = zeros (size (x)); - prev_limit = 0; - limit = 10; - cdf = 0; - v = 0; - do - xx = repmat (prev_limit:limit-1, [length(k), 1]); - nn = kron (ones (1, limit-prev_limit), n(k)); - pp = kron (ones (1, limit-prev_limit), p(k)); - pdf = binopdf (xx, nn, pp); - pdf(:,1) += cdf(v==0, end); - cdf = cumsum (pdf, 2); - r = bsxfun (@le, x(k), cdf); - [v, m(k)] = max (r, [], 2); # find first instance of x <= cdf - m(k) += prev_limit - 1; - k = k(v == 0); - - prev_limit = limit; - limit += min (limit, max (1e4/numel (k), 10)); # limit memory use - until (isempty (k) || limit >= 1000) - -endfunction - -## Vectorized binary search. -## Can handle vectors n and p, and is faster than the scalar case when the -## answer is large. -## Could be optimized to call binocdf only for a subset of the x at each stage, -## but care must be taken to handle both scalar and vector n, p. Bookkeeping -## may cost more than the extra computations. -function m = bin_search_binoinv (x, n, p) - - k = 1:length (x); - lower = zeros (size (x)); - limit = 500; # lower bound on point at which prev phase finished - while (any (k) && limit < 1e100) - cdf = binocdf (limit, n, p); - k = (x > cdf); - lower(k) = limit; - limit += limit; - endwhile - upper = max (2*lower, 1); - k = find (lower != limit/2); # elements for which above loop finished - for i = 1:ceil (log2 (max (lower))) - mid = (upper + lower)/2; - cdf = binocdf (floor(mid(:)), n, p); - r = (x <= cdf); - upper(r) = mid(r); - lower(! r) = mid(! r); - endfor - m = ceil (lower); - m(x > binocdf (m(:), n, p)) += 1; # fix off-by-one errors from binary search - -endfunction - - -%!shared x -%! x = [-1 0 0.5 1 2]; -%!assert (binoinv (x, 2*ones (1,5), 0.5*ones (1,5)), [NaN 0 1 2 NaN]) -%!assert (binoinv (x, 2, 0.5*ones (1,5)), [NaN 0 1 2 NaN]) -%!assert (binoinv (x, 2*ones (1,5), 0.5), [NaN 0 1 2 NaN]) -%!assert (binoinv (x, 2*[0 -1 NaN 1.1 1], 0.5), [NaN NaN NaN NaN NaN]) -%!assert (binoinv (x, 2, 0.5*[0 -1 NaN 3 1]), [NaN NaN NaN NaN NaN]) -%!assert (binoinv ([x(1:2) NaN x(4:5)], 2, 0.5), [NaN 0 NaN 2 NaN]) - -## Test class of input preserved -%!assert (binoinv ([x, NaN], 2, 0.5), [NaN 0 1 2 NaN NaN]) -%!assert (binoinv (single ([x, NaN]), 2, 0.5), single ([NaN 0 1 2 NaN NaN])) -%!assert (binoinv ([x, NaN], single (2), 0.5), single ([NaN 0 1 2 NaN NaN])) -%!assert (binoinv ([x, NaN], 2, single (0.5)), single ([NaN 0 1 2 NaN NaN])) - -## Test accuracy, to within +/- 1 since it is a discrete distribution -%!shared y, tol -%! y = magic (3) + 1; -%! tol = 1; -%!assert (binoinv (binocdf (1:10, 11, 0.1), 11, 0.1), 1:10, tol) -%!assert (binoinv (binocdf (1:10, 2*(1:10), 0.1), 2*(1:10), 0.1), 1:10, tol) -%!assert (binoinv (binocdf (y, 2*y, 1./y), 2*y, 1./y), y, tol) - -## Test input validation -%!error binoinv () -%!error binoinv (1) -%!error binoinv (1,2) -%!error binoinv (1,2,3,4) -%!error binoinv (ones (3), ones (2), ones (2)) -%!error binoinv (ones (2), ones (3), ones (2)) -%!error binoinv (ones (2), ones (2), ones (3)) -%!error binoinv (i, 2, 2) -%!error binoinv (2, i, 2) -%!error binoinv (2, 2, i)
--- a/scripts/statistics/distributions/binopdf.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,111 +0,0 @@ -## Copyright (C) 2012 Rik Wehbring -## Copyright (C) 1995-2016 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} binopdf (@var{x}, @var{n}, @var{p}) -## For each element of @var{x}, compute the probability density function (PDF) -## at @var{x} of the binomial distribution with parameters @var{n} and @var{p}, -## where @var{n} is the number of trials and @var{p} is the probability of -## success. -## @end deftypefn - -## Author: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: PDF of the binomial distribution - -function pdf = binopdf (x, n, p) - - if (nargin != 3) - print_usage (); - endif - - if (! isscalar (n) || ! isscalar (p)) - [retval, x, n, p] = common_size (x, n, p); - if (retval > 0) - error ("binopdf: X, N, and P must be of common size or scalars"); - endif - endif - - if (iscomplex (x) || iscomplex (n) || iscomplex (p)) - error ("binopdf: X, N, and P must not be complex"); - endif - - if (isa (x, "single") || isa (n, "single") || isa (p, "single")); - pdf = zeros (size (x), "single"); - else - pdf = zeros (size (x)); - endif - - k = (x == fix (x)) & (n == fix (n)) & (n >= 0) & (p >= 0) & (p <= 1); - - pdf(! k) = NaN; - - k &= ((x >= 0) & (x <= n)); - if (isscalar (n) && isscalar (p)) - pdf(k) = exp (gammaln (n+1) - gammaln (x(k)+1) - gammaln (n-x(k)+1) - + x(k)*log (p) + (n-x(k))*log (1-p)); - else - pdf(k) = exp (gammaln (n(k)+1) - gammaln (x(k)+1) - gammaln (n(k)-x(k)+1) - + x(k).*log (p(k)) + (n(k)-x(k)).*log (1-p(k))); - endif - - ## Special case inputs - ksp = k & (p == 0) & (x == 0); - pdf(ksp) = 1; - ksp = k & (p == 1) & (x == n); - pdf(ksp) = 1; - -endfunction - - -%!shared x,y,tol -%! if (ismac ()) -%! tol = eps (); -%! else -%! tol = 0; -%! endif -%! x = [-1 0 1 2 3]; -%! y = [0 1/4 1/2 1/4 0]; -%!assert (binopdf (x, 2*ones (1,5), 0.5*ones (1,5)), y, tol) -%!assert (binopdf (x, 2, 0.5*ones (1,5)), y, tol) -%!assert (binopdf (x, 2*ones (1,5), 0.5), y, tol) -%!assert (binopdf (x, 2*[0 -1 NaN 1.1 1], 0.5), [0 NaN NaN NaN 0]) -%!assert (binopdf (x, 2, 0.5*[0 -1 NaN 3 1]), [0 NaN NaN NaN 0]) -%!assert (binopdf ([x, NaN], 2, 0.5), [y, NaN], tol) - -## Test Special input values -%!assert (binopdf (0, 3, 0), 1) -%!assert (binopdf (2, 2, 1), 1) -%!assert (binopdf (1, 2, 1), 0) - -## Test class of input preserved -%!assert (binopdf (single ([x, NaN]), 2, 0.5), single ([y, NaN])) -%!assert (binopdf ([x, NaN], single (2), 0.5), single ([y, NaN])) -%!assert (binopdf ([x, NaN], 2, single (0.5)), single ([y, NaN])) - -## Test input validation -%!error binopdf () -%!error binopdf (1) -%!error binopdf (1,2) -%!error binopdf (1,2,3,4) -%!error binopdf (ones (3), ones (2), ones (2)) -%!error binopdf (ones (2), ones (3), ones (2)) -%!error binopdf (ones (2), ones (2), ones (3)) -%!error binopdf (i, 2, 2) -%!error binopdf (2, i, 2) -%!error binopdf (2, 2, i)
--- a/scripts/statistics/distributions/binornd.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,153 +0,0 @@ -## Copyright (C) 2012 Rik Wehbring -## Copyright (C) 1995-2016 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} binornd (@var{n}, @var{p}) -## @deftypefnx {} {} binornd (@var{n}, @var{p}, @var{r}) -## @deftypefnx {} {} binornd (@var{n}, @var{p}, @var{r}, @var{c}, @dots{}) -## @deftypefnx {} {} binornd (@var{n}, @var{p}, [@var{sz}]) -## Return a matrix of random samples from the binomial distribution with -## parameters @var{n} and @var{p}, where @var{n} is the number of trials -## and @var{p} is the probability of success. -## -## When called with a single size argument, return a square matrix with -## the dimension specified. When called with more than one scalar argument the -## first two arguments are taken as the number of rows and columns and any -## further arguments specify additional matrix dimensions. The size may also -## be specified with a vector of dimensions @var{sz}. -## -## If no size arguments are given then the result matrix is the common size of -## @var{n} and @var{p}. -## @end deftypefn - -## Author: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: Random deviates from the binomial distribution - -function rnd = binornd (n, p, varargin) - - if (nargin < 2) - print_usage (); - endif - - if (! isscalar (n) || ! isscalar (p)) - [retval, n, p] = common_size (n, p); - if (retval > 0) - error ("binornd: N and P must be of common size or scalars"); - endif - endif - - if (iscomplex (n) || iscomplex (p)) - error ("binornd: N and P must not be complex"); - endif - - if (nargin == 2) - sz = size (n); - elseif (nargin == 3) - if (isscalar (varargin{1}) && varargin{1} >= 0) - sz = [varargin{1}, varargin{1}]; - elseif (isrow (varargin{1}) && all (varargin{1} >= 0)) - sz = varargin{1}; - else - error ("binornd: dimension vector must be row vector of non-negative integers"); - endif - elseif (nargin > 3) - if (any (cellfun (@(x) (! isscalar (x) || x < 0), varargin))) - error ("binornd: dimensions must be non-negative integers"); - endif - sz = [varargin{:}]; - endif - - if (! isscalar (n) && ! isequal (size (n), sz)) - error ("binornd: N and P must be scalar or of size SZ"); - endif - - if (isa (n, "single") || isa (p, "single")) - cls = "single"; - else - cls = "double"; - endif - - if (isscalar (n) && isscalar (p)) - if ((n > 0) && (n < Inf) && (n == fix (n)) && (p >= 0) && (p <= 1)) - nel = prod (sz); - tmp = rand (n, nel); - rnd = sum (tmp < p, 1); - rnd = reshape (rnd, sz); - if (strcmp (cls, "single")) - rnd = single (rnd); - endif - elseif ((n == 0) && (p >= 0) && (p <= 1)) - rnd = zeros (sz, cls); - else - rnd = NaN (sz, cls); - endif - else - rnd = zeros (sz, cls); - - k = !(n >= 0) | !(n < Inf) | !(n == fix (n)) | !(p >= 0) | !(p <= 1); - rnd(k) = NaN; - - k = (n > 0) & (n < Inf) & (n == fix (n)) & (p >= 0) & (p <= 1); - if (any (k(:))) - N = max (n(k)); - L = sum (k(:)); - tmp = rand (N, L); - ind = repmat ((1 : N)', 1, L); - rnd(k) = sum ((tmp < repmat (p(k)(:)', N, 1)) & - (ind <= repmat (n(k)(:)', N, 1)), 1); - endif - endif - -endfunction - - -%!assert (binornd (0, 0, 1), 0) -%!assert (binornd ([0, 0], [0, 0], 1, 2), [0, 0]) - -%!assert (size (binornd (2, 1/2)), [1, 1]) -%!assert (size (binornd (2*ones (2,1), 1/2)), [2, 1]) -%!assert (size (binornd (2*ones (2,2), 1/2)), [2, 2]) -%!assert (size (binornd (2, 1/2*ones (2,1))), [2, 1]) -%!assert (size (binornd (2, 1/2*ones (2,2))), [2, 2]) -%!assert (size (binornd (2, 1/2, 3)), [3, 3]) -%!assert (size (binornd (2, 1/2, [4 1])), [4, 1]) -%!assert (size (binornd (2, 1/2, 4, 1)), [4, 1]) - -## Test class of input preserved -%!assert (class (binornd (2, 0.5)), "double") -%!assert (class (binornd (single (2), 0.5)), "single") -%!assert (class (binornd (single ([2 2]), 0.5)), "single") -%!assert (class (binornd (2, single (0.5))), "single") -%!assert (class (binornd (2, single ([0.5 0.5]))), "single") - -## Test input validation -%!error binornd () -%!error binornd (1) -%!error binornd (ones (3), ones (2)) -%!error binornd (ones (2), ones (3)) -%!error binornd (i, 2) -%!error binornd (2, i) -%!error binornd (1,2, -1) -%!error binornd (1,2, ones (2)) -%!error binornd (1,2, [2 -1 2]) -%!error binornd (1,2, 1, ones (2)) -%!error binornd (1,2, 1, -1) -%!error binornd (ones (2,2), 2, 3) -%!error binornd (ones (2,2), 2, [3, 2]) -%!error binornd (ones (2,2), 2, 2, 3)
--- a/scripts/statistics/distributions/cauchy_cdf.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,91 +0,0 @@ -## Copyright (C) 2012 Rik Wehbring -## Copyright (C) 1995-2016 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} cauchy_cdf (@var{x}) -## @deftypefnx {} {} cauchy_cdf (@var{x}, @var{location}, @var{scale}) -## For each element of @var{x}, compute the cumulative distribution function -## (CDF) at @var{x} of the Cauchy distribution with location parameter -## @var{location} and scale parameter @var{scale}. -## -## Default values are @var{location} = 0, @var{scale} = 1. -## @end deftypefn - -## Author: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: CDF of the Cauchy distribution - -function cdf = cauchy_cdf (x, location = 0, scale = 1) - - if (nargin != 1 && nargin != 3) - print_usage (); - endif - - if (! isscalar (location) || ! isscalar (scale)) - [retval, x, location, scale] = common_size (x, location, scale); - if (retval > 0) - error ("cauchy_cdf: X, LOCATION, and SCALE must be of common size or scalars"); - endif - endif - - if (iscomplex (x) || iscomplex (location) || iscomplex (scale)) - error ("cauchy_cdf: X, LOCATION, and SCALE must not be complex"); - endif - - if (isa (x, "single") || isa (location, "single") || isa (scale, "single")); - cdf = NaN (size (x), "single"); - else - cdf = NaN (size (x)); - endif - - k = ! isinf (location) & (scale > 0) & (scale < Inf); - if (isscalar (location) && isscalar (scale)) - cdf = 0.5 + atan ((x - location) / scale) / pi; - else - cdf(k) = 0.5 + atan ((x(k) - location(k)) ./ scale(k)) / pi; - endif - -endfunction - - -%!shared x,y -%! x = [-1 0 0.5 1 2]; -%! y = 1/pi * atan ((x-1) / 2) + 1/2; -%!assert (cauchy_cdf (x, ones (1,5), 2*ones (1,5)), y) -%!assert (cauchy_cdf (x, 1, 2*ones (1,5)), y) -%!assert (cauchy_cdf (x, ones (1,5), 2), y) -%!assert (cauchy_cdf (x, [-Inf 1 NaN 1 Inf], 2), [NaN y(2) NaN y(4) NaN]) -%!assert (cauchy_cdf (x, 1, 2*[0 1 NaN 1 Inf]), [NaN y(2) NaN y(4) NaN]) -%!assert (cauchy_cdf ([x(1:2) NaN x(4:5)], 1, 2), [y(1:2) NaN y(4:5)]) - -## Test class of input preserved -%!assert (cauchy_cdf ([x, NaN], 1, 2), [y, NaN]) -%!assert (cauchy_cdf (single ([x, NaN]), 1, 2), single ([y, NaN]), eps ("single")) -%!assert (cauchy_cdf ([x, NaN], single (1), 2), single ([y, NaN]), eps ("single")) -%!assert (cauchy_cdf ([x, NaN], 1, single (2)), single ([y, NaN]), eps ("single")) - -## Test input validation -%!error cauchy_cdf () -%!error cauchy_cdf (1,2) -%!error cauchy_cdf (1,2,3,4) -%!error cauchy_cdf (ones (3), ones (2), ones (2)) -%!error cauchy_cdf (ones (2), ones (3), ones (2)) -%!error cauchy_cdf (ones (2), ones (2), ones (3)) -%!error cauchy_cdf (i, 2, 2) -%!error cauchy_cdf (2, i, 2) -%!error cauchy_cdf (2, 2, i)
--- a/scripts/statistics/distributions/cauchy_inv.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,98 +0,0 @@ -## Copyright (C) 2012 Rik Wehbring -## Copyright (C) 1995-2016 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} cauchy_inv (@var{x}) -## @deftypefnx {} {} cauchy_inv (@var{x}, @var{location}, @var{scale}) -## For each element of @var{x}, compute the quantile (the inverse of the CDF) -## at @var{x} of the Cauchy distribution with location parameter -## @var{location} and scale parameter @var{scale}. -## -## Default values are @var{location} = 0, @var{scale} = 1. -## @end deftypefn - -## Author: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: Quantile function of the Cauchy distribution - -function inv = cauchy_inv (x, location = 0, scale = 1) - - if (nargin != 1 && nargin != 3) - print_usage (); - endif - - if (! isscalar (location) || ! isscalar (scale)) - [retval, x, location, scale] = common_size (x, location, scale); - if (retval > 0) - error ("cauchy_inv: X, LOCATION, and SCALE must be of common size or scalars"); - endif - endif - - if (iscomplex (x) || iscomplex (location) || iscomplex (scale)) - error ("cauchy_inv: X, LOCATION, and SCALE must not be complex"); - endif - - if (isa (x, "single") || isa (location, "single") || isa (scale, "single")) - inv = NaN (size (x), "single"); - else - inv = NaN (size (x)); - endif - - ok = ! isinf (location) & (scale > 0) & (scale < Inf); - - k = (x == 0) & ok; - inv(k) = -Inf; - - k = (x == 1) & ok; - inv(k) = Inf; - - k = (x > 0) & (x < 1) & ok; - if (isscalar (location) && isscalar (scale)) - inv(k) = location - scale * cot (pi * x(k)); - else - inv(k) = location(k) - scale(k) .* cot (pi * x(k)); - endif - -endfunction - - -%!shared x -%! x = [-1 0 0.5 1 2]; -%!assert (cauchy_inv (x, ones (1,5), 2*ones (1,5)), [NaN -Inf 1 Inf NaN], eps) -%!assert (cauchy_inv (x, 1, 2*ones (1,5)), [NaN -Inf 1 Inf NaN], eps) -%!assert (cauchy_inv (x, ones (1,5), 2), [NaN -Inf 1 Inf NaN], eps) -%!assert (cauchy_inv (x, [1 -Inf NaN Inf 1], 2), [NaN NaN NaN NaN NaN]) -%!assert (cauchy_inv (x, 1, 2*[1 0 NaN Inf 1]), [NaN NaN NaN NaN NaN]) -%!assert (cauchy_inv ([x(1:2) NaN x(4:5)], 1, 2), [NaN -Inf NaN Inf NaN]) - -## Test class of input preserved -%!assert (cauchy_inv ([x, NaN], 1, 2), [NaN -Inf 1 Inf NaN NaN], eps) -%!assert (cauchy_inv (single ([x, NaN]), 1, 2), single ([NaN -Inf 1 Inf NaN NaN]), eps ("single")) -%!assert (cauchy_inv ([x, NaN], single (1), 2), single ([NaN -Inf 1 Inf NaN NaN]), eps ("single")) -%!assert (cauchy_inv ([x, NaN], 1, single (2)), single ([NaN -Inf 1 Inf NaN NaN]), eps ("single")) - -## Test input validation -%!error cauchy_inv () -%!error cauchy_inv (1,2) -%!error cauchy_inv (1,2,3,4) -%!error cauchy_inv (ones (3), ones (2), ones (2)) -%!error cauchy_inv (ones (2), ones (3), ones (2)) -%!error cauchy_inv (ones (2), ones (2), ones (3)) -%!error cauchy_inv (i, 2, 2) -%!error cauchy_inv (2, i, 2) -%!error cauchy_inv (2, 2, i)
--- a/scripts/statistics/distributions/cauchy_pdf.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,97 +0,0 @@ -## Copyright (C) 2012 Rik Wehbring -## Copyright (C) 1995-2016 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} cauchy_pdf (@var{x}) -## @deftypefnx {} {} cauchy_pdf (@var{x}, @var{location}, @var{scale}) -## For each element of @var{x}, compute the probability density function (PDF) -## at @var{x} of the Cauchy distribution with location parameter -## @var{location} and scale parameter @var{scale} > 0. -## -## Default values are @var{location} = 0, @var{scale} = 1. -## @end deftypefn - -## Author: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: PDF of the Cauchy distribution - -function pdf = cauchy_pdf (x, location = 0, scale = 1) - - if (nargin != 1 && nargin != 3) - print_usage (); - endif - - if (! isscalar (location) || ! isscalar (scale)) - [retval, x, location, scale] = common_size (x, location, scale); - if (retval > 0) - error ("cauchy_pdf: X, LOCATION, and SCALE must be of common size or scalars"); - endif - endif - - if (iscomplex (x) || iscomplex (location) || iscomplex (scale)) - error ("cauchy_pdf: X, LOCATION, and SCALE must not be complex"); - endif - - if (isa (x, "single") || isa (location, "single") || isa (scale, "single")) - pdf = NaN (size (x), "single"); - else - pdf = NaN (size (x)); - endif - - k = ! isinf (location) & (scale > 0) & (scale < Inf); - if (isscalar (location) && isscalar (scale)) - pdf = ((1 ./ (1 + ((x - location) / scale) .^ 2)) - / pi / scale); - else - pdf(k) = ((1 ./ (1 + ((x(k) - location(k)) ./ scale(k)) .^ 2)) - / pi ./ scale(k)); - endif - -endfunction - - -%!shared x,y -%! x = [-1 0 0.5 1 2]; -%! y = 1/pi * ( 2 ./ ((x-1).^2 + 2^2) ); -%!assert (cauchy_pdf (x, ones (1,5), 2*ones (1,5)), y) -%!assert (cauchy_pdf (x, 1, 2*ones (1,5)), y) -%!assert (cauchy_pdf (x, ones (1,5), 2), y) -%!assert (cauchy_pdf (x, [-Inf 1 NaN 1 Inf], 2), [NaN y(2) NaN y(4) NaN]) -%!assert (cauchy_pdf (x, 1, 2*[0 1 NaN 1 Inf]), [NaN y(2) NaN y(4) NaN]) -%!assert (cauchy_pdf ([x, NaN], 1, 2), [y, NaN]) - -## Test class of input preserved -%!assert (cauchy_pdf (single ([x, NaN]), 1, 2), single ([y, NaN]), eps ("single")) -%!assert (cauchy_pdf ([x, NaN], single (1), 2), single ([y, NaN]), eps ("single")) -%!assert (cauchy_pdf ([x, NaN], 1, single (2)), single ([y, NaN]), eps ("single")) - -## Cauchy (0,1) == Student's T distribution with 1 DOF -%!test -%! x = rand (10, 1); -%! assert (cauchy_pdf (x, 0, 1), tpdf (x, 1), eps); - -## Test input validation -%!error cauchy_pdf () -%!error cauchy_pdf (1,2) -%!error cauchy_pdf (1,2,3,4) -%!error cauchy_pdf (ones (3), ones (2), ones (2)) -%!error cauchy_pdf (ones (2), ones (3), ones (2)) -%!error cauchy_pdf (ones (2), ones (2), ones (3)) -%!error cauchy_pdf (i, 2, 2) -%!error cauchy_pdf (2, i, 2) -%!error cauchy_pdf (2, 2, i)
--- a/scripts/statistics/distributions/cauchy_rnd.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,132 +0,0 @@ -## Copyright (C) 2012 Rik Wehbring -## Copyright (C) 1995-2016 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} cauchy_rnd (@var{location}, @var{scale}) -## @deftypefnx {} {} cauchy_rnd (@var{location}, @var{scale}, @var{r}) -## @deftypefnx {} {} cauchy_rnd (@var{location}, @var{scale}, @var{r}, @var{c}, @dots{}) -## @deftypefnx {} {} cauchy_rnd (@var{location}, @var{scale}, [@var{sz}]) -## Return a matrix of random samples from the Cauchy distribution with -## parameters @var{location} and @var{scale}. -## -## When called with a single size argument, return a square matrix with -## the dimension specified. When called with more than one scalar argument the -## first two arguments are taken as the number of rows and columns and any -## further arguments specify additional matrix dimensions. The size may also -## be specified with a vector of dimensions @var{sz}. -## -## If no size arguments are given then the result matrix is the common size of -## @var{location} and @var{scale}. -## @end deftypefn - -## Author: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: Random deviates from the Cauchy distribution - -function rnd = cauchy_rnd (location, scale, varargin) - - if (nargin < 2) - print_usage (); - endif - - if (! isscalar (location) || ! isscalar (scale)) - [retval, location, scale] = common_size (location, scale); - if (retval > 0) - error ("cauchy_rnd: LOCATION and SCALE must be of common size or scalars"); - endif - endif - - if (iscomplex (location) || iscomplex (scale)) - error ("cauchy_rnd: LOCATION and SCALE must not be complex"); - endif - - if (nargin == 2) - sz = size (location); - elseif (nargin == 3) - if (isscalar (varargin{1}) && varargin{1} >= 0) - sz = [varargin{1}, varargin{1}]; - elseif (isrow (varargin{1}) && all (varargin{1} >= 0)) - sz = varargin{1}; - else - error ("cauchy_rnd: dimension vector must be row vector of non-negative integers"); - endif - elseif (nargin > 3) - if (any (cellfun (@(x) (! isscalar (x) || x < 0), varargin))) - error ("cauchy_rnd: dimensions must be non-negative integers"); - endif - sz = [varargin{:}]; - endif - - if (! isscalar (location) && ! isequal (size (location), sz)) - error ("cauchy_rnd: LOCATION and SCALE must be scalar or of size SZ"); - endif - - if (isa (location, "single") || isa (scale, "single")) - cls = "single"; - else - cls = "double"; - endif - - if (isscalar (location) && isscalar (scale)) - if (! isinf (location) && (scale > 0) && (scale < Inf)) - rnd = location - cot (pi * rand (sz, cls)) * scale; - else - rnd = NaN (sz, cls); - endif - else - rnd = NaN (sz, cls); - - k = ! isinf (location) & (scale > 0) & (scale < Inf); - rnd(k) = location(k)(:) ... - - cot (pi * rand (sum (k(:)), 1, cls)) .* scale(k)(:); - endif - -endfunction - - -%!assert (size (cauchy_rnd (1,2)), [1, 1]) -%!assert (size (cauchy_rnd (ones (2,1), 2)), [2, 1]) -%!assert (size (cauchy_rnd (ones (2,2), 2)), [2, 2]) -%!assert (size (cauchy_rnd (1, 2*ones (2,1))), [2, 1]) -%!assert (size (cauchy_rnd (1, 2*ones (2,2))), [2, 2]) -%!assert (size (cauchy_rnd (1, 2, 3)), [3, 3]) -%!assert (size (cauchy_rnd (1, 2, [4 1])), [4, 1]) -%!assert (size (cauchy_rnd (1, 2, 4, 1)), [4, 1]) - -## Test class of input preserved -%!assert (class (cauchy_rnd (1, 2)), "double") -%!assert (class (cauchy_rnd (single (1), 2)), "single") -%!assert (class (cauchy_rnd (single ([1 1]), 2)), "single") -%!assert (class (cauchy_rnd (1, single (2))), "single") -%!assert (class (cauchy_rnd (1, single ([2 2]))), "single") - -## Test input validation -%!error cauchy_rnd () -%!error cauchy_rnd (1) -%!error cauchy_rnd (ones (3), ones (2)) -%!error cauchy_rnd (ones (2), ones (3)) -%!error cauchy_rnd (i, 2) -%!error cauchy_rnd (2, i) -%!error cauchy_rnd (1,2, -1) -%!error cauchy_rnd (1,2, ones (2)) -%!error cauchy_rnd (1,2, [2 -1 2]) -%!error cauchy_rnd (1,2, 1, ones (2)) -%!error cauchy_rnd (1,2, 1, -1) -%!error cauchy_rnd (ones (2,2), 2, 3) -%!error cauchy_rnd (ones (2,2), 2, [3, 2]) -%!error cauchy_rnd (ones (2,2), 2, 2, 3)
--- a/scripts/statistics/distributions/chi2cdf.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,72 +0,0 @@ -## Copyright (C) 2012 Rik Wehbring -## Copyright (C) 1995-2016 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} chi2cdf (@var{x}, @var{n}) -## For each element of @var{x}, compute the cumulative distribution function -## (CDF) at @var{x} of the chi-square distribution with @var{n} degrees of -## freedom. -## @end deftypefn - -## Author: TT <Teresa.Twaroch@ci.tuwien.ac.at> -## Description: CDF of the chi-square distribution - -function cdf = chi2cdf (x, n) - - if (nargin != 2) - print_usage (); - endif - - if (! isscalar (n)) - [retval, x, n] = common_size (x, n); - if (retval > 0) - error ("chi2cdf: X and N must be of common size or scalars"); - endif - endif - - if (iscomplex (x) || iscomplex (n)) - error ("chi2cdf: X and N must not be complex"); - endif - - cdf = gamcdf (x, n/2, 2); - -endfunction - - -%!shared x,y -%! x = [-1 0 0.5 1 2]; -%! y = [0, 1 - exp(-x(2:end)/2)]; -%!assert (chi2cdf (x, 2*ones (1,5)), y, eps) -%!assert (chi2cdf (x, 2), y, eps) -%!assert (chi2cdf (x, 2*[1 0 NaN 1 1]), [y(1) NaN NaN y(4:5)], eps) -%!assert (chi2cdf ([x(1:2) NaN x(4:5)], 2), [y(1:2) NaN y(4:5)], eps) - -## Test class of input preserved -%!assert (chi2cdf ([x, NaN], 2), [y, NaN], eps) -%!assert (chi2cdf (single ([x, NaN]), 2), single ([y, NaN]), eps ("single")) -%!assert (chi2cdf ([x, NaN], single (2)), single ([y, NaN]), eps ("single")) - -## Test input validation -%!error chi2cdf () -%!error chi2cdf (1) -%!error chi2cdf (1,2,3) -%!error chi2cdf (ones (3), ones (2)) -%!error chi2cdf (ones (2), ones (3)) -%!error chi2cdf (i, 2) -%!error chi2cdf (2, i)
--- a/scripts/statistics/distributions/chi2inv.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,70 +0,0 @@ -## Copyright (C) 2012 Rik Wehbring -## Copyright (C) 1995-2016 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} chi2inv (@var{x}, @var{n}) -## For each element of @var{x}, compute the quantile (the inverse of the CDF) -## at @var{x} of the chi-square distribution with @var{n} degrees of freedom. -## @end deftypefn - -## Author: TT <Teresa.Twaroch@ci.tuwien.ac.at> -## Description: Quantile function of the chi-square distribution - -function inv = chi2inv (x, n) - - if (nargin != 2) - print_usage (); - endif - - if (! isscalar (n)) - [retval, x, n] = common_size (x, n); - if (retval > 0) - error ("chi2inv: X and N must be of common size or scalars"); - endif - endif - - if (iscomplex (x) || iscomplex (n)) - error ("chi2inv: X and N must not be complex"); - endif - - inv = gaminv (x, n/2, 2); - -endfunction - - -%!shared x -%! x = [-1 0 0.3934693402873666 1 2]; -%!assert (chi2inv (x, 2*ones (1,5)), [NaN 0 1 Inf NaN], 5*eps) -%!assert (chi2inv (x, 2), [NaN 0 1 Inf NaN], 5*eps) -%!assert (chi2inv (x, 2*[0 1 NaN 1 1]), [NaN 0 NaN Inf NaN], 5*eps) -%!assert (chi2inv ([x(1:2) NaN x(4:5)], 2), [NaN 0 NaN Inf NaN], 5*eps) - -## Test class of input preserved -%!assert (chi2inv ([x, NaN], 2), [NaN 0 1 Inf NaN NaN], 5*eps) -%!assert (chi2inv (single ([x, NaN]), 2), single ([NaN 0 1 Inf NaN NaN]), 5*eps ("single")) -%!assert (chi2inv ([x, NaN], single (2)), single ([NaN 0 1 Inf NaN NaN]), 5*eps ("single")) - -## Test input validation -%!error chi2inv () -%!error chi2inv (1) -%!error chi2inv (1,2,3) -%!error chi2inv (ones (3), ones (2)) -%!error chi2inv (ones (2), ones (3)) -%!error chi2inv (i, 2) -%!error chi2inv (2, i)
--- a/scripts/statistics/distributions/chi2pdf.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,70 +0,0 @@ -## Copyright (C) 2012 Rik Wehbring -## Copyright (C) 1995-2016 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} chi2pdf (@var{x}, @var{n}) -## For each element of @var{x}, compute the probability density function (PDF) -## at @var{x} of the chi-square distribution with @var{n} degrees of freedom. -## @end deftypefn - -## Author: TT <Teresa.Twaroch@ci.tuwien.ac.at> -## Description: PDF of the chi-square distribution - -function pdf = chi2pdf (x, n) - - if (nargin != 2) - print_usage (); - endif - - if (! isscalar (n)) - [retval, x, n] = common_size (x, n); - if (retval > 0) - error ("chi2pdf: X and N must be of common size or scalars"); - endif - endif - - if (iscomplex (x) || iscomplex (n)) - error ("chi2pdf: X and N must not be complex"); - endif - - pdf = gampdf (x, n/2, 2); - -endfunction - - -%!shared x,y -%! x = [-1 0 0.5 1 Inf]; -%! y = [0, 1/2 * exp(-x(2:5)/2)]; -%!assert (chi2pdf (x, 2*ones (1,5)), y) -%!assert (chi2pdf (x, 2), y) -%!assert (chi2pdf (x, 2*[1 0 NaN 1 1]), [y(1) NaN NaN y(4:5)]) -%!assert (chi2pdf ([x, NaN], 2), [y, NaN]) - -## Test class of input preserved -%!assert (chi2pdf (single ([x, NaN]), 2), single ([y, NaN])) -%!assert (chi2pdf ([x, NaN], single (2)), single ([y, NaN])) - -## Test input validation -%!error chi2pdf () -%!error chi2pdf (1) -%!error chi2pdf (1,2,3) -%!error chi2pdf (ones (3), ones (2)) -%!error chi2pdf (ones (2), ones (3)) -%!error chi2pdf (i, 2) -%!error chi2pdf (2, i)
--- a/scripts/statistics/distributions/chi2rnd.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,116 +0,0 @@ -## Copyright (C) 2012 Rik Wehbring -## Copyright (C) 1995-2016 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} chi2rnd (@var{n}) -## @deftypefnx {} {} chi2rnd (@var{n}, @var{r}) -## @deftypefnx {} {} chi2rnd (@var{n}, @var{r}, @var{c}, @dots{}) -## @deftypefnx {} {} chi2rnd (@var{n}, [@var{sz}]) -## Return a matrix of random samples from the chi-square distribution with -## @var{n} degrees of freedom. -## -## When called with a single size argument, return a square matrix with -## the dimension specified. When called with more than one scalar argument the -## first two arguments are taken as the number of rows and columns and any -## further arguments specify additional matrix dimensions. The size may also -## be specified with a vector of dimensions @var{sz}. -## -## If no size arguments are given then the result matrix is the size of -## @var{n}. -## @end deftypefn - -## Author: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: Random deviates from the chi-square distribution - -function rnd = chi2rnd (n, varargin) - - if (nargin < 1) - print_usage (); - endif - - if (nargin == 1) - sz = size (n); - elseif (nargin == 2) - if (isscalar (varargin{1}) && varargin{1} >= 0) - sz = [varargin{1}, varargin{1}]; - elseif (isrow (varargin{1}) && all (varargin{1} >= 0)) - sz = varargin{1}; - else - error ("chi2rnd: dimension vector must be row vector of non-negative integers"); - endif - elseif (nargin > 2) - if (any (cellfun (@(x) (! isscalar (x) || x < 0), varargin))) - error ("chi2rnd: dimensions must be non-negative integers"); - endif - sz = [varargin{:}]; - endif - - if (! isscalar (n) && ! isequal (size (n), sz)) - error ("chi2rnd: N must be scalar or of size SZ"); - endif - - if (iscomplex (n)) - error ("chi2rnd: N must not be complex"); - endif - - if (isa (n, "single")) - cls = "single"; - else - cls = "double"; - endif - - if (isscalar (n)) - if ((n > 0) && (n < Inf)) - rnd = 2 * randg (n/2, sz, cls); - else - rnd = NaN (sz, cls); - endif - else - rnd = NaN (sz, cls); - - k = (n > 0) | (n < Inf); - rnd(k) = 2 * randg (n(k)/2, cls); - endif - -endfunction - - -%!assert (size (chi2rnd (2)), [1, 1]) -%!assert (size (chi2rnd (ones (2,1))), [2, 1]) -%!assert (size (chi2rnd (ones (2,2))), [2, 2]) -%!assert (size (chi2rnd (1, 3)), [3, 3]) -%!assert (size (chi2rnd (1, [4 1])), [4, 1]) -%!assert (size (chi2rnd (1, 4, 1)), [4, 1]) - -## Test class of input preserved -%!assert (class (chi2rnd (2)), "double") -%!assert (class (chi2rnd (single (2))), "single") -%!assert (class (chi2rnd (single ([2 2]))), "single") - -## Test input validation -%!error chi2rnd () -%!error chi2rnd (ones (3), ones (2)) -%!error chi2rnd (ones (2), ones (3)) -%!error chi2rnd (i) -%!error chi2rnd (1, -1) -%!error chi2rnd (1, ones (2)) -%!error chi2rnd (1, [2 -1 2]) -%!error chi2rnd (ones (2,2), 3) -%!error chi2rnd (ones (2,2), [3, 2]) -%!error chi2rnd (ones (2,2), 2, 3)
--- a/scripts/statistics/distributions/discrete_cdf.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,80 +0,0 @@ -## Copyright (C) 2012 Rik Wehbring -## Copyright (C) 2010-2016 David Bateman -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} discrete_cdf (@var{x}, @var{v}, @var{p}) -## For each element of @var{x}, compute the cumulative distribution function -## (CDF) at @var{x} of a univariate discrete distribution which assumes the -## values in @var{v} with probabilities @var{p}. -## @end deftypefn - -function cdf = discrete_cdf (x, v, p) - - if (nargin != 3) - print_usage (); - endif - - if (! isvector (v)) - error ("discrete_cdf: V must be a vector"); - elseif (any (isnan (v))) - error ("discrete_cdf: V must not have any NaN elements"); - elseif (! isvector (p) || (length (p) != length (v))) - error ("discrete_cdf: P must be a vector with length (V) elements"); - elseif (! (all (p >= 0) && any (p))) - error ("discrete_cdf: P must be a nonzero, non-negative vector"); - endif - - p = p(:) / sum (p); # Reshape and normalize probability vector - - if (isa (x, "single") || isa (v, "single") || isa (p, "single")); - cdf = NaN (size (x), "single"); - else - cdf = NaN (size (x)); - endif - - k = ! isnan (x); - [vs, vi] = sort (v); - cdf(k) = [0 ; cumsum(p(vi))](lookup (vs, x(k)) + 1); - -endfunction - - -%!shared x,v,p,y -%! x = [-1 0.1 1.1 1.9 3]; -%! v = 0.1:0.2:1.9; -%! p = 1/length(v) * ones (1, length(v)); -%! y = [0 0.1 0.6 1 1]; -%!assert (discrete_cdf ([x, NaN], v, p), [y, NaN], eps) - -## Test class of input preserved -%!assert (discrete_cdf (single ([x, NaN]), v, p), single ([y, NaN]), 2*eps ("single")) -%!assert (discrete_cdf ([x, NaN], single (v), p), single ([y, NaN]), 2*eps ("single")) -%!assert (discrete_cdf ([x, NaN], v, single (p)), single ([y, NaN]), 2*eps ("single")) - -## Test input validation -%!error discrete_cdf () -%!error discrete_cdf (1) -%!error discrete_cdf (1,2) -%!error discrete_cdf (1,2,3,4) -%!error discrete_cdf (1, ones (2), ones (2,1)) -%!error discrete_cdf (1, [1 ; NaN], ones (2,1)) -%!error discrete_cdf (1, ones (2,1), ones (1,1)) -%!error discrete_cdf (1, ones (2,1), [1 -1]) -%!error discrete_cdf (1, ones (2,1), [1 NaN]) -%!error discrete_cdf (1, ones (2,1), [0 0])
--- a/scripts/statistics/distributions/discrete_inv.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,94 +0,0 @@ -## Copyright (C) 2012 Rik Wehbring -## Copyright (C) 1996-2016 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} discrete_inv (@var{x}, @var{v}, @var{p}) -## For each element of @var{x}, compute the quantile (the inverse of the CDF) -## at @var{x} of the univariate distribution which assumes the values in -## @var{v} with probabilities @var{p}. -## @end deftypefn - -## Author: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: Quantile function of a discrete distribution - -function inv = discrete_inv (x, v, p) - - if (nargin != 3) - print_usage (); - endif - - if (! isvector (v)) - error ("discrete_inv: V must be a vector"); - elseif (! isvector (p) || (length (p) != length (v))) - error ("discrete_inv: P must be a vector with length (V) elements"); - elseif (any (isnan (p))) - error ("discrete_rnd: P must not have any NaN elements"); - elseif (! (all (p >= 0) && any (p))) - error ("discrete_inv: P must be a nonzero, non-negative vector"); - endif - - if (isa (x, "single") || isa (v, "single") || isa (p, "single")); - inv = NaN (size (x), "single"); - else - inv = NaN (size (x)); - endif - - ## FIXME: This isn't elegant. But cumsum and lookup together produce - ## different results when called with a single or a double. - if (isa (p, "single")); - p = double (p); - endif - - [v, idx] = sort (v); - p = cumsum (p(idx)(:)) / sum (p); # Reshape and normalize probability vector - - k = (x == 0); - inv(k) = v(1); - - k = (x == 1); - inv(k) = v(end); - - k = (x > 0) & (x < 1); - inv(k) = v(length (p) - lookup (sort (p, "descend"), x(k)) + 1); - -endfunction - - -%!shared x,v,p,y -%! x = [-1 0 0.1 0.5 1 2]; -%! v = 0.1:0.2:1.9; -%! p = 1/length(v) * ones (1, length(v)); -%! y = [NaN v(1) v(1) v(end/2) v(end) NaN]; -%!assert (discrete_inv ([x, NaN], v, p), [y, NaN], eps) - -## Test class of input preserved -%!assert (discrete_inv (single ([x, NaN]), v, p), single ([y, NaN]), eps ("single")) -%!assert (discrete_inv ([x, NaN], single (v), p), single ([y, NaN]), eps ("single")) -%!assert (discrete_inv ([x, NaN], v, single (p)), single ([y, NaN]), eps ("single")) - -## Test input validation -%!error discrete_inv () -%!error discrete_inv (1) -%!error discrete_inv (1,2) -%!error discrete_inv (1,2,3,4) -%!error discrete_inv (1, ones (2), ones (2,1)) -%!error discrete_inv (1, ones (2,1), ones (1,1)) -%!error discrete_inv (1, ones (2,1), [1 NaN]) -%!error discrete_inv (1, ones (2,1), [1 -1]) -%!error discrete_inv (1, ones (2,1), [0 0])
--- a/scripts/statistics/distributions/discrete_pdf.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,84 +0,0 @@ -## Copyright (C) 2012 Rik Wehbring -## Copyright (C) 1996-2016 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} discrete_pdf (@var{x}, @var{v}, @var{p}) -## For each element of @var{x}, compute the probability density function (PDF) -## at @var{x} of a univariate discrete distribution which assumes the values -## in @var{v} with probabilities @var{p}. -## @end deftypefn - -## Author: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: PDF of a discrete distribution - -function pdf = discrete_pdf (x, v, p) - - if (nargin != 3) - print_usage (); - endif - - if (! isvector (v)) - error ("discrete_pdf: V must be a vector"); - elseif (any (isnan (v))) - error ("discrete_pdf: V must not have any NaN elements"); - elseif (! isvector (p) || (length (p) != length (v))) - error ("discrete_pdf: P must be a vector with length (V) elements"); - elseif (! (all (p >= 0) && any (p))) - error ("discrete_pdf: P must be a nonzero, non-negative vector"); - endif - - ## Reshape and normalize probability vector. Values not in table get 0 prob. - p = [0 ; p(:)/sum(p)]; - - if (isa (x, "single") || isa (v, "single") || isa (p, "single")) - pdf = NaN (size (x), "single"); - else - pdf = NaN (size (x)); - endif - - k = ! isnan (x); - [vs, vi] = sort (v(:)); - pdf(k) = p([0 ; vi](lookup (vs, x(k), 'm') + 1) + 1); - -endfunction - - -%!shared x,v,p,y -%! x = [-1 0.1 1.1 1.9 3]; -%! v = 0.1:0.2:1.9; -%! p = 1/length (v) * ones (1, length (v)); -%! y = [0 0.1 0.1 0.1 0]; -%!assert (discrete_pdf ([x, NaN], v, p), [y, NaN], 5*eps) - -## Test class of input preserved -%!assert (discrete_pdf (single ([x, NaN]), v, p), single ([y, NaN]), 5*eps ("single")) -%!assert (discrete_pdf ([x, NaN], single (v), p), single ([y, NaN]), 5*eps ("single")) -%!assert (discrete_pdf ([x, NaN], v, single (p)), single ([y, NaN]), 5*eps ("single")) - -## Test input validation -%!error discrete_pdf () -%!error discrete_pdf (1) -%!error discrete_pdf (1,2) -%!error discrete_pdf (1,2,3,4) -%!error discrete_pdf (1, ones (2), ones (2,1)) -%!error discrete_pdf (1, [1 ; NaN], ones (2,1)) -%!error discrete_pdf (1, ones (2,1), ones (1,1)) -%!error discrete_pdf (1, ones (2,1), [1 -1]) -%!error discrete_pdf (1, ones (2,1), [1 NaN]) -%!error discrete_pdf (1, ones (2,1), [0 0])
--- a/scripts/statistics/distributions/discrete_rnd.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,103 +0,0 @@ -## Copyright (C) 2012 Rik Wehbring -## Copyright (C) 1996-2016 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} discrete_rnd (@var{v}, @var{p}) -## @deftypefnx {} {} discrete_rnd (@var{v}, @var{p}, @var{r}) -## @deftypefnx {} {} discrete_rnd (@var{v}, @var{p}, @var{r}, @var{c}, @dots{}) -## @deftypefnx {} {} discrete_rnd (@var{v}, @var{p}, [@var{sz}]) -## Return a matrix of random samples from the univariate distribution which -## assumes the values in @var{v} with probabilities @var{p}. -## -## When called with a single size argument, return a square matrix with -## the dimension specified. When called with more than one scalar argument the -## first two arguments are taken as the number of rows and columns and any -## further arguments specify additional matrix dimensions. The size may also -## be specified with a vector of dimensions @var{sz}. -## -## If no size arguments are given then the result matrix is the common size of -## @var{v} and @var{p}. -## @end deftypefn - -## Author: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: Random deviates from a discrete distribution - -function rnd = discrete_rnd (v, p, varargin) - - if (nargin < 2) - print_usage (); - endif - - if (! isvector (v)) - error ("discrete_rnd: V must be a vector"); - elseif (! isvector (p) || (length (p) != length (v))) - error ("discrete_rnd: P must be a vector with length (V) elements"); - elseif (any (isnan (p))) - error ("discrete_rnd: P must not have any NaN elements"); - elseif (! (all (p >= 0) && any (p))) - error ("discrete_rnd: P must be a nonzero, non-negative vector"); - endif - - if (nargin == 2) - sz = size (v); - elseif (nargin == 3) - if (isscalar (varargin{1}) && varargin{1} >= 0) - sz = [varargin{1}, varargin{1}]; - elseif (isrow (varargin{1}) && all (varargin{1} >= 0)) - sz = varargin{1}; - else - error ("discrete_rnd: dimension vector must be row vector of non-negative integers"); - endif - elseif (nargin > 3) - if (any (cellfun (@(x) (! isscalar (x) || x < 0), varargin))) - error ("discrete_rnd: dimensions must be non-negative integers"); - endif - sz = [varargin{:}]; - endif - - rnd = v(lookup (cumsum (p(1:end-1)) / sum (p), rand (sz)) + 1); - rnd = reshape (rnd, sz); - -endfunction - - -%!assert (size (discrete_rnd (1:2, 1:2, 3)), [3, 3]) -%!assert (size (discrete_rnd (1:2, 1:2, [4 1])), [4, 1]) -%!assert (size (discrete_rnd (1:2, 1:2, 4, 1)), [4, 1]) - -## Test class of input preserved -%!assert (class (discrete_rnd (1:2, 1:2)), "double") -%!assert (class (discrete_rnd (single (1:2), 1:2)), "single") -## FIXME: Maybe this should work, maybe it shouldn't. -#%!assert(class (discrete_rnd (1:2, single(1:2))), "single") - -## Test input validation -%!error discrete_rnd () -%!error discrete_rnd (1) -%!error discrete_rnd (1:2,1:2, -1) -%!error discrete_rnd (1:2,1:2, ones (2)) -%!error discrete_rnd (1:2,1:2, [2 -1 2]) -%!error discrete_rnd (1:2,1:2, 1, ones (2)) -%!error discrete_rnd (1:2,1:2, 1, -1) -## test v,p verification -%!error discrete_rnd (1, ones (2), ones (2,1)) -%!error discrete_rnd (1, ones (2,1), ones (1,1)) -%!error discrete_rnd (1, ones (2,1), [1 -1]) -%!error discrete_rnd (1, ones (2,1), [1 NaN]) -%!error discrete_rnd (1, ones (2,1), [0 0])
--- a/scripts/statistics/distributions/empirical_cdf.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,61 +0,0 @@ -## Copyright (C) 2012 Rik Wehbring -## Copyright (C) 1996-2016 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} empirical_cdf (@var{x}, @var{data}) -## For each element of @var{x}, compute the cumulative distribution function -## (CDF) at @var{x} of the empirical distribution obtained from -## the univariate sample @var{data}. -## @end deftypefn - -## Author: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: CDF of the empirical distribution - -function cdf = empirical_cdf (x, data) - - if (nargin != 2) - print_usage (); - endif - - if (! isvector (data)) - error ("empirical_cdf: DATA must be a vector"); - endif - - cdf = discrete_cdf (x, data, ones (size (data))); - -endfunction - - -%!shared x,v,y -%! x = [-1 0.1 1.1 1.9 3]; -%! v = 0.1:0.2:1.9; -%! y = [0 0.1 0.6 1 1]; -%!assert (empirical_cdf (x, v), y, eps) -%!assert (empirical_cdf ([x(1) NaN x(3:5)], v), [0 NaN 0.6 1 1], eps) - -## Test class of input preserved -%!assert (empirical_cdf ([x, NaN], v), [y, NaN], eps) -%!assert (empirical_cdf (single ([x, NaN]), v), single ([y, NaN]), eps) -%!assert (empirical_cdf ([x, NaN], single (v)), single ([y, NaN]), eps) - -## Test input validation -%!error empirical_cdf () -%!error empirical_cdf (1) -%!error empirical_cdf (1,2,3) -%!error empirical_cdf (1, ones (2))
--- a/scripts/statistics/distributions/empirical_inv.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,60 +0,0 @@ -## Copyright (C) 2012 Rik Wehbring -## Copyright (C) 1996-2016 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} empirical_inv (@var{x}, @var{data}) -## For each element of @var{x}, compute the quantile (the inverse of the CDF) -## at @var{x} of the empirical distribution obtained from the -## univariate sample @var{data}. -## @end deftypefn - -## Author: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: Quantile function of the empirical distribution - -function inv = empirical_inv (x, data) - - if (nargin != 2) - print_usage (); - endif - - if (! isvector (data)) - error ("empirical_inv: DATA must be a vector"); - endif - - inv = discrete_inv (x, data, ones (size (data))); - -endfunction - - -%!shared x,v,y -%! x = [-1 0 0.1 0.5 1 2]; -%! v = 0.1:0.2:1.9; -%! y = [NaN v(1) v(1) v(end/2) v(end) NaN]; -%!assert (empirical_inv (x, v), y, eps) - -## Test class of input preserved -%!assert (empirical_inv ([x, NaN], v), [y, NaN], eps) -%!assert (empirical_inv (single ([x, NaN]), v), single ([y, NaN]), eps) -%!assert (empirical_inv ([x, NaN], single (v)), single ([y, NaN]), eps) - -## Test input validation -%!error empirical_inv () -%!error empirical_inv (1) -%!error empirical_inv (1,2,3) -%!error empirical_inv (1, ones (2))
--- a/scripts/statistics/distributions/empirical_pdf.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,71 +0,0 @@ -## Copyright (C) 2012 Rik Wehbring -## Copyright (C) 1996-2016 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} empirical_pdf (@var{x}, @var{data}) -## For each element of @var{x}, compute the probability density function (PDF) -## at @var{x} of the empirical distribution obtained from the -## univariate sample @var{data}. -## @end deftypefn - -## Author: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: PDF of the empirical distribution - -function pdf = empirical_pdf (x, data) - - if (nargin != 2) - print_usage (); - endif - - if (! isvector (data)) - error ("empirical_pdf: DATA must be a vector"); - endif - - uniq_vals = unique (data); - if (numel (data) != numel (uniq_vals)) - ## Handle ties, multiple elements with same value - p = histc (data, uniq_vals); - data = uniq_vals; - else - p = ones (size (data)); - endif - - pdf = discrete_pdf (x, data, p); - -endfunction - - -%!shared x,v,y -%! x = [-1 0.1 1.1 1.9 3]; -%! v = 0.1:0.2:1.9; -%! y = [0 0.1 0.1 0.1 0]; -%!assert (empirical_pdf (x, v), y) - -## Test class of input preserved -%!assert (empirical_pdf (single (x), v), single (y)) -%!assert (empirical_pdf (x, single (v)), single (y)) - -## Test distribution with ties -%!assert (empirical_pdf (2, [1 2 3 2]), 0.5) - -## Test input validation -%!error empirical_pdf () -%!error empirical_pdf (1) -%!error empirical_pdf (1,2,3) -%!error empirical_inv (1, ones (2))
--- a/scripts/statistics/distributions/empirical_rnd.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,67 +0,0 @@ -## Copyright (C) 2012 Rik Wehbring -## Copyright (C) 1996-2016 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} empirical_rnd (@var{data}) -## @deftypefnx {} {} empirical_rnd (@var{data}, @var{r}) -## @deftypefnx {} {} empirical_rnd (@var{data}, @var{r}, @var{c}, @dots{}) -## @deftypefnx {} {} empirical_rnd (@var{data}, [@var{sz}]) -## Return a matrix of random samples from the empirical distribution obtained -## from the univariate sample @var{data}. -## -## When called with a single size argument, return a square matrix with -## the dimension specified. When called with more than one scalar argument the -## first two arguments are taken as the number of rows and columns and any -## further arguments specify additional matrix dimensions. The size may also -## be specified with a vector of dimensions @var{sz}. -## -## If no size arguments are given then the result matrix is a random ordering -## of the sample @var{data}. -## @end deftypefn - -## Author: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: Bootstrap samples from the empirical distribution - -function rnd = empirical_rnd (data, varargin) - - if (nargin < 1) - print_usage (); - endif - - if (! isvector (data)) - error ("empirical_rnd: DATA must be a vector"); - endif - - rnd = discrete_rnd (data, ones (size (data)), varargin{:}); - -endfunction - - -%!assert (size (empirical_rnd (ones (3, 1))), [3, 1]) -%!assert (size (empirical_rnd (1:2, [4 1])), [4, 1]) -%!assert (size (empirical_rnd (1:2, 4, 1)), [4, 1]) - -## Test class of input preserved -%!assert (class (empirical_rnd (1:2, 1)), "double") -%!assert (class (empirical_rnd (single (1:2), 1)), "single") - -## Test input validation -%!error empirical_rnd () -%!error empirical_rnd (ones (2), 1) -%!error empirical_rnd (ones (2), 1, 1)
--- a/scripts/statistics/distributions/expcdf.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,89 +0,0 @@ -## Copyright (C) 2012 Rik Wehbring -## Copyright (C) 1995-2016 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} expcdf (@var{x}, @var{lambda}) -## For each element of @var{x}, compute the cumulative distribution function -## (CDF) at @var{x} of the exponential distribution with mean @var{lambda}. -## -## The arguments can be of common size or scalars. -## @end deftypefn - -## Author: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: CDF of the exponential distribution - -function cdf = expcdf (x, lambda) - - if (nargin != 2) - print_usage (); - endif - - if (! isscalar (lambda)) - [retval, x, lambda] = common_size (x, lambda); - if (retval > 0) - error ("expcdf: X and LAMBDA must be of common size or scalars"); - endif - endif - - if (iscomplex (x) || iscomplex (lambda)) - error ("expcdf: X and LAMBDA must not be complex"); - endif - - if (isa (x, "single") || isa (lambda, "single")) - cdf = zeros (size (x), "single"); - else - cdf = zeros (size (x)); - endif - - k = isnan (x) | !(lambda > 0); - cdf(k) = NaN; - - k = (x == Inf) & (lambda > 0); - cdf(k) = 1; - - k = (x > 0) & (x < Inf) & (lambda > 0); - if (isscalar (lambda)) - cdf(k) = 1 - exp (-x(k) / lambda); - else - cdf(k) = 1 - exp (-x(k) ./ lambda(k)); - endif - -endfunction - - -%!shared x,y -%! x = [-1 0 0.5 1 Inf]; -%! y = [0, 1 - exp(-x(2:end)/2)]; -%!assert (expcdf (x, 2*ones (1,5)), y) -%!assert (expcdf (x, 2), y) -%!assert (expcdf (x, 2*[1 0 NaN 1 1]), [y(1) NaN NaN y(4:5)]) - -## Test class of input preserved -%!assert (expcdf ([x, NaN], 2), [y, NaN]) -%!assert (expcdf (single ([x, NaN]), 2), single ([y, NaN])) -%!assert (expcdf ([x, NaN], single (2)), single ([y, NaN])) - -## Test input validation -%!error expcdf () -%!error expcdf (1) -%!error expcdf (1,2,3) -%!error expcdf (ones (3), ones (2)) -%!error expcdf (ones (2), ones (3)) -%!error expcdf (i, 2) -%!error expcdf (2, i)
--- a/scripts/statistics/distributions/expinv.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,94 +0,0 @@ -## Copyright (C) 2012 Rik Wehbring -## Copyright (C) 1995-2016 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} expinv (@var{x}, @var{lambda}) -## For each element of @var{x}, compute the quantile (the inverse of the CDF) -## at @var{x} of the exponential distribution with mean @var{lambda}. -## @end deftypefn - -## Author: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: Quantile function of the exponential distribution - -function inv = expinv (x, lambda) - - if (nargin != 2) - print_usage (); - endif - - if (! isscalar (lambda)) - [retval, x, lambda] = common_size (x, lambda); - if (retval > 0) - error ("expinv: X and LAMBDA must be of common size or scalars"); - endif - endif - - if (iscomplex (x) || iscomplex (lambda)) - error ("expinv: X and LAMBDA must not be complex"); - endif - - if (! isscalar (x)) - sz = size (x); - else - sz = size (lambda); - endif - - if (iscomplex (x) || iscomplex (lambda)) - error ("expinv: X and LAMBDA must not be complex"); - endif - - if (isa (x, "single") || isa (lambda, "single")) - inv = NaN (size (x), "single"); - else - inv = NaN (size (x)); - endif - - k = (x == 1) & (lambda > 0); - inv(k) = Inf; - - k = (x >= 0) & (x < 1) & (lambda > 0); - if (isscalar (lambda)) - inv(k) = - lambda * log (1 - x(k)); - else - inv(k) = - lambda(k) .* log (1 - x(k)); - endif - -endfunction - - -%!shared x -%! x = [-1 0 0.3934693402873666 1 2]; -%!assert (expinv (x, 2*ones (1,5)), [NaN 0 1 Inf NaN], eps) -%!assert (expinv (x, 2), [NaN 0 1 Inf NaN], eps) -%!assert (expinv (x, 2*[1 0 NaN 1 1]), [NaN NaN NaN Inf NaN], eps) -%!assert (expinv ([x(1:2) NaN x(4:5)], 2), [NaN 0 NaN Inf NaN], eps) - -## Test class of input preserved -%!assert (expinv ([x, NaN], 2), [NaN 0 1 Inf NaN NaN], eps) -%!assert (expinv (single ([x, NaN]), 2), single ([NaN 0 1 Inf NaN NaN]), eps) -%!assert (expinv ([x, NaN], single (2)), single ([NaN 0 1 Inf NaN NaN]), eps) - -## Test input validation -%!error expinv () -%!error expinv (1) -%!error expinv (1,2,3) -%!error expinv (ones (3), ones (2)) -%!error expinv (ones (2), ones (3)) -%!error expinv (i, 2) -%!error expinv (2, i)
--- a/scripts/statistics/distributions/exppdf.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,83 +0,0 @@ -## Copyright (C) 2012 Rik Wehbring -## Copyright (C) 1995-2016 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} exppdf (@var{x}, @var{lambda}) -## For each element of @var{x}, compute the probability density function (PDF) -## at @var{x} of the exponential distribution with mean @var{lambda}. -## @end deftypefn - -## Author: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: PDF of the exponential distribution - -function pdf = exppdf (x, lambda) - - if (nargin != 2) - print_usage (); - endif - - if (! isscalar (lambda)) - [retval, x, lambda] = common_size (x, lambda); - if (retval > 0) - error ("exppdf: X and LAMBDA must be of common size or scalars"); - endif - endif - - if (iscomplex (x) || iscomplex (lambda)) - error ("exppdf: X and LAMBDA must not be complex"); - endif - - if (isa (x, "single") || isa (lambda, "single")) - pdf = zeros (size (x), "single"); - else - pdf = zeros (size (x)); - endif - - k = isnan (x) | !(lambda > 0); - pdf(k) = NaN; - - k = (x >= 0) & (x < Inf) & (lambda > 0); - if (isscalar (lambda)) - pdf(k) = exp (-x(k) / lambda) / lambda; - else - pdf(k) = exp (-x(k) ./ lambda(k)) ./ lambda(k); - endif - -endfunction - - -%!shared x,y -%! x = [-1 0 0.5 1 Inf]; -%! y = gampdf (x, 1, 2); -%!assert (exppdf (x, 2*ones (1,5)), y) -%!assert (exppdf (x, 2*[1 0 NaN 1 1]), [y(1) NaN NaN y(4:5)]) -%!assert (exppdf ([x, NaN], 2), [y, NaN]) - -## Test class of input preserved -%!assert (exppdf (single ([x, NaN]), 2), single ([y, NaN])) -%!assert (exppdf ([x, NaN], single (2)), single ([y, NaN])) - -## Test input validation -%!error exppdf () -%!error exppdf (1) -%!error exppdf (1,2,3) -%!error exppdf (ones (3), ones (2)) -%!error exppdf (ones (2), ones (3)) -%!error exppdf (i, 2) -%!error exppdf (2, i)
--- a/scripts/statistics/distributions/exprnd.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,116 +0,0 @@ -## Copyright (C) 2012 Rik Wehbring -## Copyright (C) 1995-2016 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} exprnd (@var{lambda}) -## @deftypefnx {} {} exprnd (@var{lambda}, @var{r}) -## @deftypefnx {} {} exprnd (@var{lambda}, @var{r}, @var{c}, @dots{}) -## @deftypefnx {} {} exprnd (@var{lambda}, [@var{sz}]) -## Return a matrix of random samples from the exponential distribution with -## mean @var{lambda}. -## -## When called with a single size argument, return a square matrix with -## the dimension specified. When called with more than one scalar argument the -## first two arguments are taken as the number of rows and columns and any -## further arguments specify additional matrix dimensions. The size may also -## be specified with a vector of dimensions @var{sz}. -## -## If no size arguments are given then the result matrix is the size of -## @var{lambda}. -## @end deftypefn - -## Author: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: Random deviates from the exponential distribution - -function rnd = exprnd (lambda, varargin) - - if (nargin < 1) - print_usage (); - endif - - if (nargin == 1) - sz = size (lambda); - elseif (nargin == 2) - if (isscalar (varargin{1}) && varargin{1} >= 0) - sz = [varargin{1}, varargin{1}]; - elseif (isrow (varargin{1}) && all (varargin{1} >= 0)) - sz = varargin{1}; - else - error ("exprnd: dimension vector must be row vector of non-negative integers"); - endif - elseif (nargin > 2) - if (any (cellfun (@(x) (! isscalar (x) || x < 0), varargin))) - error ("exprnd: dimensions must be non-negative integers"); - endif - sz = [varargin{:}]; - endif - - if (! isscalar (lambda) && ! isequal (size (lambda), sz)) - error ("exprnd: LAMBDA must be scalar or of size SZ"); - endif - - if (iscomplex (lambda)) - error ("exprnd: LAMBDA must not be complex"); - endif - - if (isa (lambda, "single")) - cls = "single"; - else - cls = "double"; - endif - - if (isscalar (lambda)) - if ((lambda > 0) && (lambda < Inf)) - rnd = rande (sz, cls) * lambda; - else - rnd = NaN (sz, cls); - endif - else - rnd = NaN (sz, cls); - - k = (lambda > 0) & (lambda < Inf); - rnd(k) = rande (sum (k(:)), 1, cls) .* lambda(k)(:); - endif - -endfunction - - -%!assert (size (exprnd (2)), [1, 1]) -%!assert (size (exprnd (ones (2,1))), [2, 1]) -%!assert (size (exprnd (ones (2,2))), [2, 2]) -%!assert (size (exprnd (1, 3)), [3, 3]) -%!assert (size (exprnd (1, [4 1])), [4, 1]) -%!assert (size (exprnd (1, 4, 1)), [4, 1]) - -## Test class of input preserved -%!assert (class (exprnd (1)), "double") -%!assert (class (exprnd (single (1))), "single") -%!assert (class (exprnd (single ([1 1]))), "single") - -## Test input validation -%!error exprnd () -%!error exprnd (1, -1) -%!error exprnd (1, ones (2)) -%!error exprnd (i) -%!error exprnd (1, [2 -1 2]) -%!error exprnd (1, 2, -1) -%!error exprnd (1, 2, ones (2)) -%!error exprnd (ones (2,2), 3) -%!error exprnd (ones (2,2), [3, 2]) -%!error exprnd (ones (2,2), 2, 3)
--- a/scripts/statistics/distributions/fcdf.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,95 +0,0 @@ -## Copyright (C) 2012 Rik Wehbring -## Copyright (C) 1995-2016 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} fcdf (@var{x}, @var{m}, @var{n}) -## For each element of @var{x}, compute the cumulative distribution function -## (CDF) at @var{x} of the F distribution with @var{m} and @var{n} degrees of -## freedom. -## @end deftypefn - -## Author: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: CDF of the F distribution - -function cdf = fcdf (x, m, n) - - if (nargin != 3) - print_usage (); - endif - - if (! isscalar (m) || ! isscalar (n)) - [retval, x, m, n] = common_size (x, m, n); - if (retval > 0) - error ("fcdf: X, M, and N must be of common size or scalars"); - endif - endif - - if (iscomplex (x) || iscomplex (m) || iscomplex (n)) - error ("fcdf: X, M, and N must not be complex"); - endif - - if (isa (x, "single") || isa (m, "single") || isa (n, "single")) - cdf = zeros (size (x), "single"); - else - cdf = zeros (size (x)); - endif - - k = isnan (x) | !(m > 0) | !(m < Inf) | !(n > 0) | !(n < Inf); - cdf(k) = NaN; - - k = (x == Inf) & (m > 0) & (m < Inf) & (n > 0) & (n < Inf); - cdf(k) = 1; - - k = (x > 0) & (x < Inf) & (m > 0) & (m < Inf) & (n > 0) & (n < Inf); - if (isscalar (m) && isscalar (n)) - cdf(k) = 1 - betainc (1 ./ (1 + m * x(k) / n), n/2, m/2); - else - cdf(k) = 1 - betainc (1 ./ (1 + m(k) .* x(k) ./ n(k)), n(k)/2, m(k)/2); - endif - -endfunction - - -%!shared x,y -%! x = [-1 0 0.5 1 2 Inf]; -%! y = [0 0 1/3 1/2 2/3 1]; -%!assert (fcdf (x, 2*ones (1,6), 2*ones (1,6)), y, eps) -%!assert (fcdf (x, 2, 2*ones (1,6)), y, eps) -%!assert (fcdf (x, 2*ones (1,6), 2), y, eps) -%!assert (fcdf (x, [0 NaN Inf 2 2 2], 2), [NaN NaN NaN y(4:6)], eps) -%!assert (fcdf (x, 2, [0 NaN Inf 2 2 2]), [NaN NaN NaN y(4:6)], eps) -%!assert (fcdf ([x(1:2) NaN x(4:6)], 2, 2), [y(1:2) NaN y(4:6)], eps) - -## Test class of input preserved -%!assert (fcdf ([x, NaN], 2, 2), [y, NaN], eps) -%!assert (fcdf (single ([x, NaN]), 2, 2), single ([y, NaN]), eps ("single")) -%!assert (fcdf ([x, NaN], single (2), 2), single ([y, NaN]), eps ("single")) -%!assert (fcdf ([x, NaN], 2, single (2)), single ([y, NaN]), eps ("single")) - -## Test input validation -%!error fcdf () -%!error fcdf (1) -%!error fcdf (1,2) -%!error fcdf (1,2,3,4) -%!error fcdf (ones (3), ones (2), ones (2)) -%!error fcdf (ones (2), ones (3), ones (2)) -%!error fcdf (ones (2), ones (2), ones (3)) -%!error fcdf (i, 2, 2) -%!error fcdf (2, i, 2) -%!error fcdf (2, 2, i)
--- a/scripts/statistics/distributions/finv.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,92 +0,0 @@ -## Copyright (C) 2012 Rik Wehbring -## Copyright (C) 1995-2016 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} finv (@var{x}, @var{m}, @var{n}) -## For each element of @var{x}, compute the quantile (the inverse of the CDF) -## at @var{x} of the F distribution with @var{m} and @var{n} degrees of -## freedom. -## @end deftypefn - -## Author: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: Quantile function of the F distribution - -function inv = finv (x, m, n) - - if (nargin != 3) - print_usage (); - endif - - if (! isscalar (m) || ! isscalar (n)) - [retval, x, m, n] = common_size (x, m, n); - if (retval > 0) - error ("finv: X, M, and N must be of common size or scalars"); - endif - endif - - if (iscomplex (x) || iscomplex (m) || iscomplex (n)) - error ("finv: X, M, and N must not be complex"); - endif - - if (isa (x, "single") || isa (m, "single") || isa (n, "single")) - inv = NaN (size (x), "single"); - else - inv = NaN (size (x)); - endif - - k = (x == 1) & (m > 0) & (m < Inf) & (n > 0) & (n < Inf); - inv(k) = Inf; - - k = (x >= 0) & (x < 1) & (m > 0) & (m < Inf) & (n > 0) & (n < Inf); - if (isscalar (m) && isscalar (n)) - inv(k) = ((1 ./ betainv (1 - x(k), n/2, m/2) - 1) * n / m); - else - inv(k) = ((1 ./ betainv (1 - x(k), n(k)/2, m(k)/2) - 1) - .* n(k) ./ m(k)); - endif - -endfunction - - -%!shared x -%! x = [-1 0 0.5 1 2]; -%!assert (finv (x, 2*ones (1,5), 2*ones (1,5)), [NaN 0 1 Inf NaN]) -%!assert (finv (x, 2, 2*ones (1,5)), [NaN 0 1 Inf NaN]) -%!assert (finv (x, 2*ones (1,5), 2), [NaN 0 1 Inf NaN]) -%!assert (finv (x, [2 -Inf NaN Inf 2], 2), [NaN NaN NaN NaN NaN]) -%!assert (finv (x, 2, [2 -Inf NaN Inf 2]), [NaN NaN NaN NaN NaN]) -%!assert (finv ([x(1:2) NaN x(4:5)], 2, 2), [NaN 0 NaN Inf NaN]) - -## Test class of input preserved -%!assert (finv ([x, NaN], 2, 2), [NaN 0 1 Inf NaN NaN]) -%!assert (finv (single ([x, NaN]), 2, 2), single ([NaN 0 1 Inf NaN NaN])) -%!assert (finv ([x, NaN], single (2), 2), single ([NaN 0 1 Inf NaN NaN])) -%!assert (finv ([x, NaN], 2, single (2)), single ([NaN 0 1 Inf NaN NaN])) - -## Test input validation -%!error finv () -%!error finv (1) -%!error finv (1,2) -%!error finv (1,2,3,4) -%!error finv (ones (3), ones (2), ones (2)) -%!error finv (ones (2), ones (3), ones (2)) -%!error finv (ones (2), ones (2), ones (3)) -%!error finv (i, 2, 2) -%!error finv (2, i, 2) -%!error finv (2, 2, i)
--- a/scripts/statistics/distributions/fpdf.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,104 +0,0 @@ -## Copyright (C) 2012 Rik Wehbring -## Copyright (C) 1995-2016 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} fpdf (@var{x}, @var{m}, @var{n}) -## For each element of @var{x}, compute the probability density function (PDF) -## at @var{x} of the F distribution with @var{m} and @var{n} degrees of -## freedom. -## @end deftypefn - -## Author: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: PDF of the F distribution - -function pdf = fpdf (x, m, n) - - if (nargin != 3) - print_usage (); - endif - - if (! isscalar (m) || ! isscalar (n)) - [retval, x, m, n] = common_size (x, m, n); - if (retval > 0) - error ("fpdf: X, M, and N must be of common size or scalars"); - endif - endif - - if (iscomplex (x) || iscomplex (m) || iscomplex (n)) - error ("fpdf: X, M, and N must not be complex"); - endif - - if (isa (x, "single") || isa (m, "single") || isa (n, "single")) - pdf = zeros (size (x), "single"); - else - pdf = zeros (size (x)); - endif - - k = isnan (x) | !(m > 0) | !(m < Inf) | !(n > 0) | !(n < Inf); - pdf(k) = NaN; - - k = (x > 0) & (x < Inf) & (m > 0) & (m < Inf) & (n > 0) & (n < Inf); - if (isscalar (m) && isscalar (n)) - tmp = m / n * x(k); - pdf(k) = (exp ((m/2 - 1) * log (tmp) - - ((m + n) / 2) * log (1 + tmp)) - * (m / n) ./ beta (m/2, n/2)); - else - tmp = m(k) .* x(k) ./ n(k); - pdf(k) = (exp ((m(k)/2 - 1) .* log (tmp) - - ((m(k) + n(k)) / 2) .* log (1 + tmp)) - .* (m(k) ./ n(k)) ./ beta (m(k)/2, n(k)/2)); - endif - -endfunction - - -## F (x, 1, m) == T distribution (sqrt (x), m) / sqrt (x) -%!test -%! x = rand (10,1); -%! x = x(x > 0.1 & x < 0.9); -%! y = tpdf (sqrt (x), 2) ./ sqrt (x); -%! assert (fpdf (x, 1, 2), y, 5*eps); - -%!shared x,y -%! x = [-1 0 0.5 1 2]; -%! y = [0 0 4/9 1/4 1/9]; -%!assert (fpdf (x, 2*ones (1,5), 2*ones (1,5)), y, eps) -%!assert (fpdf (x, 2, 2*ones (1,5)), y, eps) -%!assert (fpdf (x, 2*ones (1,5), 2), y, eps) -%!assert (fpdf (x, [0 NaN Inf 2 2], 2), [NaN NaN NaN y(4:5)], eps) -%!assert (fpdf (x, 2, [0 NaN Inf 2 2]), [NaN NaN NaN y(4:5)], eps) -%!assert (fpdf ([x, NaN], 2, 2), [y, NaN], eps) - -## Test class of input preserved -%!assert (fpdf (single ([x, NaN]), 2, 2), single ([y, NaN]), eps ("single")) -%!assert (fpdf ([x, NaN], single (2), 2), single ([y, NaN]), eps ("single")) -%!assert (fpdf ([x, NaN], 2, single (2)), single ([y, NaN]), eps ("single")) - -## Test input validation -%!error fpdf () -%!error fpdf (1) -%!error fpdf (1,2) -%!error fpdf (1,2,3,4) -%!error fpdf (ones (3), ones (2), ones (2)) -%!error fpdf (ones (2), ones (3), ones (2)) -%!error fpdf (ones (2), ones (2), ones (3)) -%!error fpdf (i, 2, 2) -%!error fpdf (2, i, 2) -%!error fpdf (2, 2, i)
--- a/scripts/statistics/distributions/frnd.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,131 +0,0 @@ -## Copyright (C) 2012 Rik Wehbring -## Copyright (C) 1995-2016 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} frnd (@var{m}, @var{n}) -## @deftypefnx {} {} frnd (@var{m}, @var{n}, @var{r}) -## @deftypefnx {} {} frnd (@var{m}, @var{n}, @var{r}, @var{c}, @dots{}) -## @deftypefnx {} {} frnd (@var{m}, @var{n}, [@var{sz}]) -## Return a matrix of random samples from the F distribution with -## @var{m} and @var{n} degrees of freedom. -## -## When called with a single size argument, return a square matrix with -## the dimension specified. When called with more than one scalar argument the -## first two arguments are taken as the number of rows and columns and any -## further arguments specify additional matrix dimensions. The size may also -## be specified with a vector of dimensions @var{sz}. -## -## If no size arguments are given then the result matrix is the common size of -## @var{m} and @var{n}. -## @end deftypefn - -## Author: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: Random deviates from the F distribution - -function rnd = frnd (m, n, varargin) - - if (nargin < 2) - print_usage (); - endif - - if (! isscalar (m) || ! isscalar (n)) - [retval, m, n] = common_size (m, n); - if (retval > 0) - error ("frnd: M and N must be of common size or scalars"); - endif - endif - - if (iscomplex (m) || iscomplex (n)) - error ("frnd: M and N must not be complex"); - endif - - if (nargin == 2) - sz = size (m); - elseif (nargin == 3) - if (isscalar (varargin{1}) && varargin{1} >= 0) - sz = [varargin{1}, varargin{1}]; - elseif (isrow (varargin{1}) && all (varargin{1} >= 0)) - sz = varargin{1}; - else - error ("frnd: dimension vector must be row vector of non-negative integers"); - endif - elseif (nargin > 3) - if (any (cellfun (@(x) (! isscalar (x) || x < 0), varargin))) - error ("frnd: dimensions must be non-negative integers"); - endif - sz = [varargin{:}]; - endif - - if (! isscalar (m) && ! isequal (size (m), sz)) - error ("frnd: M and N must be scalar or of size SZ"); - endif - - if (isa (m, "single") || isa (n, "single")) - cls = "single"; - else - cls = "double"; - endif - - if (isscalar (m) && isscalar (n)) - if ((m > 0) && (m < Inf) && (n > 0) && (n < Inf)) - rnd = n/m * randg (m/2, sz, cls) ./ randg (n/2, sz, cls); - else - rnd = NaN (sz, cls); - endif - else - rnd = NaN (sz, cls); - - k = (m > 0) & (m < Inf) & (n > 0) & (n < Inf); - rnd(k) = n(k) ./ m(k) .* randg (m(k)/2, cls) ./ randg (n(k)/2, cls); - endif - -endfunction - - -%!assert (size (frnd (1,2)), [1, 1]) -%!assert (size (frnd (ones (2,1), 2)), [2, 1]) -%!assert (size (frnd (ones (2,2), 2)), [2, 2]) -%!assert (size (frnd (1, 2*ones (2,1))), [2, 1]) -%!assert (size (frnd (1, 2*ones (2,2))), [2, 2]) -%!assert (size (frnd (1, 2, 3)), [3, 3]) -%!assert (size (frnd (1, 2, [4 1])), [4, 1]) -%!assert (size (frnd (1, 2, 4, 1)), [4, 1]) - -## Test class of input preserved -%!assert (class (frnd (1, 2)), "double") -%!assert (class (frnd (single (1), 2)), "single") -%!assert (class (frnd (single ([1 1]), 2)), "single") -%!assert (class (frnd (1, single (2))), "single") -%!assert (class (frnd (1, single ([2 2]))), "single") - -## Test input validation -%!error frnd () -%!error frnd (1) -%!error frnd (ones (3), ones (2)) -%!error frnd (ones (2), ones (3)) -%!error frnd (i, 2) -%!error frnd (2, i) -%!error frnd (1,2, -1) -%!error frnd (1,2, ones (2)) -%!error frnd (1, 2, [2 -1 2]) -%!error frnd (1,2, 1, ones (2)) -%!error frnd (1,2, 1, -1) -%!error frnd (ones (2,2), 2, 3) -%!error frnd (ones (2,2), 2, [3, 2]) -%!error frnd (ones (2,2), 2, 2, 3)
--- a/scripts/statistics/distributions/gamcdf.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,90 +0,0 @@ -## Copyright (C) 2012 Rik Wehbring -## Copyright (C) 1995-2016 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} gamcdf (@var{x}, @var{a}, @var{b}) -## For each element of @var{x}, compute the cumulative distribution function -## (CDF) at @var{x} of the Gamma distribution with shape parameter @var{a} and -## scale @var{b}. -## @end deftypefn - -## Author: TT <Teresa.Twaroch@ci.tuwien.ac.at> -## Description: CDF of the Gamma distribution - -function cdf = gamcdf (x, a, b) - - if (nargin != 3) - print_usage (); - endif - - if (! isscalar (a) || ! isscalar (b)) - [retval, x, a, b] = common_size (x, a, b); - if (retval > 0) - error ("gamcdf: X, A, and B must be of common size or scalars"); - endif - endif - - if (iscomplex (x) || iscomplex (a) || iscomplex (b)) - error ("gamcdf: X, A, and B must not be complex"); - endif - - if (isa (x, "single") || isa (a, "single") || isa (b, "single")) - cdf = zeros (size (x), "single"); - else - cdf = zeros (size (x)); - endif - - k = isnan (x) | !(a > 0) | !(a < Inf) | !(b > 0) | !(b < Inf); - cdf(k) = NaN; - - k = (x > 0) & (a > 0) & (a < Inf) & (b > 0) & (b < Inf); - if (isscalar (a) && isscalar (b)) - cdf(k) = gammainc (x(k) / b, a); - else - cdf(k) = gammainc (x(k) ./ b(k), a(k)); - endif - -endfunction - - -%!shared x,y -%! x = [-1 0 0.5 1 2 Inf]; -%! y = [0, gammainc(x(2:end), 1)]; -%!assert (gamcdf (x, ones (1,6), ones (1,6)), y) -%!assert (gamcdf (x, 1, ones (1,6)), y) -%!assert (gamcdf (x, ones (1,6), 1), y) -%!assert (gamcdf (x, [0 -Inf NaN Inf 1 1], 1), [NaN NaN NaN NaN y(5:6)]) -%!assert (gamcdf (x, 1, [0 -Inf NaN Inf 1 1]), [NaN NaN NaN NaN y(5:6)]) -%!assert (gamcdf ([x(1:2) NaN x(4:6)], 1, 1), [y(1:2) NaN y(4:6)]) - -## Test class of input preserved -%!assert (gamcdf ([x, NaN], 1, 1), [y, NaN]) -%!assert (gamcdf (single ([x, NaN]), 1, 1), single ([y, NaN]), eps ("single")) - -## Test input validation -%!error gamcdf () -%!error gamcdf (1) -%!error gamcdf (1,2) -%!error gamcdf (1,2,3,4) -%!error gamcdf (ones (3), ones (2), ones (2)) -%!error gamcdf (ones (2), ones (3), ones (2)) -%!error gamcdf (ones (2), ones (2), ones (3)) -%!error gamcdf (i, 2, 2) -%!error gamcdf (2, i, 2) -%!error gamcdf (2, 2, i)
--- a/scripts/statistics/distributions/gaminv.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,131 +0,0 @@ -## Copyright (C) 2012 Rik Wehbring -## Copyright (C) 1995-2016 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} gaminv (@var{x}, @var{a}, @var{b}) -## For each element of @var{x}, compute the quantile (the inverse of the CDF) -## at @var{x} of the Gamma distribution with shape parameter @var{a} and -## scale @var{b}. -## @end deftypefn - -## Author: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: Quantile function of the Gamma distribution - -function inv = gaminv (x, a, b) - - if (nargin != 3) - print_usage (); - endif - - if (! isscalar (a) || ! isscalar (b)) - [retval, x, a, b] = common_size (x, a, b); - if (retval > 0) - error ("gaminv: X, A, and B must be of common size or scalars"); - endif - endif - - if (iscomplex (x) || iscomplex (a) || iscomplex (b)) - error ("gaminv: X, A, and B must not be complex"); - endif - - if (isa (x, "single") || isa (a, "single") || isa (b, "single")) - inv = zeros (size (x), "single"); - else - inv = zeros (size (x)); - endif - - k = ((x < 0) | (x > 1) | isnan (x) - | !(a > 0) | !(a < Inf) | !(b > 0) | !(b < Inf)); - inv(k) = NaN; - - k = (x == 1) & (a > 0) & (a < Inf) & (b > 0) & (b < Inf); - inv(k) = Inf; - - k = find ((x > 0) & (x < 1) & (a > 0) & (a < Inf) & (b > 0) & (b < Inf)); - if (! isempty (k)) - if (! isscalar (a) || ! isscalar (b)) - a = a(k); - b = b(k); - y = a .* b; - else - y = a * b * ones (size (k)); - endif - x = x(k); - - if (isa (x, "single")) - myeps = eps ("single"); - else - myeps = eps; - endif - - l = find (x < myeps); - if (any (l)) - y(l) = sqrt (myeps) * ones (length (l), 1); - endif - - y_new = y; - loopcnt = 0; - do - y_old = y_new; - h = (gamcdf (y_old, a, b) - x) ./ gampdf (y_old, a, b); - y_new = y_old - h; - ind = find (y_new <= myeps); - if (any (ind)) - y_new(ind) = y_old(ind) / 10; - h = y_old - y_new; - endif - until (max (abs (h)) < sqrt (myeps) || ++loopcnt == 40) - - if (loopcnt == 40) - warning ("gaminv: calculation failed to converge for some values"); - endif - - inv(k) = y_new; - - endif - -endfunction - - -%!shared x -%! x = [-1 0 0.63212055882855778 1 2]; -%!assert (gaminv (x, ones (1,5), ones (1,5)), [NaN 0 1 Inf NaN], eps) -%!assert (gaminv (x, 1, ones (1,5)), [NaN 0 1 Inf NaN], eps) -%!assert (gaminv (x, ones (1,5), 1), [NaN 0 1 Inf NaN], eps) -%!assert (gaminv (x, [1 -Inf NaN Inf 1], 1), [NaN NaN NaN NaN NaN]) -%!assert (gaminv (x, 1, [1 -Inf NaN Inf 1]), [NaN NaN NaN NaN NaN]) -%!assert (gaminv ([x(1:2) NaN x(4:5)], 1, 1), [NaN 0 NaN Inf NaN]) - -## Test class of input preserved -%!assert (gaminv ([x, NaN], 1, 1), [NaN 0 1 Inf NaN NaN], eps) -%!assert (gaminv (single ([x, NaN]), 1, 1), single ([NaN 0 1 Inf NaN NaN]), eps ("single")) -%!assert (gaminv ([x, NaN], single (1), 1), single ([NaN 0 1 Inf NaN NaN]), eps ("single")) -%!assert (gaminv ([x, NaN], 1, single (1)), single ([NaN 0 1 Inf NaN NaN]), eps ("single")) - -## Test input validation -%!error gaminv () -%!error gaminv (1) -%!error gaminv (1,2) -%!error gaminv (1,2,3,4) -%!error gaminv (ones (3), ones (2), ones (2)) -%!error gaminv (ones (2), ones (3), ones (2)) -%!error gaminv (ones (2), ones (2), ones (3)) -%!error gaminv (i, 2, 2) -%!error gaminv (2, i, 2) -%!error gaminv (2, 2, i)
--- a/scripts/statistics/distributions/gampdf.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,102 +0,0 @@ -## Copyright (C) 2012 Rik Wehbring -## Copyright (C) 1995-2016 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} gampdf (@var{x}, @var{a}, @var{b}) -## For each element of @var{x}, return the probability density function -## (PDF) at @var{x} of the Gamma distribution with shape parameter @var{a} and -## scale @var{b}. -## @end deftypefn - -## Author: TT <Teresa.Twaroch@ci.tuwien.ac.at> -## Description: PDF of the Gamma distribution - -function pdf = gampdf (x, a, b) - - if (nargin != 3) - print_usage (); - endif - - if (! isscalar (a) || ! isscalar (b)) - [retval, x, a, b] = common_size (x, a, b); - if (retval > 0) - error ("gampdf: X, A, and B must be of common size or scalars"); - endif - endif - - if (iscomplex (x) || iscomplex (a) || iscomplex (b)) - error ("gampdf: X, A, and B must not be complex"); - endif - - if (isa (x, "single") || isa (a, "single") || isa (b, "single")) - pdf = zeros (size (x), "single"); - else - pdf = zeros (size (x)); - endif - - k = !(a > 0) | !(b > 0) | isnan (x); - pdf(k) = NaN; - - k = (x >= 0) & (a > 0) & (a <= 1) & (b > 0); - if (isscalar (a) && isscalar (b)) - pdf(k) = (x(k) .^ (a - 1)) ... - .* exp (- x(k) / b) / gamma (a) / (b ^ a); - else - pdf(k) = (x(k) .^ (a(k) - 1)) ... - .* exp (- x(k) ./ b(k)) ./ gamma (a(k)) ./ (b(k) .^ a(k)); - endif - - k = (x >= 0) & (a > 1) & (b > 0); - if (isscalar (a) && isscalar (b)) - pdf(k) = exp (- a * log (b) + (a-1) * log (x(k)) - - x(k) / b - gammaln (a)); - else - pdf(k) = exp (- a(k) .* log (b(k)) + (a(k)-1) .* log (x(k)) - - x(k) ./ b(k) - gammaln (a(k))); - endif - -endfunction - - -%!shared x,y -%! x = [-1 0 0.5 1 Inf]; -%! y = [0 exp(-x(2:end))]; -%!assert (gampdf (x, ones (1,5), ones (1,5)), y) -%!assert (gampdf (x, 1, ones (1,5)), y) -%!assert (gampdf (x, ones (1,5), 1), y) -%!assert (gampdf (x, [0 -Inf NaN Inf 1], 1), [NaN NaN NaN NaN y(5)]) -%!assert (gampdf (x, 1, [0 -Inf NaN Inf 1]), [NaN NaN NaN 0 y(5)]) -%!assert (gampdf ([x, NaN], 1, 1), [y, NaN]) - -## Test class of input preserved -%!assert (gampdf (single ([x, NaN]), 1, 1), single ([y, NaN])) -%!assert (gampdf ([x, NaN], single (1), 1), single ([y, NaN])) -%!assert (gampdf ([x, NaN], 1, single (1)), single ([y, NaN])) - -## Test input validation -%!error gampdf () -%!error gampdf (1) -%!error gampdf (1,2) -%!error gampdf (1,2,3,4) -%!error gampdf (ones (3), ones (2), ones (2)) -%!error gampdf (ones (2), ones (3), ones (2)) -%!error gampdf (ones (2), ones (2), ones (3)) -%!error gampdf (i, 2, 2) -%!error gampdf (2, i, 2) -%!error gampdf (2, 2, i)
--- a/scripts/statistics/distributions/gamrnd.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,131 +0,0 @@ -## Copyright (C) 2012 Rik Wehbring -## Copyright (C) 1995-2016 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} gamrnd (@var{a}, @var{b}) -## @deftypefnx {} {} gamrnd (@var{a}, @var{b}, @var{r}) -## @deftypefnx {} {} gamrnd (@var{a}, @var{b}, @var{r}, @var{c}, @dots{}) -## @deftypefnx {} {} gamrnd (@var{a}, @var{b}, [@var{sz}]) -## Return a matrix of random samples from the Gamma distribution with -## shape parameter @var{a} and scale @var{b}. -## -## When called with a single size argument, return a square matrix with -## the dimension specified. When called with more than one scalar argument the -## first two arguments are taken as the number of rows and columns and any -## further arguments specify additional matrix dimensions. The size may also -## be specified with a vector of dimensions @var{sz}. -## -## If no size arguments are given then the result matrix is the common size of -## @var{a} and @var{b}. -## @end deftypefn - -## Author: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: Random deviates from the Gamma distribution - -function rnd = gamrnd (a, b, varargin) - - if (nargin < 2) - print_usage (); - endif - - if (! isscalar (a) || ! isscalar (b)) - [retval, a, b] = common_size (a, b); - if (retval > 0) - error ("gamrnd: A and B must be of common size or scalars"); - endif - endif - - if (iscomplex (a) || iscomplex (b)) - error ("gamrnd: A and B must not be complex"); - endif - - if (nargin == 2) - sz = size (a); - elseif (nargin == 3) - if (isscalar (varargin{1}) && varargin{1} >= 0) - sz = [varargin{1}, varargin{1}]; - elseif (isrow (varargin{1}) && all (varargin{1} >= 0)) - sz = varargin{1}; - else - error ("gamrnd: dimension vector must be row vector of non-negative integers"); - endif - elseif (nargin > 3) - if (any (cellfun (@(x) (! isscalar (x) || x < 0), varargin))) - error ("gamrnd: dimensions must be non-negative integers"); - endif - sz = [varargin{:}]; - endif - - if (! isscalar (a) && ! isequal (size (a), sz)) - error ("gamrnd: A and B must be scalar or of size SZ"); - endif - - if (isa (a, "single") || isa (b, "single")) - cls = "single"; - else - cls = "double"; - endif - - if (isscalar (a) && isscalar (b)) - if ((a > 0) && (a < Inf) && (b > 0) && (b < Inf)) - rnd = b * randg (a, sz, cls); - else - rnd = NaN (sz, cls); - endif - else - rnd = NaN (sz, cls); - - k = (a > 0) & (a < Inf) & (b > 0) & (b < Inf); - rnd(k) = b(k) .* randg (a(k), cls); - endif - -endfunction - - -%!assert (size (gamrnd (1,2)), [1, 1]) -%!assert (size (gamrnd (ones (2,1), 2)), [2, 1]) -%!assert (size (gamrnd (ones (2,2), 2)), [2, 2]) -%!assert (size (gamrnd (1, 2*ones (2,1))), [2, 1]) -%!assert (size (gamrnd (1, 2*ones (2,2))), [2, 2]) -%!assert (size (gamrnd (1, 2, 3)), [3, 3]) -%!assert (size (gamrnd (1, 2, [4 1])), [4, 1]) -%!assert (size (gamrnd (1, 2, 4, 1)), [4, 1]) - -## Test class of input preserved -%!assert (class (gamrnd (1, 2)), "double") -%!assert (class (gamrnd (single (1), 2)), "single") -%!assert (class (gamrnd (single ([1 1]), 2)), "single") -%!assert (class (gamrnd (1, single (2))), "single") -%!assert (class (gamrnd (1, single ([2 2]))), "single") - -## Test input validation -%!error gamrnd () -%!error gamrnd (1) -%!error gamrnd (ones (3), ones (2)) -%!error gamrnd (ones (2), ones (3)) -%!error gamrnd (i, 2) -%!error gamrnd (2, i) -%!error gamrnd (1,2, -1) -%!error gamrnd (1,2, ones (2)) -%!error gamrnd (1, 2, [2 -1 2]) -%!error gamrnd (1,2, 1, ones (2)) -%!error gamrnd (1,2, 1, -1) -%!error gamrnd (ones (2,2), 2, 3) -%!error gamrnd (ones (2,2), 2, [3, 2]) -%!error gamrnd (ones (2,2), 2, 2, 3)
--- a/scripts/statistics/distributions/geocdf.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,91 +0,0 @@ -## Copyright (C) 2012 Rik Wehbring -## Copyright (C) 1995-2016 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} geocdf (@var{x}, @var{p}) -## For each element of @var{x}, compute the cumulative distribution function -## (CDF) at @var{x} of the geometric distribution with parameter @var{p}. -## -## The geometric distribution models the number of failures (@var{x}-1) of a -## Bernoulli trial with probability @var{p} before the first success (@var{x}). -## @end deftypefn - -## Author: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: CDF of the geometric distribution - -function cdf = geocdf (x, p) - - if (nargin != 2) - print_usage (); - endif - - if (! isscalar (p)) - [retval, x, p] = common_size (x, p); - if (retval > 0) - error ("geocdf: X and P must be of common size or scalars"); - endif - endif - - if (iscomplex (x) || iscomplex (p)) - error ("geocdf: X and P must not be complex"); - endif - - if (isa (x, "single") || isa (p, "single")) - cdf = zeros (size (x), "single"); - else - cdf = zeros (size (x)); - endif - - k = isnan (x) | !(p >= 0) | !(p <= 1); - cdf(k) = NaN; - - k = (x == Inf) & (p >= 0) & (p <= 1); - cdf(k) = 1; - - k = (x >= 0) & (x < Inf) & (x == fix (x)) & (p > 0) & (p <= 1); - if (isscalar (p)) - cdf(k) = 1 - ((1 - p) .^ (x(k) + 1)); - else - cdf(k) = 1 - ((1 - p(k)) .^ (x(k) + 1)); - endif - -endfunction - - -%!shared x,y -%! x = [-1 0 1 Inf]; -%! y = [0 0.5 0.75 1]; -%!assert (geocdf (x, 0.5*ones (1,4)), y) -%!assert (geocdf (x, 0.5), y) -%!assert (geocdf (x, 0.5*[-1 NaN 4 1]), [NaN NaN NaN y(4)]) -%!assert (geocdf ([x(1:2) NaN x(4)], 0.5), [y(1:2) NaN y(4)]) - -## Test class of input preserved -%!assert (geocdf ([x, NaN], 0.5), [y, NaN]) -%!assert (geocdf (single ([x, NaN]), 0.5), single ([y, NaN])) -%!assert (geocdf ([x, NaN], single (0.5)), single ([y, NaN])) - -## Test input validation -%!error geocdf () -%!error geocdf (1) -%!error geocdf (1,2,3) -%!error geocdf (ones (3), ones (2)) -%!error geocdf (ones (2), ones (3)) -%!error geocdf (i, 2) -%!error geocdf (2, i)
--- a/scripts/statistics/distributions/geoinv.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,87 +0,0 @@ -## Copyright (C) 2012 Rik Wehbring -## Copyright (C) 1995-2016 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} geoinv (@var{x}, @var{p}) -## For each element of @var{x}, compute the quantile (the inverse of the CDF) -## at @var{x} of the geometric distribution with parameter @var{p}. -## -## The geometric distribution models the number of failures (@var{x}-1) of a -## Bernoulli trial with probability @var{p} before the first success (@var{x}). -## @end deftypefn - -## Author: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: Quantile function of the geometric distribution - -function inv = geoinv (x, p) - - if (nargin != 2) - print_usage (); - endif - - if (! isscalar (p)) - [retval, x, p] = common_size (x, p); - if (retval > 0) - error ("geoinv: X and P must be of common size or scalars"); - endif - endif - - if (iscomplex (x) || iscomplex (p)) - error ("geoinv: X and P must not be complex"); - endif - - if (isa (x, "single") || isa (p, "single")) - inv = NaN (size (x), "single"); - else - inv = NaN (size (x)); - endif - - k = (x == 1) & (p >= 0) & (p <= 1); - inv(k) = Inf; - - k = (x >= 0) & (x < 1) & (p > 0) & (p <= 1); - if (isscalar (p)) - inv(k) = max (ceil (log (1 - x(k)) / log (1 - p)) - 1, 0); - else - inv(k) = max (ceil (log (1 - x(k)) ./ log (1 - p(k))) - 1, 0); - endif - -endfunction - - -%!shared x -%! x = [-1 0 0.75 1 2]; -%!assert (geoinv (x, 0.5*ones (1,5)), [NaN 0 1 Inf NaN]) -%!assert (geoinv (x, 0.5), [NaN 0 1 Inf NaN]) -%!assert (geoinv (x, 0.5*[1 -1 NaN 4 1]), [NaN NaN NaN NaN NaN]) -%!assert (geoinv ([x(1:2) NaN x(4:5)], 0.5), [NaN 0 NaN Inf NaN]) - -## Test class of input preserved -%!assert (geoinv ([x, NaN], 0.5), [NaN 0 1 Inf NaN NaN]) -%!assert (geoinv (single ([x, NaN]), 0.5), single ([NaN 0 1 Inf NaN NaN])) -%!assert (geoinv ([x, NaN], single (0.5)), single ([NaN 0 1 Inf NaN NaN])) - -## Test input validation -%!error geoinv () -%!error geoinv (1) -%!error geoinv (1,2,3) -%!error geoinv (ones (3), ones (2)) -%!error geoinv (ones (2), ones (3)) -%!error geoinv (i, 2) -%!error geoinv (2, i)
--- a/scripts/statistics/distributions/geopdf.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,87 +0,0 @@ -## Copyright (C) 2012 Rik Wehbring -## Copyright (C) 1995-2016 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} geopdf (@var{x}, @var{p}) -## For each element of @var{x}, compute the probability density function (PDF) -## at @var{x} of the geometric distribution with parameter @var{p}. -## -## The geometric distribution models the number of failures (@var{x}-1) of a -## Bernoulli trial with probability @var{p} before the first success (@var{x}). -## @end deftypefn - -## Author: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: PDF of the geometric distribution - -function pdf = geopdf (x, p) - - if (nargin != 2) - print_usage (); - endif - - if (! isscalar (p)) - [retval, x, p] = common_size (x, p); - if (retval > 0) - error ("geopdf: X and P must be of common size or scalars"); - endif - endif - - if (iscomplex (x) || iscomplex (p)) - error ("geopdf: X and P must not be complex"); - endif - - if (isa (x, "single") || isa (p, "single")) - pdf = zeros (size (x), "single"); - else - pdf = zeros (size (x)); - endif - - k = isnan (x) | (x == Inf) | !(p >= 0) | !(p <= 1); - pdf(k) = NaN; - - k = (x >= 0) & (x < Inf) & (x == fix (x)) & (p > 0) & (p <= 1); - if (isscalar (p)) - pdf(k) = p * ((1 - p) .^ x(k)); - else - pdf(k) = p(k) .* ((1 - p(k)) .^ x(k)); - endif - -endfunction - - -%!shared x,y -%! x = [-1 0 1 Inf]; -%! y = [0, 1/2, 1/4, NaN]; -%!assert (geopdf (x, 0.5*ones (1,4)), y) -%!assert (geopdf (x, 0.5), y) -%!assert (geopdf (x, 0.5*[-1 NaN 4 1]), [NaN NaN NaN y(4)]) -%!assert (geopdf ([x, NaN], 0.5), [y, NaN]) - -## Test class of input preserved -%!assert (geopdf (single ([x, NaN]), 0.5), single ([y, NaN]), 5*eps ("single")) -%!assert (geopdf ([x, NaN], single (0.5)), single ([y, NaN]), 5*eps ("single")) - -## Test input validation -%!error geopdf () -%!error geopdf (1) -%!error geopdf (1,2,3) -%!error geopdf (ones (3), ones (2)) -%!error geopdf (ones (2), ones (3)) -%!error geopdf (i, 2) -%!error geopdf (2, i)
--- a/scripts/statistics/distributions/geornd.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,127 +0,0 @@ -## Copyright (C) 2012 Rik Wehbring -## Copyright (C) 1995-2016 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} geornd (@var{p}) -## @deftypefnx {} {} geornd (@var{p}, @var{r}) -## @deftypefnx {} {} geornd (@var{p}, @var{r}, @var{c}, @dots{}) -## @deftypefnx {} {} geornd (@var{p}, [@var{sz}]) -## Return a matrix of random samples from the geometric distribution with -## parameter @var{p}. -## -## When called with a single size argument, return a square matrix with -## the dimension specified. When called with more than one scalar argument the -## first two arguments are taken as the number of rows and columns and any -## further arguments specify additional matrix dimensions. The size may also -## be specified with a vector of dimensions @var{sz}. -## -## If no size arguments are given then the result matrix is the size of -## @var{p}. -## -## The geometric distribution models the number of failures (@var{x}-1) of a -## Bernoulli trial with probability @var{p} before the first success (@var{x}). -## @end deftypefn - -## Author: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: Random deviates from the geometric distribution - -function rnd = geornd (p, varargin) - - if (nargin < 1) - print_usage (); - endif - - if (nargin == 1) - sz = size (p); - elseif (nargin == 2) - if (isscalar (varargin{1}) && varargin{1} >= 0) - sz = [varargin{1}, varargin{1}]; - elseif (isrow (varargin{1}) && all (varargin{1} >= 0)) - sz = varargin{1}; - else - error ("geornd: dimension vector must be row vector of non-negative integers"); - endif - elseif (nargin > 2) - if (any (cellfun (@(x) (! isscalar (x) || x < 0), varargin))) - error ("geornd: dimensions must be non-negative integers"); - endif - sz = [varargin{:}]; - endif - - if (! isscalar (p) && ! isequal (size (p), sz)) - error ("geornd: P must be scalar or of size SZ"); - endif - - if (iscomplex (p)) - error ("geornd: P must not be complex"); - endif - - if (isa (p, "single")) - cls = "single"; - else - cls = "double"; - endif - - if (isscalar (p)) - if (p > 0 && p < 1); - rnd = floor (- rande (sz, cls) ./ log (1 - p)); - elseif (p == 0) - rnd = Inf (sz, cls); - elseif (p == 1) - rnd = zeros (sz, cls); - elseif (p < 0 || p > 1) - rnd = NaN (sz, cls); - endif - else - rnd = floor (- rande (sz, cls) ./ log (1 - p)); - - k = !(p >= 0) | !(p <= 1); - rnd(k) = NaN; - - k = (p == 0); - rnd(k) = Inf; - endif - -endfunction - - -%!assert (size (geornd (0.5)), [1, 1]) -%!assert (size (geornd (0.5*ones (2,1))), [2, 1]) -%!assert (size (geornd (0.5*ones (2,2))), [2, 2]) -%!assert (size (geornd (0.5, 3)), [3, 3]) -%!assert (size (geornd (0.5, [4 1])), [4, 1]) -%!assert (size (geornd (0.5, 4, 1)), [4, 1]) - -## Test class of input preserved -%!assert (class (geornd (0.5)), "double") -%!assert (class (geornd (single (0.5))), "single") -%!assert (class (geornd (single ([0.5 0.5]))), "single") -%!assert (class (geornd (single (0))), "single") -%!assert (class (geornd (single (1))), "single") - -## Test input validation -%!error geornd () -%!error geornd (ones (3), ones (2)) -%!error geornd (ones (2), ones (3)) -%!error geornd (i) -%!error geornd (1, -1) -%!error geornd (1, ones (2)) -%!error geornd (1, [2 -1 2]) -%!error geornd (ones (2,2), 2, 3) -%!error geornd (ones (2,2), 3, 2)
--- a/scripts/statistics/distributions/hygecdf.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,109 +0,0 @@ -## Copyright (C) 2012 Rik Wehbring -## Copyright (C) 1997-2016 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} hygecdf (@var{x}, @var{t}, @var{m}, @var{n}) -## Compute the cumulative distribution function (CDF) at @var{x} of the -## hypergeometric distribution with parameters @var{t}, @var{m}, and @var{n}. -## -## This is the probability of obtaining not more than @var{x} marked items -## when randomly drawing a sample of size @var{n} without replacement from a -## population of total size @var{t} containing @var{m} marked items. -## -## The parameters @var{t}, @var{m}, and @var{n} must be positive integers -## with @var{m} and @var{n} not greater than @var{t}. -## @end deftypefn - -## Author: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: CDF of the hypergeometric distribution - -function cdf = hygecdf (x, t, m, n) - - if (nargin != 4) - print_usage (); - endif - - if (! isscalar (t) || ! isscalar (m) || ! isscalar (n)) - [retval, x, t, m, n] = common_size (x, t, m, n); - if (retval > 0) - error ("hygecdf: X, T, M, and N must be of common size or scalars"); - endif - endif - - if (iscomplex (x) || iscomplex (t) || iscomplex (m) || iscomplex (n)) - error ("hygecdf: X, T, M, and N must not be complex"); - endif - - if (isa (x, "single") || isa (t, "single") - || isa (m, "single") || isa (n, "single")) - cdf = NaN (size (x), "single"); - else - cdf = NaN (size (x)); - endif - - ok = ((t >= 0) & (m >= 0) & (n > 0) & (m <= t) & (n <= t) & - (t == fix (t)) & (m == fix (m)) & (n == fix (n))); - - if (isscalar (t)) - if (ok) - cdf = discrete_cdf (x, 0 : n, hygepdf (0 : n, t, m, n)); - endif - else - for i = find (ok(:)') # Must be row vector arg to for loop - v = 0 : n(i); - cdf(i) = discrete_cdf (x(i), v, hygepdf (v, t(i), m(i), n(i))); - endfor - endif - -endfunction - - -%!shared x,y -%! x = [-1 0 1 2 3]; -%! y = [0 1/6 5/6 1 1]; -%!assert (hygecdf (x, 4*ones (1,5), 2, 2), y, eps) -%!assert (hygecdf (x, 4, 2*ones (1,5), 2), y, eps) -%!assert (hygecdf (x, 4, 2, 2*ones (1,5)), y, eps) -%!assert (hygecdf (x, 4*[1 -1 NaN 1.1 1], 2, 2), [y(1) NaN NaN NaN y(5)], eps) -%!assert (hygecdf (x, 4, 2*[1 -1 NaN 1.1 1], 2), [y(1) NaN NaN NaN y(5)], eps) -%!assert (hygecdf (x, 4, 5, 2), [NaN NaN NaN NaN NaN]) -%!assert (hygecdf (x, 4, 2, 2*[1 -1 NaN 1.1 1]), [y(1) NaN NaN NaN y(5)], eps) -%!assert (hygecdf (x, 4, 2, 5), [NaN NaN NaN NaN NaN]) -%!assert (hygecdf ([x(1:2) NaN x(4:5)], 4, 2, 2), [y(1:2) NaN y(4:5)], eps) - -## Test class of input preserved -%!assert (hygecdf ([x, NaN], 4, 2, 2), [y, NaN], eps) -%!assert (hygecdf (single ([x, NaN]), 4, 2, 2), single ([y, NaN]), eps ("single")) -%!assert (hygecdf ([x, NaN], single (4), 2, 2), single ([y, NaN]), eps ("single")) -%!assert (hygecdf ([x, NaN], 4, single (2), 2), single ([y, NaN]), eps ("single")) -%!assert (hygecdf ([x, NaN], 4, 2, single (2)), single ([y, NaN]), eps ("single")) - -## Test input validation -%!error hygecdf () -%!error hygecdf (1) -%!error hygecdf (1,2) -%!error hygecdf (1,2,3) -%!error hygecdf (1,2,3,4,5) -%!error hygecdf (ones (2), ones (3), 1, 1) -%!error hygecdf (1, ones (2), ones (3), 1) -%!error hygecdf (1, 1, ones (2), ones (3)) -%!error hygecdf (i, 2, 2, 2) -%!error hygecdf (2, i, 2, 2) -%!error hygecdf (2, 2, i, 2) -%!error hygecdf (2, 2, 2, i)
--- a/scripts/statistics/distributions/hygeinv.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,115 +0,0 @@ -## Copyright (C) 2012 Rik Wehbring -## Copyright (C) 1997-2016 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} hygeinv (@var{x}, @var{t}, @var{m}, @var{n}) -## For each element of @var{x}, compute the quantile (the inverse of the CDF) -## at @var{x} of the hypergeometric distribution with parameters -## @var{t}, @var{m}, and @var{n}. -## -## This is the probability of obtaining @var{x} marked items when randomly -## drawing a sample of size @var{n} without replacement from a population of -## total size @var{t} containing @var{m} marked items. -## -## The parameters @var{t}, @var{m}, and @var{n} must be positive integers -## with @var{m} and @var{n} not greater than @var{t}. -## @end deftypefn - -## Author: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: Random deviates from the hypergeometric distribution - -function inv = hygeinv (x, t, m, n) - - if (nargin != 4) - print_usage (); - endif - - if (! isscalar (t) || ! isscalar (m) || ! isscalar (n)) - [retval, x, t, m, n] = common_size (x, t, m, n); - if (retval > 0) - error ("hygeinv: X, T, M, and N must be of common size or scalars"); - endif - endif - - if (iscomplex (x) || iscomplex (t) || iscomplex (m) || iscomplex (n)) - error ("hygeinv: X, T, M, and N must not be complex"); - endif - - if (isa (x, "single") || isa (t, "single") - || isa (m, "single") || isa (n, "single")) - inv = NaN (size (x), "single"); - else - inv = NaN (size (x)); - endif - - ok = ((t >= 0) & (m >= 0) & (n > 0) & (m <= t) & (n <= t) & - (t == fix (t)) & (m == fix (m)) & (n == fix (n))); - - if (isscalar (t)) - if (ok) - inv = discrete_inv (x, 0 : n, hygepdf (0 : n, t, m, n)); - inv(x == 0) = 0; # Hack to return correct value for start of distribution - endif - else - for i = find (ok(:)') # Must be row vector arg to for loop - v = 0 : n(i); - if (x(i) == 0) - inv(i) = 0; # Hack to return correct value for start of distribution - else - inv(i) = discrete_inv (x(i), v, hygepdf (v, t(i), m(i), n(i))); - endif - endfor - endif - -endfunction - - -%!shared x -%! x = [-1 0 0.5 1 2]; -%!assert (hygeinv (x, 4*ones (1,5), 2*ones (1,5), 2*ones (1,5)), [NaN 0 1 2 NaN]) -%!assert (hygeinv (x, 4*ones (1,5), 2, 2), [NaN 0 1 2 NaN]) -%!assert (hygeinv (x, 4, 2*ones (1,5), 2), [NaN 0 1 2 NaN]) -%!assert (hygeinv (x, 4, 2, 2*ones (1,5)), [NaN 0 1 2 NaN]) -%!assert (hygeinv (x, 4*[1 -1 NaN 1.1 1], 2, 2), [NaN NaN NaN NaN NaN]) -%!assert (hygeinv (x, 4, 2*[1 -1 NaN 1.1 1], 2), [NaN NaN NaN NaN NaN]) -%!assert (hygeinv (x, 4, 5, 2), [NaN NaN NaN NaN NaN]) -%!assert (hygeinv (x, 4, 2, 2*[1 -1 NaN 1.1 1]), [NaN NaN NaN NaN NaN]) -%!assert (hygeinv (x, 4, 2, 5), [NaN NaN NaN NaN NaN]) -%!assert (hygeinv ([x(1:2) NaN x(4:5)], 4, 2, 2), [NaN 0 NaN 2 NaN]) - -## Test class of input preserved -%!assert (hygeinv ([x, NaN], 4, 2, 2), [NaN 0 1 2 NaN NaN]) -%!assert (hygeinv (single ([x, NaN]), 4, 2, 2), single ([NaN 0 1 2 NaN NaN])) -%!assert (hygeinv ([x, NaN], single (4), 2, 2), single ([NaN 0 1 2 NaN NaN])) -%!assert (hygeinv ([x, NaN], 4, single (2), 2), single ([NaN 0 1 2 NaN NaN])) -%!assert (hygeinv ([x, NaN], 4, 2, single (2)), single ([NaN 0 1 2 NaN NaN])) - -## Test input validation -%!error hygeinv () -%!error hygeinv (1) -%!error hygeinv (1,2) -%!error hygeinv (1,2,3) -%!error hygeinv (1,2,3,4,5) -%!error hygeinv (ones (2), ones (3), 1, 1) -%!error hygeinv (1, ones (2), ones (3), 1) -%!error hygeinv (1, 1, ones (2), ones (3)) -%!error hygeinv (i, 2, 2, 2) -%!error hygeinv (2, i, 2, 2) -%!error hygeinv (2, 2, i, 2) -%!error hygeinv (2, 2, 2, i)
--- a/scripts/statistics/distributions/hygepdf.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,113 +0,0 @@ -## Copyright (C) 2012 Rik Wehbring -## Copyright (C) 1996-2016 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} hygepdf (@var{x}, @var{t}, @var{m}, @var{n}) -## Compute the probability density function (PDF) at @var{x} of the -## hypergeometric distribution with parameters @var{t}, @var{m}, and @var{n}. -## -## This is the probability of obtaining @var{x} marked items when randomly -## drawing a sample of size @var{n} without replacement from a population of -## total size @var{t} containing @var{m} marked items. -## -## The parameters @var{t}, @var{m}, and @var{n} must be positive integers -## with @var{m} and @var{n} not greater than @var{t}. -## @end deftypefn - -## Author: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: PDF of the hypergeometric distribution - -function pdf = hygepdf (x, t, m, n) - - if (nargin != 4) - print_usage (); - endif - - if (! isscalar (t) || ! isscalar (m) || ! isscalar (n)) - [retval, x, t, m, n] = common_size (x, t, m, n); - if (retval > 0) - error ("hygepdf: X, T, M, and N must be of common size or scalars"); - endif - endif - - if (iscomplex (x) || iscomplex (t) || iscomplex (m) || iscomplex (n)) - error ("hygepdf: X, T, M, and N must not be complex"); - endif - - if (isa (x, "single") || isa (t, "single") - || isa (m, "single") || isa (n, "single")) - pdf = zeros (size (x), "single"); - else - pdf = zeros (size (x)); - endif - - ## everything in nel gives NaN - nel = (isnan (x) | (t < 0) | (m < 0) | (n <= 0) | (m > t) | (n > t) | - (t != fix (t)) | (m != fix (m)) | (n != fix (n))); - ## everything in zel gives 0 unless in nel - zel = ((x != fix (x)) | (x < 0) | (x > m) | (n < x) | (n-x > t-m)); - - pdf(nel) = NaN; - - k = ! nel & ! zel; - if (any (k(:))) - if (isscalar (t) && isscalar (m) && isscalar (n)) - pdf(k) = (bincoeff (m, x(k)) .* bincoeff (t-m, n-x(k)) - / bincoeff (t, n)); - else - pdf(k) = (bincoeff (m(k), x(k)) .* bincoeff (t(k)-m(k), n(k)-x(k)) - ./ bincoeff (t(k), n(k))); - endif - endif - -endfunction - - -%!shared x,y -%! x = [-1 0 1 2 3]; -%! y = [0 1/6 4/6 1/6 0]; -%!assert (hygepdf (x, 4*ones (1,5), 2, 2), y) -%!assert (hygepdf (x, 4, 2*ones (1,5), 2), y) -%!assert (hygepdf (x, 4, 2, 2*ones (1,5)), y) -%!assert (hygepdf (x, 4*[1 -1 NaN 1.1 1], 2, 2), [0 NaN NaN NaN 0]) -%!assert (hygepdf (x, 4, 2*[1 -1 NaN 1.1 1], 2), [0 NaN NaN NaN 0]) -%!assert (hygepdf (x, 4, 5, 2), [NaN NaN NaN NaN NaN]) -%!assert (hygepdf (x, 4, 2, 2*[1 -1 NaN 1.1 1]), [0 NaN NaN NaN 0]) -%!assert (hygepdf (x, 4, 2, 5), [NaN NaN NaN NaN NaN]) -%!assert (hygepdf ([x, NaN], 4, 2, 2), [y, NaN], eps) - -## Test class of input preserved -%!assert (hygepdf (single ([x, NaN]), 4, 2, 2), single ([y, NaN])) -%!assert (hygepdf ([x, NaN], single (4), 2, 2), single ([y, NaN])) -%!assert (hygepdf ([x, NaN], 4, single (2), 2), single ([y, NaN])) -%!assert (hygepdf ([x, NaN], 4, 2, single (2)), single ([y, NaN])) - -## Test input validation -%!error hygepdf () -%!error hygepdf (1) -%!error hygepdf (1,2) -%!error hygepdf (1,2,3) -%!error hygepdf (1,2,3,4,5) -%!error hygepdf (1, ones (3), ones (2), ones (2)) -%!error hygepdf (1, ones (2), ones (3), ones (2)) -%!error hygepdf (1, ones (2), ones (2), ones (3)) -%!error hygepdf (i, 2, 2, 2) -%!error hygepdf (2, i, 2, 2) -%!error hygepdf (2, 2, i, 2) -%!error hygepdf (2, 2, 2, i)
--- a/scripts/statistics/distributions/hygernd.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,147 +0,0 @@ -## Copyright (C) 2012 Rik Wehbring -## Copyright (C) 1997-2016 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} hygernd (@var{t}, @var{m}, @var{n}) -## @deftypefnx {} {} hygernd (@var{t}, @var{m}, @var{n}, @var{r}) -## @deftypefnx {} {} hygernd (@var{t}, @var{m}, @var{n}, @var{r}, @var{c}, @dots{}) -## @deftypefnx {} {} hygernd (@var{t}, @var{m}, @var{n}, [@var{sz}]) -## Return a matrix of random samples from the hypergeometric distribution -## with parameters @var{t}, @var{m}, and @var{n}. -## -## The parameters @var{t}, @var{m}, and @var{n} must be positive integers -## with @var{m} and @var{n} not greater than @var{t}. -## -## When called with a single size argument, return a square matrix with -## the dimension specified. When called with more than one scalar argument the -## first two arguments are taken as the number of rows and columns and any -## further arguments specify additional matrix dimensions. The size may also -## be specified with a vector of dimensions @var{sz}. -## -## If no size arguments are given then the result matrix is the common size of -## @var{t}, @var{m}, and @var{n}. -## @end deftypefn - -function rnd = hygernd (t, m, n, varargin) - - if (nargin < 3) - print_usage (); - endif - - if (! isscalar (t) || ! isscalar (m) || ! isscalar (n)) - [retval, t, m, n] = common_size (t, m, n); - if (retval > 0) - error ("hygernd: T, M, and N must be of common size or scalars"); - endif - endif - - if (iscomplex (t) || iscomplex (m) || iscomplex (n)) - error ("hygernd: T, M, and N must not be complex"); - endif - - if (nargin == 3) - sz = size (t); - elseif (nargin == 4) - if (isscalar (varargin{1}) && varargin{1} >= 0) - sz = [varargin{1}, varargin{1}]; - elseif (isrow (varargin{1}) && all (varargin{1} >= 0)) - sz = varargin{1}; - else - error ("hygernd: dimension vector must be row vector of non-negative integers"); - endif - elseif (nargin > 4) - if (any (cellfun (@(x) (! isscalar (x) || x < 0), varargin))) - error ("hygernd: dimensions must be non-negative integers"); - endif - sz = [varargin{:}]; - endif - - if (! isscalar (t) && ! isequal (size (t), sz)) - error ("hygernd: T, M, and N must be scalar or of size SZ"); - endif - - if (isa (t, "single") || isa (m, "single") || isa (n, "single")) - cls = "single"; - else - cls = "double"; - endif - - ok = ((t >= 0) & (m >= 0) & (n > 0) & (m <= t) & (n <= t) & - (t == fix (t)) & (m == fix (m)) & (n == fix (n))); - - if (isscalar (t)) - if (ok) - v = 0:n; - p = hygepdf (v, t, m, n); - rnd = v(lookup (cumsum (p(1:end-1)) / sum (p), rand (sz)) + 1); - rnd = reshape (rnd, sz); - if (strcmp (cls, "single")) - rnd = single (rnd); - endif - else - rnd = NaN (sz, cls); - endif - else - rnd = NaN (sz, cls); - rn = rand (sz); - for i = find (ok(:)') # Must be row vector arg to for loop - v = 0 : n(i); - p = hygepdf (v, t(i), m(i), n(i)); - rnd(i) = v(lookup (cumsum (p(1 : end-1)) / sum (p), rn(i)) + 1); - endfor - endif - -endfunction - - -%!assert (size (hygernd (4,2,2)), [1, 1]) -%!assert (size (hygernd (4*ones (2,1), 2,2)), [2, 1]) -%!assert (size (hygernd (4*ones (2,2), 2,2)), [2, 2]) -%!assert (size (hygernd (4, 2*ones (2,1), 2)), [2, 1]) -%!assert (size (hygernd (4, 2*ones (2,2), 2)), [2, 2]) -%!assert (size (hygernd (4, 2, 2*ones (2,1))), [2, 1]) -%!assert (size (hygernd (4, 2, 2*ones (2,2))), [2, 2]) -%!assert (size (hygernd (4, 2, 2, 3)), [3, 3]) -%!assert (size (hygernd (4, 2, 2, [4 1])), [4, 1]) -%!assert (size (hygernd (4, 2, 2, 4, 1)), [4, 1]) - -%!assert (class (hygernd (4,2,2)), "double") -%!assert (class (hygernd (single (4),2,2)), "single") -%!assert (class (hygernd (single ([4 4]),2,2)), "single") -%!assert (class (hygernd (4,single (2),2)), "single") -%!assert (class (hygernd (4,single ([2 2]),2)), "single") -%!assert (class (hygernd (4,2,single (2))), "single") -%!assert (class (hygernd (4,2,single ([2 2]))), "single") - -## Test input validation -%!error hygernd () -%!error hygernd (1) -%!error hygernd (1,2) -%!error hygernd (ones (3), ones (2), ones (2), 2) -%!error hygernd (ones (2), ones (3), ones (2), 2) -%!error hygernd (ones (2), ones (2), ones (3), 2) -%!error hygernd (i, 2, 2) -%!error hygernd (2, i, 2) -%!error hygernd (2, 2, i) -%!error hygernd (4,2,2, -1) -%!error hygernd (4,2,2, ones (2)) -%!error hygernd (4,2,2, [2 -1 2]) -%!error hygernd (4*ones (2),2,2, 3) -%!error hygernd (4*ones (2),2,2, [3, 2]) -%!error hygernd (4*ones (2),2,2, 3, 2)
--- a/scripts/statistics/distributions/kolmogorov_smirnov_cdf.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,96 +0,0 @@ -## Copyright (C) 2012 Rik Wehbring -## Copyright (C) 1995-2016 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} kolmogorov_smirnov_cdf (@var{x}, @var{tol}) -## Return the cumulative distribution function (CDF) at @var{x} of the -## Kolmogorov-Smirnov distribution. -## -## This is defined as -## @tex -## $$ Q(x) = \sum_{k=-\infty}^\infty (-1)^k \exp (-2 k^2 x^2) $$ -## @end tex -## @ifnottex -## -## @example -## @group -## Inf -## Q(x) = SUM (-1)^k exp (-2 k^2 x^2) -## k = -Inf -## @end group -## @end example -## -## @end ifnottex -## @noindent -## for @var{x} > 0. -## -## The optional parameter @var{tol} specifies the precision up to which -## the series should be evaluated; the default is @var{tol} = @code{eps}. -## @end deftypefn - -## Author: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: CDF of the Kolmogorov-Smirnov distribution - -function cdf = kolmogorov_smirnov_cdf (x, tol) - - if (nargin < 1 || nargin > 2) - print_usage (); - endif - - if (nargin == 1) - if (isa (x, "single")) - tol = eps ("single"); - else - tol = eps; - endif - else - if (! (isscalar (tol) && (tol > 0))) - error ("kolmogorov_smirnov_cdf: TOL must be a positive scalar"); - endif - endif - - if (numel (x) == 0) - error ("kolmogorov_smirnov_cdf: X must not be empty"); - endif - - cdf = zeros (size (x)); - - ind = find (x > 0); - if (length (ind) > 0) - if (columns (ind) < rows (ind)) - y = x(ind.'); - else - y = x(ind); - endif - K = ceil (sqrt (- log (tol) / 2) / min (y)); - k = (1:K)'; - A = exp (- 2 * k.^2 * y.^2); - odd = find (rem (k, 2) == 1); - A(odd,:) = -A(odd,:); - cdf(ind) = 1 + 2 * sum (A); - endif - -endfunction - - -## Test input validation -%!error kolmogorov_smirnov_cdf () -%!error kolmogorov_smirnov_cdf (1,2,3) -%!error kolmogorov_smirnov_cdf (1, ones (2)) -%!error kolmogorov_smirnov_cdf ([], 1)
--- a/scripts/statistics/distributions/laplace_cdf.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,55 +0,0 @@ -## Copyright (C) 2012 Rik Wehbring -## Copyright (C) 1995-2016 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} laplace_cdf (@var{x}) -## For each element of @var{x}, compute the cumulative distribution function -## (CDF) at @var{x} of the Laplace distribution. -## @end deftypefn - -## Author: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: CDF of the Laplace distribution - -function cdf = laplace_cdf (x) - - if (nargin != 1) - print_usage (); - endif - - if (iscomplex (x)) - error ("laplace_cdf: X must not be complex"); - endif - - cdf = (1 + sign (x) .* (1 - exp (- abs (x)))) / 2; - -endfunction - - -%!shared x,y -%! x = [-Inf -log(2) 0 log(2) Inf]; -%! y = [0, 1/4, 1/2, 3/4, 1]; -%!assert (laplace_cdf ([x, NaN]), [y, NaN]) - -## Test class of input preserved -%!assert (laplace_cdf (single ([x, NaN])), single ([y, NaN])) - -## Test input validation -%!error laplace_cdf () -%!error laplace_cdf (1,2) -%!error laplace_cdf (i)
--- a/scripts/statistics/distributions/laplace_inv.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,63 +0,0 @@ -## Copyright (C) 2012 Rik Wehbring -## Copyright (C) 1995-2016 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} laplace_inv (@var{x}) -## For each element of @var{x}, compute the quantile (the inverse of the CDF) -## at @var{x} of the Laplace distribution. -## @end deftypefn - -## Author: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: Quantile function of the Laplace distribution - -function inv = laplace_inv (x) - - if (nargin != 1) - print_usage (); - endif - - if (iscomplex (x)) - error ("laplace_inv: X must not be complex"); - endif - - if (isa (x, "single")) - inv = NaN (size (x), "single"); - else - inv = NaN (size (x)); - endif - - k = (x >= 0) & (x <= 1); - inv(k) = ((x(k) < 1/2) .* log (2 * x(k)) - - (x(k) > 1/2) .* log (2 * (1 - x(k)))); - -endfunction - - -%!shared x -%! x = [-1 0 0.5 1 2]; -%!assert (laplace_inv (x), [NaN -Inf 0 Inf NaN]) - -## Test class of input preserved -%!assert (laplace_inv ([x, NaN]), [NaN -Inf 0 Inf NaN NaN]) -%!assert (laplace_inv (single ([x, NaN])), single ([NaN -Inf 0 Inf NaN NaN])) - -## Test input validation -%!error laplace_inv () -%!error laplace_inv (1,2) -%!error laplace_inv (i)
--- a/scripts/statistics/distributions/laplace_pdf.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,55 +0,0 @@ -## Copyright (C) 2012 Rik Wehbring -## Copyright (C) 1995-2016 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} laplace_pdf (@var{x}) -## For each element of @var{x}, compute the probability density function (PDF) -## at @var{x} of the Laplace distribution. -## @end deftypefn - -## Author: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: PDF of the Laplace distribution - -function pdf = laplace_pdf (x) - - if (nargin != 1) - print_usage (); - endif - - if (iscomplex (x)) - error ("laplace_pdf: X must not be complex"); - endif - - pdf = exp (- abs (x)) / 2; - -endfunction - - -%!shared x,y -%! x = [-Inf -log(2) 0 log(2) Inf]; -%! y = [0, 1/4, 1/2, 1/4, 0]; -%!assert (laplace_pdf ([x, NaN]), [y, NaN]) - -## Test class of input preserved -%!assert (laplace_pdf (single ([x, NaN])), single ([y, NaN])) - -## Test input validation -%!error laplace_pdf () -%!error laplace_pdf (1,2) -%!error laplace_pdf (i)
--- a/scripts/statistics/distributions/laplace_rnd.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,73 +0,0 @@ -## Copyright (C) 2012 Rik Wehbring -## Copyright (C) 1995-2016 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} laplace_rnd (@var{r}) -## @deftypefnx {} {} laplace_rnd (@var{r}, @var{c}, @dots{}) -## @deftypefnx {} {} laplace_rnd ([@var{sz}]) -## Return a matrix of random samples from the Laplace distribution. -## -## When called with a single size argument, return a square matrix with -## the dimension specified. When called with more than one scalar argument the -## first two arguments are taken as the number of rows and columns and any -## further arguments specify additional matrix dimensions. The size may also -## be specified with a vector of dimensions @var{sz}. -## @end deftypefn - -## Author: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: Random deviates from the Laplace distribution - -function rnd = laplace_rnd (varargin) - - if (nargin < 1) - print_usage (); - endif - - if (nargin == 1) - if (isscalar (varargin{1}) && varargin{1} >= 0) - sz = [varargin{1}, varargin{1}]; - elseif (isrow (varargin{1}) && all (varargin{1} >= 0)) - sz = varargin{1}(:)'; - else - error ("laplace_rnd: dimension vector must be row vector of non-negative integers"); - endif - elseif (nargin > 1) - if (any (cellfun (@(x) (! isscalar (x) || x < 0), varargin))) - error ("laplace_rnd: dimensions must be non-negative integers"); - endif - sz = [varargin{:}]; - endif - - tmp = rand (sz); - rnd = (tmp < 1/2) .* log (2 * tmp) - (tmp > 1/2) .* log (2 * (1 - tmp)); - -endfunction - - -%!assert (size (laplace_rnd (3)), [3, 3]) -%!assert (size (laplace_rnd ([4 1])), [4, 1]) -%!assert (size (laplace_rnd (4,1)), [4, 1]) - -## Test input validation -%!error laplace_rnd () -%!error laplace_rnd (-1) -%!error laplace_rnd (ones (2)) -%!error laplace_rnd ([2 -1 2]) -%!error laplace_rnd (1, ones (2)) -%!error laplace_rnd (1, -1)
--- a/scripts/statistics/distributions/logistic_cdf.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,55 +0,0 @@ -## Copyright (C) 2012 Rik Wehbring -## Copyright (C) 1995-2016 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} logistic_cdf (@var{x}) -## For each element of @var{x}, compute the cumulative distribution function -## (CDF) at @var{x} of the logistic distribution. -## @end deftypefn - -## Author: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: CDF of the logistic distribution - -function cdf = logistic_cdf (x) - - if (nargin != 1) - print_usage (); - endif - - if (iscomplex (x)) - error ("logistic_cdf: X must not be complex"); - endif - - cdf = 1 ./ (1 + exp (-x)); - -endfunction - - -%!shared x,y -%! x = [-Inf -log(3) 0 log(3) Inf]; -%! y = [0, 1/4, 1/2, 3/4, 1]; -%!assert (logistic_cdf ([x, NaN]), [y, NaN], eps) - -## Test class of input preserved -%!assert (logistic_cdf (single ([x, NaN])), single ([y, NaN]), eps ("single")) - -## Test input validation -%!error logistic_cdf () -%!error logistic_cdf (1,2) -%!error logistic_cdf (i)
--- a/scripts/statistics/distributions/logistic_inv.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,68 +0,0 @@ -## Copyright (C) 2012 Rik Wehbring -## Copyright (C) 1995-2016 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} logistic_inv (@var{x}) -## For each element of @var{x}, compute the quantile (the inverse of the CDF) -## at @var{x} of the logistic distribution. -## @end deftypefn - -## Author: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: Quantile function of the logistic distribution - -function inv = logistic_inv (x) - - if (nargin != 1) - print_usage (); - endif - - if (iscomplex (x)) - error ("logistic_inv: X must not be complex"); - endif - - if (isa (x, "single")) - inv = NaN (size (x), "single"); - else - inv = NaN (size (x)); - endif - - k = (x == 0); - inv(k) = -Inf; - - k = (x == 1); - inv(k) = Inf; - - k = (x > 0) & (x < 1); - inv(k) = - log (1 ./ x(k) - 1); - -endfunction - - -%!shared x -%! x = [-1 0 0.5 1 2]; -%!assert (logistic_inv (x), [NaN -Inf 0 Inf NaN]) - -## Test class of input preserved -%!assert (logistic_inv ([x, NaN]), [NaN -Inf 0 Inf NaN NaN]) -%!assert (logistic_inv (single ([x, NaN])), single ([NaN -Inf 0 Inf NaN NaN])) - -## Test input validation -%!error logistic_inv () -%!error logistic_inv (1,2) -%!error logistic_inv (i)
--- a/scripts/statistics/distributions/logistic_pdf.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,55 +0,0 @@ -## Copyright (C) 1995-2017 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} logistic_pdf (@var{x}) -## For each element of @var{x}, compute the PDF at @var{x} of the -## logistic distribution. -## @end deftypefn - -## Author: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: PDF of the logistic distribution - -function pdf = logistic_pdf (x) - - if (nargin != 1) - print_usage (); - endif - - if (iscomplex (x)) - error ("logistic_pdf: X must not be complex"); - endif - - cdf = logistic_cdf (x); - pdf = cdf .* (1 - cdf); - -endfunction - - -%!shared x,y -%! x = [-Inf -log(4) 0 log(4) Inf]; -%! y = [0, 0.16, 1/4, 0.16, 0]; -%!assert (logistic_pdf ([x, NaN]), [y, NaN], eps) - -## Test class of input preserved -%!assert (logistic_pdf (single ([x, NaN])), single ([y, NaN]), eps ("single")) - -## Test input validation -%!error logistic_pdf () -%!error logistic_pdf (1,2) -%!error logistic_pdf (i)
--- a/scripts/statistics/distributions/logistic_rnd.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,72 +0,0 @@ -## Copyright (C) 2012 Rik Wehbring -## Copyright (C) 1995-2016 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} logistic_rnd (@var{r}) -## @deftypefnx {} {} logistic_rnd (@var{r}, @var{c}, @dots{}) -## @deftypefnx {} {} logistic_rnd ([@var{sz}]) -## Return a matrix of random samples from the logistic distribution. -## -## When called with a single size argument, return a square matrix with -## the dimension specified. When called with more than one scalar argument the -## first two arguments are taken as the number of rows and columns and any -## further arguments specify additional matrix dimensions. The size may also -## be specified with a vector of dimensions @var{sz}. -## @end deftypefn - -## Author: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: Random deviates from the logistic distribution - -function rnd = logistic_rnd (varargin) - - if (nargin < 1) - print_usage (); - endif - - if (nargin == 1) - if (isscalar (varargin{1}) && varargin{1} >= 0) - sz = [varargin{1}, varargin{1}]; - elseif (isrow (varargin{1}) && all (varargin{1} >= 0)) - sz = varargin{1}; - else - error ("logistic_rnd: dimension vector must be row vector of non-negative integers"); - endif - elseif (nargin > 1) - if (any (cellfun (@(x) (! isscalar (x) || x < 0), varargin))) - error ("logistic_rnd: dimensions must be non-negative integers"); - endif - sz = [varargin{:}]; - endif - - rnd = - log (1 ./ rand (sz) - 1); - -endfunction - - -%!assert (size (logistic_rnd (3)), [3, 3]) -%!assert (size (logistic_rnd ([4 1])), [4, 1]) -%!assert (size (logistic_rnd (4,1)), [4, 1]) - -## Test input validation -%!error logistic_rnd () -%!error logistic_rnd (-1) -%!error logistic_rnd (ones (2)) -%!error logistic_rnd ([2 -1 2]) -%!error logistic_rnd (1, ones (2)) -%!error logistic_rnd (1, -1)
--- a/scripts/statistics/distributions/logncdf.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,100 +0,0 @@ -## Copyright (C) 2012 Rik Wehbring -## Copyright (C) 1995-2016 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} logncdf (@var{x}) -## @deftypefnx {} {} logncdf (@var{x}, @var{mu}, @var{sigma}) -## For each element of @var{x}, compute the cumulative distribution function -## (CDF) at @var{x} of the lognormal distribution with parameters -## @var{mu} and @var{sigma}. -## -## If a random variable follows this distribution, its logarithm is normally -## distributed with mean @var{mu} and standard deviation @var{sigma}. -## -## Default values are @var{mu} = 0, @var{sigma} = 1. -## @end deftypefn - -## Author: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: CDF of the log normal distribution - -function cdf = logncdf (x, mu = 0, sigma = 1) - - if (nargin != 1 && nargin != 3) - print_usage (); - endif - - if (! isscalar (mu) || ! isscalar (sigma)) - [retval, x, mu, sigma] = common_size (x, mu, sigma); - if (retval > 0) - error ("logncdf: X, MU, and SIGMA must be of common size or scalars"); - endif - endif - - if (iscomplex (x) || iscomplex (mu) || iscomplex (sigma)) - error ("logncdf: X, MU, and SIGMA must not be complex"); - endif - - if (isa (x, "single") || isa (mu, "single") || isa (sigma, "single")) - cdf = zeros (size (x), "single"); - else - cdf = zeros (size (x)); - endif - - k = isnan (x) | !(sigma > 0) | !(sigma < Inf); - cdf(k) = NaN; - - k = (x == Inf) & (sigma > 0) & (sigma < Inf); - cdf(k) = 1; - - k = (x > 0) & (x < Inf) & (sigma > 0) & (sigma < Inf); - if (isscalar (mu) && isscalar (sigma)) - cdf(k) = stdnormal_cdf ((log (x(k)) - mu) / sigma); - else - cdf(k) = stdnormal_cdf ((log (x(k)) - mu(k)) ./ sigma(k)); - endif - -endfunction - - -%!shared x,y -%! x = [-1 0 1 e Inf]; -%! y = [0, 0, 0.5, 1/2+1/2*erf(1/2), 1]; -%!assert (logncdf (x, zeros (1,5), sqrt(2)*ones (1,5)), y, eps) -%!assert (logncdf (x, 0, sqrt(2)*ones (1,5)), y, eps) -%!assert (logncdf (x, zeros (1,5), sqrt(2)), y, eps) -%!assert (logncdf (x, [0 1 NaN 0 1], sqrt(2)), [0 0 NaN y(4:5)], eps) -%!assert (logncdf (x, 0, sqrt(2)*[0 NaN Inf 1 1]), [NaN NaN NaN y(4:5)], eps) -%!assert (logncdf ([x(1:3) NaN x(5)], 0, sqrt(2)), [y(1:3) NaN y(5)], eps) - -## Test class of input preserved -%!assert (logncdf ([x, NaN], 0, sqrt(2)), [y, NaN], eps) -%!assert (logncdf (single ([x, NaN]), 0, sqrt(2)), single ([y, NaN]), eps ("single")) -%!assert (logncdf ([x, NaN], single (0), sqrt(2)), single ([y, NaN]), eps ("single")) -%!assert (logncdf ([x, NaN], 0, single (sqrt(2))), single ([y, NaN]), eps ("single")) - -## Test input validation -%!error logncdf () -%!error logncdf (1,2) -%!error logncdf (1,2,3,4) -%!error logncdf (ones (3), ones (2), ones (2)) -%!error logncdf (ones (2), ones (3), ones (2)) -%!error logncdf (ones (2), ones (2), ones (3)) -%!error logncdf (i, 2, 2) -%!error logncdf (2, i, 2) -%!error logncdf (2, 2, i)
--- a/scripts/statistics/distributions/logninv.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,99 +0,0 @@ -## Copyright (C) 2012 Rik Wehbring -## Copyright (C) 1995-2016 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} logninv (@var{x}) -## @deftypefnx {} {} logninv (@var{x}, @var{mu}, @var{sigma}) -## For each element of @var{x}, compute the quantile (the inverse of the CDF) -## at @var{x} of the lognormal distribution with parameters -## @var{mu} and @var{sigma}. -## -## If a random variable follows this distribution, its logarithm is normally -## distributed with mean @var{mu} and standard deviation @var{sigma}. -## -## Default values are @var{mu} = 0, @var{sigma} = 1. -## @end deftypefn - -## Author: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: Quantile function of the log normal distribution - -function inv = logninv (x, mu = 0, sigma = 1) - - if (nargin != 1 && nargin != 3) - print_usage (); - endif - - if (! isscalar (mu) || ! isscalar (sigma)) - [retval, x, mu, sigma] = common_size (x, mu, sigma); - if (retval > 0) - error ("logninv: X, MU, and SIGMA must be of common size or scalars"); - endif - endif - - if (iscomplex (x) || iscomplex (mu) || iscomplex (sigma)) - error ("logninv: X, MU, and SIGMA must not be complex"); - endif - - if (isa (x, "single") || isa (mu, "single") || isa (sigma, "single")) - inv = NaN (size (x), "single"); - else - inv = NaN (size (x)); - endif - - k = !(x >= 0) | !(x <= 1) | !(sigma > 0) | !(sigma < Inf); - inv(k) = NaN; - - k = (x == 1) & (sigma > 0) & (sigma < Inf); - inv(k) = Inf; - - k = (x >= 0) & (x < 1) & (sigma > 0) & (sigma < Inf); - if (isscalar (mu) && isscalar (sigma)) - inv(k) = exp (mu) .* exp (sigma .* stdnormal_inv (x(k))); - else - inv(k) = exp (mu(k)) .* exp (sigma(k) .* stdnormal_inv (x(k))); - endif - -endfunction - - -%!shared x -%! x = [-1 0 0.5 1 2]; -%!assert (logninv (x, ones (1,5), ones (1,5)), [NaN 0 e Inf NaN]) -%!assert (logninv (x, 1, ones (1,5)), [NaN 0 e Inf NaN]) -%!assert (logninv (x, ones (1,5), 1), [NaN 0 e Inf NaN]) -%!assert (logninv (x, [1 1 NaN 0 1], 1), [NaN 0 NaN Inf NaN]) -%!assert (logninv (x, 1, [1 0 NaN Inf 1]), [NaN NaN NaN NaN NaN]) -%!assert (logninv ([x(1:2) NaN x(4:5)], 1, 2), [NaN 0 NaN Inf NaN]) - -## Test class of input preserved -%!assert (logninv ([x, NaN], 1, 1), [NaN 0 e Inf NaN NaN]) -%!assert (logninv (single ([x, NaN]), 1, 1), single ([NaN 0 e Inf NaN NaN])) -%!assert (logninv ([x, NaN], single (1), 1), single ([NaN 0 e Inf NaN NaN])) -%!assert (logninv ([x, NaN], 1, single (1)), single ([NaN 0 e Inf NaN NaN])) - -## Test input validation -%!error logninv () -%!error logninv (1,2) -%!error logninv (1,2,3,4) -%!error logninv (ones (3), ones (2), ones (2)) -%!error logninv (ones (2), ones (3), ones (2)) -%!error logninv (ones (2), ones (2), ones (3)) -%!error logninv (i, 2, 2) -%!error logninv (2, i, 2) -%!error logninv (2, 2, i)
--- a/scripts/statistics/distributions/lognpdf.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,96 +0,0 @@ -## Copyright (C) 2012 Rik Wehbring -## Copyright (C) 1995-2016 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} lognpdf (@var{x}) -## @deftypefnx {} {} lognpdf (@var{x}, @var{mu}, @var{sigma}) -## For each element of @var{x}, compute the probability density function (PDF) -## at @var{x} of the lognormal distribution with parameters -## @var{mu} and @var{sigma}. -## -## If a random variable follows this distribution, its logarithm is normally -## distributed with mean @var{mu} and standard deviation @var{sigma}. -## -## Default values are @var{mu} = 0, @var{sigma} = 1. -## @end deftypefn - -## Author: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: PDF of the log normal distribution - -function pdf = lognpdf (x, mu = 0, sigma = 1) - - if (nargin != 1 && nargin != 3) - print_usage (); - endif - - if (! isscalar (mu) || ! isscalar (sigma)) - [retval, x, mu, sigma] = common_size (x, mu, sigma); - if (retval > 0) - error ("lognpdf: X, MU, and SIGMA must be of common size or scalars"); - endif - endif - - if (iscomplex (x) || iscomplex (mu) || iscomplex (sigma)) - error ("lognpdf: X, MU, and SIGMA must not be complex"); - endif - - if (isa (x, "single") || isa (mu, "single") || isa (sigma, "single")) - pdf = zeros (size (x), "single"); - else - pdf = zeros (size (x)); - endif - - k = isnan (x) | !(sigma > 0) | !(sigma < Inf); - pdf(k) = NaN; - - k = (x > 0) & (x < Inf) & (sigma > 0) & (sigma < Inf); - if (isscalar (mu) && isscalar (sigma)) - pdf(k) = normpdf (log (x(k)), mu, sigma) ./ x(k); - else - pdf(k) = normpdf (log (x(k)), mu(k), sigma(k)) ./ x(k); - endif - -endfunction - - -%!shared x,y -%! x = [-1 0 e Inf]; -%! y = [0, 0, 1/(e*sqrt(2*pi)) * exp(-1/2), 0]; -%!assert (lognpdf (x, zeros (1,4), ones (1,4)), y, eps) -%!assert (lognpdf (x, 0, ones (1,4)), y, eps) -%!assert (lognpdf (x, zeros (1,4), 1), y, eps) -%!assert (lognpdf (x, [0 1 NaN 0], 1), [0 0 NaN y(4)], eps) -%!assert (lognpdf (x, 0, [0 NaN Inf 1]), [NaN NaN NaN y(4)], eps) -%!assert (lognpdf ([x, NaN], 0, 1), [y, NaN], eps) - -## Test class of input preserved -%!assert (lognpdf (single ([x, NaN]), 0, 1), single ([y, NaN]), eps ("single")) -%!assert (lognpdf ([x, NaN], single (0), 1), single ([y, NaN]), eps ("single")) -%!assert (lognpdf ([x, NaN], 0, single (1)), single ([y, NaN]), eps ("single")) - -## Test input validation -%!error lognpdf () -%!error lognpdf (1,2) -%!error lognpdf (1,2,3,4) -%!error lognpdf (ones (3), ones (2), ones (2)) -%!error lognpdf (ones (2), ones (3), ones (2)) -%!error lognpdf (ones (2), ones (2), ones (3)) -%!error lognpdf (i, 2, 2) -%!error lognpdf (2, i, 2) -%!error lognpdf (2, 2, i)
--- a/scripts/statistics/distributions/lognrnd.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,131 +0,0 @@ -## Copyright (C) 2012 Rik Wehbring -## Copyright (C) 1995-2016 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} lognrnd (@var{mu}, @var{sigma}) -## @deftypefnx {} {} lognrnd (@var{mu}, @var{sigma}, @var{r}) -## @deftypefnx {} {} lognrnd (@var{mu}, @var{sigma}, @var{r}, @var{c}, @dots{}) -## @deftypefnx {} {} lognrnd (@var{mu}, @var{sigma}, [@var{sz}]) -## Return a matrix of random samples from the lognormal distribution with -## parameters @var{mu} and @var{sigma}. -## -## When called with a single size argument, return a square matrix with -## the dimension specified. When called with more than one scalar argument the -## first two arguments are taken as the number of rows and columns and any -## further arguments specify additional matrix dimensions. The size may also -## be specified with a vector of dimensions @var{sz}. -## -## If no size arguments are given then the result matrix is the common size of -## @var{mu} and @var{sigma}. -## @end deftypefn - -## Author: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: Random deviates from the log normal distribution - -function rnd = lognrnd (mu, sigma, varargin) - - if (nargin < 2) - print_usage (); - endif - - if (! isscalar (mu) || ! isscalar (sigma)) - [retval, mu, sigma] = common_size (mu, sigma); - if (retval > 0) - error ("lognrnd: MU and SIGMA must be of common size or scalars"); - endif - endif - - if (iscomplex (mu) || iscomplex (sigma)) - error ("lognrnd: MU and SIGMA must not be complex"); - endif - - if (nargin == 2) - sz = size (mu); - elseif (nargin == 3) - if (isscalar (varargin{1}) && varargin{1} >= 0) - sz = [varargin{1}, varargin{1}]; - elseif (isrow (varargin{1}) && all (varargin{1} >= 0)) - sz = varargin{1}; - else - error ("lognrnd: dimension vector must be row vector of non-negative integers"); - endif - elseif (nargin > 3) - if (any (cellfun (@(x) (! isscalar (x) || x < 0), varargin))) - error ("lognrnd: dimensions must be non-negative integers"); - endif - sz = [varargin{:}]; - endif - - if (! isscalar (mu) && ! isequal (size (mu), sz)) - error ("lognrnd: MU and SIGMA must be scalar or of size SZ"); - endif - - if (isa (mu, "single") || isa (sigma, "single")) - cls = "single"; - else - cls = "double"; - endif - - if (isscalar (mu) && isscalar (sigma)) - if ((sigma > 0) && (sigma < Inf)) - rnd = exp (mu + sigma * randn (sz, cls)); - else - rnd = NaN (sz, cls); - endif - else - rnd = exp (mu + sigma .* randn (sz, cls)); - - k = (sigma < 0) | (sigma == Inf); - rnd(k) = NaN; - endif - -endfunction - - -%!assert (size (lognrnd (1,2)), [1, 1]) -%!assert (size (lognrnd (ones (2,1), 2)), [2, 1]) -%!assert (size (lognrnd (ones (2,2), 2)), [2, 2]) -%!assert (size (lognrnd (1, 2*ones (2,1))), [2, 1]) -%!assert (size (lognrnd (1, 2*ones (2,2))), [2, 2]) -%!assert (size (lognrnd (1, 2, 3)), [3, 3]) -%!assert (size (lognrnd (1, 2, [4 1])), [4, 1]) -%!assert (size (lognrnd (1, 2, 4, 1)), [4, 1]) - -## Test class of input preserved -%!assert (class (lognrnd (1, 2)), "double") -%!assert (class (lognrnd (single (1), 2)), "single") -%!assert (class (lognrnd (single ([1 1]), 2)), "single") -%!assert (class (lognrnd (1, single (2))), "single") -%!assert (class (lognrnd (1, single ([2 2]))), "single") - -## Test input validation -%!error lognrnd () -%!error lognrnd (1) -%!error lognrnd (ones (3), ones (2)) -%!error lognrnd (ones (2), ones (3)) -%!error lognrnd (i, 2) -%!error lognrnd (2, i) -%!error lognrnd (1,2, -1) -%!error lognrnd (1,2, ones (2)) -%!error lognrnd (1, 2, [2 -1 2]) -%!error lognrnd (1,2, 1, ones (2)) -%!error lognrnd (1,2, 1, -1) -%!error lognrnd (ones (2,2), 2, 3) -%!error lognrnd (ones (2,2), 2, [3, 2]) -%!error lognrnd (ones (2,2), 2, 2, 3)
--- a/scripts/statistics/distributions/module.mk Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,103 +0,0 @@ -FCN_FILE_DIRS += scripts/statistics/distributions - -%canon_reldir%_FCN_FILES = \ - %reldir%/betacdf.m \ - %reldir%/betainv.m \ - %reldir%/betapdf.m \ - %reldir%/betarnd.m \ - %reldir%/binocdf.m \ - %reldir%/binoinv.m \ - %reldir%/binopdf.m \ - %reldir%/binornd.m \ - %reldir%/cauchy_cdf.m \ - %reldir%/cauchy_inv.m \ - %reldir%/cauchy_pdf.m \ - %reldir%/cauchy_rnd.m \ - %reldir%/chi2cdf.m \ - %reldir%/chi2inv.m \ - %reldir%/chi2pdf.m \ - %reldir%/chi2rnd.m \ - %reldir%/discrete_cdf.m \ - %reldir%/discrete_inv.m \ - %reldir%/discrete_pdf.m \ - %reldir%/discrete_rnd.m \ - %reldir%/empirical_cdf.m \ - %reldir%/empirical_inv.m \ - %reldir%/empirical_pdf.m \ - %reldir%/empirical_rnd.m \ - %reldir%/expcdf.m \ - %reldir%/expinv.m \ - %reldir%/exppdf.m \ - %reldir%/exprnd.m \ - %reldir%/fcdf.m \ - %reldir%/finv.m \ - %reldir%/fpdf.m \ - %reldir%/frnd.m \ - %reldir%/gamcdf.m \ - %reldir%/gaminv.m \ - %reldir%/gampdf.m \ - %reldir%/gamrnd.m \ - %reldir%/geocdf.m \ - %reldir%/geoinv.m \ - %reldir%/geopdf.m \ - %reldir%/geornd.m \ - %reldir%/hygecdf.m \ - %reldir%/hygeinv.m \ - %reldir%/hygepdf.m \ - %reldir%/hygernd.m \ - %reldir%/kolmogorov_smirnov_cdf.m \ - %reldir%/laplace_cdf.m \ - %reldir%/laplace_inv.m \ - %reldir%/laplace_pdf.m \ - %reldir%/laplace_rnd.m \ - %reldir%/logistic_cdf.m \ - %reldir%/logistic_inv.m \ - %reldir%/logistic_pdf.m \ - %reldir%/logistic_rnd.m \ - %reldir%/logncdf.m \ - %reldir%/logninv.m \ - %reldir%/lognpdf.m \ - %reldir%/lognrnd.m \ - %reldir%/nbincdf.m \ - %reldir%/nbininv.m \ - %reldir%/nbinpdf.m \ - %reldir%/nbinrnd.m \ - %reldir%/normcdf.m \ - %reldir%/norminv.m \ - %reldir%/normpdf.m \ - %reldir%/normrnd.m \ - %reldir%/poisscdf.m \ - %reldir%/poissinv.m \ - %reldir%/poisspdf.m \ - %reldir%/poissrnd.m \ - %reldir%/stdnormal_cdf.m \ - %reldir%/stdnormal_inv.m \ - %reldir%/stdnormal_pdf.m \ - %reldir%/stdnormal_rnd.m \ - %reldir%/tcdf.m \ - %reldir%/tinv.m \ - %reldir%/tpdf.m \ - %reldir%/trnd.m \ - %reldir%/unidcdf.m \ - %reldir%/unidinv.m \ - %reldir%/unidpdf.m \ - %reldir%/unidrnd.m \ - %reldir%/unifcdf.m \ - %reldir%/unifinv.m \ - %reldir%/unifpdf.m \ - %reldir%/unifrnd.m \ - %reldir%/wblcdf.m \ - %reldir%/wblinv.m \ - %reldir%/wblpdf.m \ - %reldir%/wblrnd.m \ - %reldir%/wienrnd.m - -%canon_reldir%dir = $(fcnfiledir)/statistics/distributions - -%canon_reldir%_DATA = $(%canon_reldir%_FCN_FILES) - -FCN_FILES += $(%canon_reldir%_FCN_FILES) - -PKG_ADD_FILES += %reldir%/PKG_ADD - -DIRSTAMP_FILES += %reldir%/$(octave_dirstamp)
--- a/scripts/statistics/distributions/nbincdf.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,103 +0,0 @@ -## Copyright (C) 2012 Rik Wehbring -## Copyright (C) 1995-2016 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} nbincdf (@var{x}, @var{n}, @var{p}) -## For each element of @var{x}, compute the cumulative distribution function -## (CDF) at @var{x} of the negative binomial distribution with parameters -## @var{n} and @var{p}. -## -## When @var{n} is integer this is the Pascal distribution. -## When @var{n} is extended to real numbers this is the Polya distribution. -## -## The number of failures in a Bernoulli experiment with success probability -## @var{p} before the @var{n}-th success follows this distribution. -## @end deftypefn - -## Author: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: CDF of the Pascal (negative binomial) distribution - -function cdf = nbincdf (x, n, p) - - if (nargin != 3) - print_usage (); - endif - - if (! isscalar (n) || ! isscalar (p)) - [retval, x, n, p] = common_size (x, n, p); - if (retval > 0) - error ("nbincdf: X, N, and P must be of common size or scalars"); - endif - endif - - if (iscomplex (x) || iscomplex (n) || iscomplex (p)) - error ("nbincdf: X, N, and P must not be complex"); - endif - - if (isa (x, "single") || isa (n, "single") || isa (p, "single")) - cdf = zeros (size (x), "single"); - else - cdf = zeros (size (x)); - endif - - k = (isnan (x) | isnan (n) | (n < 1) | (n == Inf) - | (p < 0) | (p > 1) | isnan (p)); - cdf(k) = NaN; - - k = (x == Inf) & (n > 0) & (n < Inf) & (p >= 0) & (p <= 1); - cdf(k) = 1; - - k = ((x >= 0) & (x < Inf) & (x == fix (x)) - & (n > 0) & (n < Inf) & (p > 0) & (p <= 1)); - if (isscalar (n) && isscalar (p)) - cdf(k) = 1 - betainc (1-p, x(k)+1, n); - else - cdf(k) = 1 - betainc (1-p(k), x(k)+1, n(k)); - endif - -endfunction - - -%!shared x,y -%! x = [-1 0 1 2 Inf]; -%! y = [0 1/2 3/4 7/8 1]; -%!assert (nbincdf (x, ones (1,5), 0.5*ones (1,5)), y) -%!assert (nbincdf (x, 1, 0.5*ones (1,5)), y) -%!assert (nbincdf (x, ones (1,5), 0.5), y) -%!assert (nbincdf ([x(1:3) 0 x(5)], [0 1 NaN 1.5 Inf], 0.5), [NaN 1/2 NaN nbinpdf(0,1.5,0.5) NaN], eps) -%!assert (nbincdf (x, 1, 0.5*[-1 NaN 4 1 1]), [NaN NaN NaN y(4:5)]) -%!assert (nbincdf ([x(1:2) NaN x(4:5)], 1, 0.5), [y(1:2) NaN y(4:5)]) - -## Test class of input preserved -%!assert (nbincdf ([x, NaN], 1, 0.5), [y, NaN]) -%!assert (nbincdf (single ([x, NaN]), 1, 0.5), single ([y, NaN])) -%!assert (nbincdf ([x, NaN], single (1), 0.5), single ([y, NaN])) -%!assert (nbincdf ([x, NaN], 1, single (0.5)), single ([y, NaN])) - -## Test input validation -%!error nbincdf () -%!error nbincdf (1) -%!error nbincdf (1,2) -%!error nbincdf (1,2,3,4) -%!error nbincdf (ones (3), ones (2), ones (2)) -%!error nbincdf (ones (2), ones (3), ones (2)) -%!error nbincdf (ones (2), ones (2), ones (3)) -%!error nbincdf (i, 2, 2) -%!error nbincdf (2, i, 2) -%!error nbincdf (2, 2, i)
--- a/scripts/statistics/distributions/nbininv.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,170 +0,0 @@ -## Copyright (C) 2016-2017 Lachlan Andrew -## Copyright (C) 2012-2016 Rik Wehbring -## Copyright (C) 1995-2012 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} nbininv (@var{x}, @var{n}, @var{p}) -## For each element of @var{x}, compute the quantile (the inverse of the CDF) -## at @var{x} of the negative binomial distribution with parameters -## @var{n} and @var{p}. -## -## When @var{n} is integer this is the Pascal distribution. -## When @var{n} is extended to real numbers this is the Polya distribution. -## -## The number of failures in a Bernoulli experiment with success probability -## @var{p} before the @var{n}-th success follows this distribution. -## @end deftypefn - -function inv = nbininv (x, n, p) - - if (nargin != 3) - print_usage (); - endif - - if (! isscalar (n) || ! isscalar (p)) - [retval, x, n, p] = common_size (x, n, p); - if (retval > 0) - error ("nbininv: X, N, and P must be of common size or scalars"); - endif - endif - - if (iscomplex (x) || iscomplex (n) || iscomplex (p)) - error ("nbininv: X, N, and P must not be complex"); - endif - - if (isa (x, "single") || isa (n, "single") || isa (p, "single")) - inv = zeros (size (x), "single"); - else - inv = zeros (size (x)); - endif - - k = (isnan (x) | (x < 0) | (x > 1) | isnan (n) | (n < 1) | (n == Inf) - | isnan (p) | (p < 0) | (p > 1)); - inv(k) = NaN; - - k = (x == 1) & (n > 0) & (n < Inf) & (p >= 0) & (p <= 1); - inv(k) = Inf; - - k = find ((x >= 0) & (x < 1) & (n > 0) & (n < Inf) - & (p > 0) & (p <= 1)); - if (! isempty (k)) - x = x(k); - m = zeros (size (k)); - if (isscalar (n) && isscalar (p)) - [m, unfinished] = scalar_nbininv (x(:), n, p); - m(unfinished) = bin_search_nbininv (x(unfinished), n, p); - else - m = bin_search_nbininv (x, n(k), p(k)); - endif - inv(k) = m; - endif - -endfunction - - -## Core algorithm to calculate the inverse negative binomial, for n and p real -## scalars and y a column vector, and for which the output is not NaN or Inf. -## Compute CDF in batches of doubling size until CDF > x, or answer > 500. -## Return the locations of unfinished cases in k. -function [m, k] = scalar_nbininv (x, n, p) - - k = 1:length (x); - m = zeros (size (x)); - prev_limit = 0; - limit = 10; - do - cdf = nbincdf (prev_limit:limit, n, p); - r = bsxfun (@le, x(k), cdf); - [v, m(k)] = max (r, [], 2); # find first instance of x <= cdf - m(k) += prev_limit - 1; - k = k(v == 0); - - prev_limit = limit; - limit += limit; - until (isempty (k) || limit >= 1000) - -endfunction - -## Vectorized binary search. -## Can handle vectors n and p, and is faster than the scalar case when the -## answer is large. -## Could be optimized to call nbincdf only for a subset of the x at each stage, -## but care must be taken to handle both scalar and vector n,p. Bookkeeping -## may cost more than the extra computations. -function m = bin_search_nbininv (x, n, p) - - k = 1:length (x); - lower = zeros (size (x)); - limit = 1; - while (any (k) && limit < 1e100) - cdf = nbincdf (limit, n, p); - k = (x > cdf); - lower(k) = limit; - limit += limit; - endwhile - upper = max (2*lower, 1); - k = find (lower != limit/2); # elements for which above loop finished - for i = 1:ceil (log2 (max (lower))) - mid = (upper + lower)/2; - cdf = nbincdf (floor (mid), n, p); - r = (x <= cdf); - upper(r) = mid(r); - lower(! r) = mid(! r); - endfor - m = ceil (lower); - m(x > nbincdf (m, n, p)) += 1; # fix off-by-one errors from binary search - -endfunction - - -%!shared x -%! x = [-1 0 3/4 1 2]; -%!assert (nbininv (x, ones (1,5), 0.5*ones (1,5)), [NaN 0 1 Inf NaN]) -%!assert (nbininv (x, 1, 0.5*ones (1,5)), [NaN 0 1 Inf NaN]) -%!assert (nbininv (x, ones (1,5), 0.5), [NaN 0 1 Inf NaN]) -%!assert (nbininv (x, [1 0 NaN Inf 1], 0.5), [NaN NaN NaN NaN NaN]) -%!assert (nbininv (x, [1 0 1.5 Inf 1], 0.5), [NaN NaN 2 NaN NaN]) -%!assert (nbininv (x, 1, 0.5*[1 -Inf NaN Inf 1]), [NaN NaN NaN NaN NaN]) -%!assert (nbininv ([x(1:2) NaN x(4:5)], 1, 0.5), [NaN 0 NaN Inf NaN]) - -## Test class of input preserved -%!assert (nbininv ([x, NaN], 1, 0.5), [NaN 0 1 Inf NaN NaN]) -%!assert (nbininv (single ([x, NaN]), 1, 0.5), single ([NaN 0 1 Inf NaN NaN])) -%!assert (nbininv ([x, NaN], single (1), 0.5), single ([NaN 0 1 Inf NaN NaN])) -%!assert (nbininv ([x, NaN], 1, single (0.5)), single ([NaN 0 1 Inf NaN NaN])) - -## Test accuracy, to within +/- 1 since it is a discrete distribution -%!shared y, tol -%! y = magic (3) + 1; -%! tol = 1; -%!assert (nbininv (nbincdf (1:10, 3, 0.1), 3, 0.1), 1:10, tol) -%!assert (nbininv (nbincdf (1:10, 3./(1:10), 0.1), 3./(1:10), 0.1), 1:10, tol) -%!assert (nbininv (nbincdf (y, 3./y, 1./y), 3./y, 1./y), y, tol) - -## Test input validation -%!error nbininv () -%!error nbininv (1) -%!error nbininv (1,2) -%!error nbininv (1,2,3,4) -%!error nbininv (ones (3), ones (2), ones (2)) -%!error nbininv (ones (2), ones (3), ones (2)) -%!error nbininv (ones (2), ones (2), ones (3)) -%!error nbininv (i, 2, 2) -%!error nbininv (2, i, 2) -%!error nbininv (2, 2, i)
--- a/scripts/statistics/distributions/nbinpdf.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,100 +0,0 @@ -## Copyright (C) 2012 Rik Wehbring -## Copyright (C) 1995-2016 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} nbinpdf (@var{x}, @var{n}, @var{p}) -## For each element of @var{x}, compute the probability density function (PDF) -## at @var{x} of the negative binomial distribution with parameters -## @var{n} and @var{p}. -## -## When @var{n} is integer this is the Pascal distribution. -## When @var{n} is extended to real numbers this is the Polya distribution. -## -## The number of failures in a Bernoulli experiment with success probability -## @var{p} before the @var{n}-th success follows this distribution. -## @end deftypefn - -## Author: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: PDF of the Pascal (negative binomial) distribution - -function pdf = nbinpdf (x, n, p) - - if (nargin != 3) - print_usage (); - endif - - if (! isscalar (n) || ! isscalar (p)) - [retval, x, n, p] = common_size (x, n, p); - if (retval > 0) - error ("nbinpdf: X, N, and P must be of common size or scalars"); - endif - endif - - if (iscomplex (x) || iscomplex (n) || iscomplex (p)) - error ("nbinpdf: X, N, and P must not be complex"); - endif - - if (isa (x, "single") || isa (n, "single") || isa (p, "single")) - pdf = NaN (size (x), "single"); - else - pdf = NaN (size (x)); - endif - - ok = (x < Inf) & (x == fix (x)) & (n > 0) & (n < Inf) & (p >= 0) & (p <= 1); - - k = (x < 0) & ok; - pdf(k) = 0; - - k = (x >= 0) & ok; - if (isscalar (n) && isscalar (p)) - pdf(k) = bincoeff (-n, x(k)) .* (p ^ n) .* ((p - 1) .^ x(k)); - else - pdf(k) = bincoeff (-n(k), x(k)) .* (p(k) .^ n(k)) .* ((p(k) - 1) .^ x(k)); - endif - - -endfunction - - -%!shared x,y -%! x = [-1 0 1 2 Inf]; -%! y = [0 1/2 1/4 1/8 NaN]; -%!assert (nbinpdf (x, ones (1,5), 0.5*ones (1,5)), y) -%!assert (nbinpdf (x, 1, 0.5*ones (1,5)), y) -%!assert (nbinpdf (x, ones (1,5), 0.5), y) -%!assert (nbinpdf (x, [0 1 NaN 1.5 Inf], 0.5), [NaN 1/2 NaN 1.875*0.5^1.5/4 NaN], eps) -%!assert (nbinpdf (x, 1, 0.5*[-1 NaN 4 1 1]), [NaN NaN NaN y(4:5)]) -%!assert (nbinpdf ([x, NaN], 1, 0.5), [y, NaN]) - -## Test class of input preserved -%!assert (nbinpdf (single ([x, NaN]), 1, 0.5), single ([y, NaN])) -%!assert (nbinpdf ([x, NaN], single (1), 0.5), single ([y, NaN])) -%!assert (nbinpdf ([x, NaN], 1, single (0.5)), single ([y, NaN])) - -## Test input validation -%!error nbinpdf () -%!error nbinpdf (1) -%!error nbinpdf (1,2) -%!error nbinpdf (1,2,3,4) -%!error nbinpdf (ones (3), ones (2), ones (2)) -%!error nbinpdf (ones (2), ones (3), ones (2)) -%!error nbinpdf (ones (2), ones (2), ones (3)) -%!error nbinpdf (i, 2, 2) -%!error nbinpdf (2, i, 2) -%!error nbinpdf (2, 2, i)
--- a/scripts/statistics/distributions/nbinrnd.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,136 +0,0 @@ -## Copyright (C) 2012 Rik Wehbring -## Copyright (C) 1995-2016 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} nbinrnd (@var{n}, @var{p}) -## @deftypefnx {} {} nbinrnd (@var{n}, @var{p}, @var{r}) -## @deftypefnx {} {} nbinrnd (@var{n}, @var{p}, @var{r}, @var{c}, @dots{}) -## @deftypefnx {} {} nbinrnd (@var{n}, @var{p}, [@var{sz}]) -## Return a matrix of random samples from the negative binomial distribution -## with parameters @var{n} and @var{p}. -## -## When called with a single size argument, return a square matrix with -## the dimension specified. When called with more than one scalar argument the -## first two arguments are taken as the number of rows and columns and any -## further arguments specify additional matrix dimensions. The size may also -## be specified with a vector of dimensions @var{sz}. -## -## If no size arguments are given then the result matrix is the common size of -## @var{n} and @var{p}. -## @end deftypefn - -## Author: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: Random deviates from the Pascal distribution - -function rnd = nbinrnd (n, p, varargin) - - if (nargin < 2) - print_usage (); - endif - - if (! isscalar (n) || ! isscalar (p)) - [retval, n, p] = common_size (n, p); - if (retval > 0) - error ("nbinrnd: N and P must be of common size or scalars"); - endif - endif - - if (iscomplex (n) || iscomplex (p)) - error ("nbinrnd: N and P must not be complex"); - endif - - if (nargin == 2) - sz = size (n); - elseif (nargin == 3) - if (isscalar (varargin{1}) && varargin{1} >= 0) - sz = [varargin{1}, varargin{1}]; - elseif (isrow (varargin{1}) && all (varargin{1} >= 0)) - sz = varargin{1}; - else - error ("nbinrnd: dimension vector must be row vector of non-negative integers"); - endif - elseif (nargin > 3) - if (any (cellfun (@(x) (! isscalar (x) || x < 0), varargin))) - error ("nbinrnd: dimensions must be non-negative integers"); - endif - sz = [varargin{:}]; - endif - - if (! isscalar (n) && ! isequal (size (n), sz)) - error ("nbinrnd: N and P must be scalar or of size SZ"); - endif - - if (isa (n, "single") || isa (p, "single")) - cls = "single"; - else - cls = "double"; - endif - - if (isscalar (n) && isscalar (p)) - if ((n > 0) && (n < Inf) && (p > 0) && (p <= 1)) - rnd = randp ((1 - p) ./ p .* randg (n, sz, cls), cls); - elseif ((n > 0) && (n < Inf) && (p == 0)) - rnd = zeros (sz, cls); - else - rnd = NaN (sz, cls); - endif - else - rnd = NaN (sz, cls); - - k = (n > 0) & (n < Inf) & (p == 0); - rnd(k) = 0; - - k = (n > 0) & (n < Inf) & (p > 0) & (p <= 1); - rnd(k) = randp ((1 - p(k)) ./ p(k) .* randg (n(k), cls)); - endif - -endfunction - - -%!assert (size (nbinrnd (2, 1/2)), [1, 1]) -%!assert (size (nbinrnd (2*ones (2,1), 1/2)), [2, 1]) -%!assert (size (nbinrnd (2*ones (2,2), 1/2)), [2, 2]) -%!assert (size (nbinrnd (2, 1/2*ones (2,1))), [2, 1]) -%!assert (size (nbinrnd (2, 1/2*ones (2,2))), [2, 2]) -%!assert (size (nbinrnd (2, 1/2, 3)), [3, 3]) -%!assert (size (nbinrnd (2, 1/2, [4 1])), [4, 1]) -%!assert (size (nbinrnd (2, 1/2, 4, 1)), [4, 1]) - -## Test class of input preserved -%!assert (class (nbinrnd (2, 1/2)), "double") -%!assert (class (nbinrnd (single (2), 1/2)), "single") -%!assert (class (nbinrnd (single ([2 2]), 1/2)), "single") -%!assert (class (nbinrnd (2, single (1/2))), "single") -%!assert (class (nbinrnd (2, single ([1/2 1/2]))), "single") - -## Test input validation -%!error nbinrnd () -%!error nbinrnd (1) -%!error nbinrnd (ones (3), ones (2)) -%!error nbinrnd (ones (2), ones (3)) -%!error nbinrnd (i, 2) -%!error nbinrnd (2, i) -%!error nbinrnd (1,2, -1) -%!error nbinrnd (1,2, ones (2)) -%!error nbinrnd (1, 2, [2 -1 2]) -%!error nbinrnd (1,2, 1, ones (2)) -%!error nbinrnd (1,2, 1, -1) -%!error nbinrnd (ones (2,2), 2, 3) -%!error nbinrnd (ones (2,2), 2, [3, 2]) -%!error nbinrnd (ones (2,2), 2, 2, 3)
--- a/scripts/statistics/distributions/normcdf.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,98 +0,0 @@ -## Copyright (C) 2012 Rik Wehbring -## Copyright (C) 1995-2016 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} normcdf (@var{x}) -## @deftypefnx {} {} normcdf (@var{x}, @var{mu}, @var{sigma}) -## For each element of @var{x}, compute the cumulative distribution function -## (CDF) at @var{x} of the normal distribution with mean @var{mu} and -## standard deviation @var{sigma}. -## -## Default values are @var{mu} = 0, @var{sigma} = 1. -## @end deftypefn - -## Author: TT <Teresa.Twaroch@ci.tuwien.ac.at> -## Description: CDF of the normal distribution - -function cdf = normcdf (x, mu = 0, sigma = 1) - - if (nargin != 1 && nargin != 3) - print_usage (); - endif - - if (! isscalar (mu) || ! isscalar (sigma)) - [retval, x, mu, sigma] = common_size (x, mu, sigma); - if (retval > 0) - error ("normcdf: X, MU, and SIGMA must be of common size or scalars"); - endif - endif - - if (iscomplex (x) || iscomplex (mu) || iscomplex (sigma)) - error ("normcdf: X, MU, and SIGMA must not be complex"); - endif - - if (isa (x, "single") || isa (mu, "single") || isa (sigma, "single")); - cdf = zeros (size (x), "single"); - else - cdf = zeros (size (x)); - endif - - if (isscalar (mu) && isscalar (sigma)) - if (isfinite (mu) && (sigma > 0) && (sigma < Inf)) - cdf = stdnormal_cdf ((x - mu) / sigma); - else - cdf = NaN (size (x), class (cdf)); - endif - else - k = ! isfinite (mu) | !(sigma > 0) | !(sigma < Inf); - cdf(k) = NaN; - - k = ! k; - cdf(k) = stdnormal_cdf ((x(k) - mu(k)) ./ sigma(k)); - endif - -endfunction - - -%!shared x,y -%! x = [-Inf 1 2 Inf]; -%! y = [0, 0.5, 1/2*(1+erf(1/sqrt(2))), 1]; -%!assert (normcdf (x, ones (1,4), ones (1,4)), y) -%!assert (normcdf (x, 1, ones (1,4)), y) -%!assert (normcdf (x, ones (1,4), 1), y) -%!assert (normcdf (x, [0 -Inf NaN Inf], 1), [y(1) NaN NaN NaN]) -%!assert (normcdf (x, 1, [Inf NaN -1 0]), [NaN NaN NaN NaN]) -%!assert (normcdf ([x(1:2) NaN x(4)], 1, 1), [y(1:2) NaN y(4)]) - -## Test class of input preserved -%!assert (normcdf ([x, NaN], 1, 1), [y, NaN]) -%!assert (normcdf (single ([x, NaN]), 1, 1), single ([y, NaN]), eps ("single")) -%!assert (normcdf ([x, NaN], single (1), 1), single ([y, NaN]), eps ("single")) -%!assert (normcdf ([x, NaN], 1, single (1)), single ([y, NaN]), eps ("single")) - -## Test input validation -%!error normcdf () -%!error normcdf (1,2) -%!error normcdf (1,2,3,4) -%!error normcdf (ones (3), ones (2), ones (2)) -%!error normcdf (ones (2), ones (3), ones (2)) -%!error normcdf (ones (2), ones (2), ones (3)) -%!error normcdf (i, 2, 2) -%!error normcdf (2, i, 2) -%!error normcdf (2, 2, i)
--- a/scripts/statistics/distributions/norminv.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,92 +0,0 @@ -## Copyright (C) 2012 Rik Wehbring -## Copyright (C) 1995-2016 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} norminv (@var{x}) -## @deftypefnx {} {} norminv (@var{x}, @var{mu}, @var{sigma}) -## For each element of @var{x}, compute the quantile (the inverse of the CDF) -## at @var{x} of the normal distribution with mean @var{mu} and -## standard deviation @var{sigma}. -## -## Default values are @var{mu} = 0, @var{sigma} = 1. -## @end deftypefn - -## Author: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: Quantile function of the normal distribution - -function inv = norminv (x, mu = 0, sigma = 1) - - if (nargin != 1 && nargin != 3) - print_usage (); - endif - - if (! isscalar (mu) || ! isscalar (sigma)) - [retval, x, mu, sigma] = common_size (x, mu, sigma); - if (retval > 0) - error ("norminv: X, MU, and SIGMA must be of common size or scalars"); - endif - endif - - if (iscomplex (x) || iscomplex (mu) || iscomplex (sigma)) - error ("norminv: X, MU, and SIGMA must not be complex"); - endif - - if (isa (x, "single") || isa (mu, "single") || isa (sigma, "single")) - inv = NaN (size (x), "single"); - else - inv = NaN (size (x)); - endif - - if (isscalar (mu) && isscalar (sigma)) - if (isfinite (mu) && (sigma > 0) && (sigma < Inf)) - inv = mu + sigma * stdnormal_inv (x); - endif - else - k = isfinite (mu) & (sigma > 0) & (sigma < Inf); - inv(k) = mu(k) + sigma(k) .* stdnormal_inv (x(k)); - endif - -endfunction - - -%!shared x -%! x = [-1 0 0.5 1 2]; -%!assert (norminv (x, ones (1,5), ones (1,5)), [NaN -Inf 1 Inf NaN]) -%!assert (norminv (x, 1, ones (1,5)), [NaN -Inf 1 Inf NaN]) -%!assert (norminv (x, ones (1,5), 1), [NaN -Inf 1 Inf NaN]) -%!assert (norminv (x, [1 -Inf NaN Inf 1], 1), [NaN NaN NaN NaN NaN]) -%!assert (norminv (x, 1, [1 0 NaN Inf 1]), [NaN NaN NaN NaN NaN]) -%!assert (norminv ([x(1:2) NaN x(4:5)], 1, 1), [NaN -Inf NaN Inf NaN]) - -## Test class of input preserved -%!assert (norminv ([x, NaN], 1, 1), [NaN -Inf 1 Inf NaN NaN]) -%!assert (norminv (single ([x, NaN]), 1, 1), single ([NaN -Inf 1 Inf NaN NaN])) -%!assert (norminv ([x, NaN], single (1), 1), single ([NaN -Inf 1 Inf NaN NaN])) -%!assert (norminv ([x, NaN], 1, single (1)), single ([NaN -Inf 1 Inf NaN NaN])) - -## Test input validation -%!error norminv () -%!error norminv (1,2) -%!error norminv (1,2,3,4) -%!error norminv (ones (3), ones (2), ones (2)) -%!error norminv (ones (2), ones (3), ones (2)) -%!error norminv (ones (2), ones (2), ones (3)) -%!error norminv (i, 2, 2) -%!error norminv (2, i, 2) -%!error norminv (2, 2, i)
--- a/scripts/statistics/distributions/normpdf.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,97 +0,0 @@ -## Copyright (C) 2012 Rik Wehbring -## Copyright (C) 1995-2016 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} normpdf (@var{x}) -## @deftypefnx {} {} normpdf (@var{x}, @var{mu}, @var{sigma}) -## For each element of @var{x}, compute the probability density function (PDF) -## at @var{x} of the normal distribution with mean @var{mu} and -## standard deviation @var{sigma}. -## -## Default values are @var{mu} = 0, @var{sigma} = 1. -## @end deftypefn - -## Author: TT <Teresa.Twaroch@ci.tuwien.ac.at> -## Description: PDF of the normal distribution - -function pdf = normpdf (x, mu = 0, sigma = 1) - - if (nargin != 1 && nargin != 3) - print_usage (); - endif - - if (! isscalar (mu) || ! isscalar (sigma)) - [retval, x, mu, sigma] = common_size (x, mu, sigma); - if (retval > 0) - error ("normpdf: X, MU, and SIGMA must be of common size or scalars"); - endif - endif - - if (iscomplex (x) || iscomplex (mu) || iscomplex (sigma)) - error ("normpdf: X, MU, and SIGMA must not be complex"); - endif - - if (isa (x, "single") || isa (mu, "single") || isa (sigma, "single")) - pdf = zeros (size (x), "single"); - else - pdf = zeros (size (x)); - endif - - if (isscalar (mu) && isscalar (sigma)) - if (isfinite (mu) && (sigma > 0) && (sigma < Inf)) - pdf = stdnormal_pdf ((x - mu) / sigma) / sigma; - else - pdf = NaN (size (x), class (pdf)); - endif - else - k = isinf (mu) | !(sigma > 0) | !(sigma < Inf); - pdf(k) = NaN; - - k = ! isinf (mu) & (sigma > 0) & (sigma < Inf); - pdf(k) = stdnormal_pdf ((x(k) - mu(k)) ./ sigma(k)) ./ sigma(k); - endif - -endfunction - - -%!shared x,y -%! x = [-Inf 1 2 Inf]; -%! y = 1/sqrt(2*pi)*exp (-(x-1).^2/2); -%!assert (normpdf (x, ones (1,4), ones (1,4)), y) -%!assert (normpdf (x, 1, ones (1,4)), y) -%!assert (normpdf (x, ones (1,4), 1), y) -%!assert (normpdf (x, [0 -Inf NaN Inf], 1), [y(1) NaN NaN NaN]) -%!assert (normpdf (x, 1, [Inf NaN -1 0]), [NaN NaN NaN NaN]) -%!assert (normpdf ([x, NaN], 1, 1), [y, NaN]) - -## Test class of input preserved -%!assert (normpdf (single ([x, NaN]), 1, 1), single ([y, NaN]), eps ("single")) -%!assert (normpdf ([x, NaN], single (1), 1), single ([y, NaN]), eps ("single")) -%!assert (normpdf ([x, NaN], 1, single (1)), single ([y, NaN]), eps ("single")) - -## Test input validation -%!error normpdf () -%!error normpdf (1,2) -%!error normpdf (1,2,3,4) -%!error normpdf (ones (3), ones (2), ones (2)) -%!error normpdf (ones (2), ones (3), ones (2)) -%!error normpdf (ones (2), ones (2), ones (3)) -%!error normpdf (i, 2, 2) -%!error normpdf (2, i, 2) -%!error normpdf (2, 2, i)
--- a/scripts/statistics/distributions/normrnd.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,130 +0,0 @@ -## Copyright (C) 2012 Rik Wehbring -## Copyright (C) 1995-2016 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} normrnd (@var{mu}, @var{sigma}) -## @deftypefnx {} {} normrnd (@var{mu}, @var{sigma}, @var{r}) -## @deftypefnx {} {} normrnd (@var{mu}, @var{sigma}, @var{r}, @var{c}, @dots{}) -## @deftypefnx {} {} normrnd (@var{mu}, @var{sigma}, [@var{sz}]) -## Return a matrix of random samples from the normal distribution with -## parameters mean @var{mu} and standard deviation @var{sigma}. -## -## When called with a single size argument, return a square matrix with -## the dimension specified. When called with more than one scalar argument the -## first two arguments are taken as the number of rows and columns and any -## further arguments specify additional matrix dimensions. The size may also -## be specified with a vector of dimensions @var{sz}. -## -## If no size arguments are given then the result matrix is the common size of -## @var{mu} and @var{sigma}. -## @end deftypefn - -## Author: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: Random deviates from the normal distribution - -function rnd = normrnd (mu, sigma, varargin) - - if (nargin < 2) - print_usage (); - endif - - if (! isscalar (mu) || ! isscalar (sigma)) - [retval, mu, sigma] = common_size (mu, sigma); - if (retval > 0) - error ("normrnd: MU and SIGMA must be of common size or scalars"); - endif - endif - - if (iscomplex (mu) || iscomplex (sigma)) - error ("normrnd: MU and SIGMA must not be complex"); - endif - - if (nargin == 2) - sz = size (mu); - elseif (nargin == 3) - if (isscalar (varargin{1}) && varargin{1} >= 0) - sz = [varargin{1}, varargin{1}]; - elseif (isrow (varargin{1}) && all (varargin{1} >= 0)) - sz = varargin{1}; - else - error ("normrnd: dimension vector must be row vector of non-negative integers"); - endif - elseif (nargin > 3) - if (any (cellfun (@(x) (! isscalar (x) || x < 0), varargin))) - error ("normrnd: dimensions must be non-negative integers"); - endif - sz = [varargin{:}]; - endif - - if (! isscalar (mu) && ! isequal (size (mu), sz)) - error ("normrnd: MU and SIGMA must be scalar or of size SZ"); - endif - - if (isa (mu, "single") || isa (sigma, "single")) - cls = "single"; - else - cls = "double"; - endif - - if (isscalar (mu) && isscalar (sigma)) - if (isfinite (mu) && (sigma >= 0) && (sigma < Inf)) - rnd = mu + sigma * randn (sz, cls); - else - rnd = NaN (sz, cls); - endif - else - rnd = mu + sigma .* randn (sz, cls); - k = ! isfinite (mu) | !(sigma >= 0) | !(sigma < Inf); - rnd(k) = NaN; - endif - -endfunction - - -%!assert (size (normrnd (1,2)), [1, 1]) -%!assert (size (normrnd (ones (2,1), 2)), [2, 1]) -%!assert (size (normrnd (ones (2,2), 2)), [2, 2]) -%!assert (size (normrnd (1, 2*ones (2,1))), [2, 1]) -%!assert (size (normrnd (1, 2*ones (2,2))), [2, 2]) -%!assert (size (normrnd (1, 2, 3)), [3, 3]) -%!assert (size (normrnd (1, 2, [4 1])), [4, 1]) -%!assert (size (normrnd (1, 2, 4, 1)), [4, 1]) - -## Test class of input preserved -%!assert (class (normrnd (1, 2)), "double") -%!assert (class (normrnd (single (1), 2)), "single") -%!assert (class (normrnd (single ([1 1]), 2)), "single") -%!assert (class (normrnd (1, single (2))), "single") -%!assert (class (normrnd (1, single ([2 2]))), "single") - -## Test input validation -%!error normrnd () -%!error normrnd (1) -%!error normrnd (ones (3), ones (2)) -%!error normrnd (ones (2), ones (3)) -%!error normrnd (i, 2) -%!error normrnd (2, i) -%!error normrnd (1,2, -1) -%!error normrnd (1,2, ones (2)) -%!error normrnd (1, 2, [2 -1 2]) -%!error normrnd (1,2, 1, ones (2)) -%!error normrnd (1,2, 1, -1) -%!error normrnd (ones (2,2), 2, 3) -%!error normrnd (ones (2,2), 2, [3, 2]) -%!error normrnd (ones (2,2), 2, 2, 3)
--- a/scripts/statistics/distributions/poisscdf.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,88 +0,0 @@ -## Copyright (C) 2012 Rik Wehbring -## Copyright (C) 1995-2016 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} poisscdf (@var{x}, @var{lambda}) -## For each element of @var{x}, compute the cumulative distribution function -## (CDF) at @var{x} of the Poisson distribution with parameter @var{lambda}. -## @end deftypefn - -## Author: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: CDF of the Poisson distribution - -function cdf = poisscdf (x, lambda) - - if (nargin != 2) - print_usage (); - endif - - if (! isscalar (lambda)) - [retval, x, lambda] = common_size (x, lambda); - if (retval > 0) - error ("poisscdf: X and LAMBDA must be of common size or scalars"); - endif - endif - - if (iscomplex (x) || iscomplex (lambda)) - error ("poisscdf: X and LAMBDA must not be complex"); - endif - - if (isa (x, "single") || isa (lambda, "single")) - cdf = zeros (size (x), "single"); - else - cdf = zeros (size (x)); - endif - - k = isnan (x) | !(lambda > 0); - cdf(k) = NaN; - - k = (x == Inf) & (lambda > 0); - cdf(k) = 1; - - k = (x >= 0) & (x < Inf) & (lambda > 0); - if (isscalar (lambda)) - cdf(k) = 1 - gammainc (lambda, floor (x(k)) + 1); - else - cdf(k) = 1 - gammainc (lambda(k), floor (x(k)) + 1); - endif - -endfunction - - -%!shared x,y -%! x = [-1 0 1 2 Inf]; -%! y = [0, gammainc(1, (x(2:4) +1), "upper"), 1]; -%!assert (poisscdf (x, ones (1,5)), y) -%!assert (poisscdf (x, 1), y) -%!assert (poisscdf (x, [1 0 NaN 1 1]), [y(1) NaN NaN y(4:5)]) -%!assert (poisscdf ([x(1:2) NaN Inf x(5)], 1), [y(1:2) NaN 1 y(5)]) - -## Test class of input preserved -%!assert (poisscdf ([x, NaN], 1), [y, NaN]) -%!assert (poisscdf (single ([x, NaN]), 1), single ([y, NaN]), eps ("single")) -%!assert (poisscdf ([x, NaN], single (1)), single ([y, NaN]), eps ("single")) - -## Test input validation -%!error poisscdf () -%!error poisscdf (1) -%!error poisscdf (1,2,3) -%!error poisscdf (ones (3), ones (2)) -%!error poisscdf (ones (2), ones (3)) -%!error poisscdf (i, 2) -%!error poisscdf (2, i)
--- a/scripts/statistics/distributions/poissinv.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,212 +0,0 @@ -## Copyright (C) 1995-2017 Kurt Hornik -## Copyright (C) 2016 Lachlan Andrew -## Copyright (C) 2014 Mike Giles -## Copyright (C) 2012 Rik Wehbring -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} poissinv (@var{x}, @var{lambda}) -## For each element of @var{x}, compute the quantile (the inverse of the CDF) -## at @var{x} of the Poisson distribution with parameter @var{lambda}. -## @end deftypefn - -## Author: Lachlan <lachlanbis@gmail.com> -## based on code by -## KH <Kurt.Hornik@wu-wien.ac.at> -## Mike Giles <mike.giles@maths.ox.ac.uk> -## Description: Quantile function of the Poisson distribution - -function inv = poissinv (x, lambda) - - if (nargin != 2) - print_usage (); - endif - - if (! isscalar (lambda)) - [retval, x, lambda] = common_size (x, lambda); - if (retval > 0) - error ("poissinv: X and LAMBDA must be of common size or scalars"); - endif - endif - - if (iscomplex (x) || iscomplex (lambda)) - error ("poissinv: X and LAMBDA must not be complex"); - endif - - if (isa (x, "single") || isa (lambda, "single")) - inv = zeros (size (x), "single"); - else - inv = zeros (size (x)); - endif - - k = (x < 0) | (x > 1) | isnan (x) | !(lambda > 0); - inv(k) = NaN; - - k = (x == 1) & (lambda > 0); - inv(k) = Inf; - - k = (x > 0) & (x < 1) & (lambda > 0); - if (any (k(:))) - limit = 20; # After 'limit' iterations, use approx - if (isscalar (lambda)) - cdf = [(cumsum (poisspdf (0:limit-1,lambda))), 2]; - y = x(:); # force to column - r = bsxfun (@le, y(k), cdf); - [~, inv(k)] = max (r, [], 2); # find first instance of x <= cdf - inv(k) -= 1; - else - kk = find (k); - cdf = exp (-lambda(kk)); - for i = 1:limit - m = find (cdf < x(kk)); - if (isempty (m)) - break; - else - inv(kk(m)) += 1; - cdf(m) += poisspdf (i, lambda(kk(m))); - endif - endfor - endif - - ## Use Mike Giles's magic when inv isn't < limit - k &= (inv == limit); - if (any (k(:))) - if (isscalar (lambda)) - lam = repmat (lambda, size (x)); - else - lam = lambda; - endif - inv(k) = analytic_approx (x(k), lam(k)); - endif - endif - -endfunction - - -## The following is based on Mike Giles's CUDA implementation, -## [http://people.maths.ox.ac.uk/gilesm/codes/poissinv/poissinv_cuda.h] -## which is copyright by the University of Oxford -## and is provided under the terms of the GNU GPLv3 license: -## http://www.gnu.org/licenses/gpl.html - -function inv = analytic_approx (x, lambda) - - s = norminv (x, 0, 1) ./ sqrt (lambda); - k = (s > -0.6833501) & (s < 1.777993); - ## use polynomial approximations in central region - if (any (k)) - lam = lambda(k); - if (isscalar (s)) - sk = s; - else - sk = s(k); - endif - - ## polynomial approximation to f^{-1}(s) - 1 - rm = 2.82298751e-07; - rm = -2.58136133e-06 + rm.*sk; - rm = 1.02118025e-05 + rm.*sk; - rm = -2.37996199e-05 + rm.*sk; - rm = 4.05347462e-05 + rm.*sk; - rm = -6.63730967e-05 + rm.*sk; - rm = 0.000124762566 + rm.*sk; - rm = -0.000256970731 + rm.*sk; - rm = 0.000558953132 + rm.*sk; - rm = -0.00133129194 + rm.*sk; - rm = 0.00370367937 + rm.*sk; - rm = -0.0138888706 + rm.*sk; - rm = 0.166666667 + rm.*sk; - rm = sk + sk.*(rm.*sk); - - ## polynomial approximation to correction c0(r) - - t = 1.86386867e-05; - t = -0.000207319499 + t.*rm; - t = 0.0009689451 + t.*rm; - t = -0.00247340054 + t.*rm; - t = 0.00379952985 + t.*rm; - t = -0.00386717047 + t.*rm; - t = 0.00346960934 + t.*rm; - t = -0.00414125511 + t.*rm; - t = 0.00586752093 + t.*rm; - t = -0.00838583787 + t.*rm; - t = 0.0132793933 + t.*rm; - t = -0.027775536 + t.*rm; - t = 0.333333333 + t.*rm; - - ## O(1/lam) correction - - y = -0.00014585224; - y = 0.00146121529 + y.*rm; - y = -0.00610328845 + y.*rm; - y = 0.0138117964 + y.*rm; - y = -0.0186988746 + y.*rm; - y = 0.0168155118 + y.*rm; - y = -0.013394797 + y.*rm; - y = 0.0135698573 + y.*rm; - y = -0.0155377333 + y.*rm; - y = 0.0174065334 + y.*rm; - y = -0.0198011178 + y.*rm; - y ./= lam; - - inv(k) = floor (lam + (y+t)+lam.*rm); - endif - - k = ! k & (s > -sqrt (2)); - if (any (k)) - ## Newton iteration - r = 1 + s(k); - r2 = r + 1; - while (any (abs (r - r2) > 1e-5)) - t = log (r); - r2 = r; - s2 = sqrt (2 * ((1-r) + r.*t)); - s2(r<1) *= -1; - r = r2 - (s2 - s(k)) .* s2 ./ t; - if (r < 0.1 * r2) - r = 0.1 * r2; - endif - endwhile - t = log (r); - y = lambda(k) .* r + log (sqrt (2*r.*((1-r) + r.*t)) ./ abs (r-1)) ./ t; - inv(k) = floor (y - 0.0218 ./ (y + 0.065 * lambda(k))); - endif - -endfunction - - -%!shared x -%! x = [-1 0 0.5 1 2]; -%!assert (poissinv (x, ones (1,5)), [NaN 0 1 Inf NaN]) -%!assert (poissinv (x, 1), [NaN 0 1 Inf NaN]) -%!assert (poissinv (x, [1 0 NaN 1 1]), [NaN NaN NaN Inf NaN]) -%!assert (poissinv ([x(1:2) NaN x(4:5)], 1), [NaN 0 NaN Inf NaN]) - -## Test class of input preserved -%!assert (poissinv ([x, NaN], 1), [NaN 0 1 Inf NaN NaN]) -%!assert (poissinv (single ([x, NaN]), 1), single ([NaN 0 1 Inf NaN NaN])) -%!assert (poissinv ([x, NaN], single (1)), single ([NaN 0 1 Inf NaN NaN])) - -## Test input validation -%!error poissinv () -%!error poissinv (1) -%!error poissinv (1,2,3) -%!error poissinv (ones (3), ones (2)) -%!error poissinv (ones (2), ones (3)) -%!error poissinv (i, 2) -%!error poissinv (2, i)
--- a/scripts/statistics/distributions/poisspdf.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,84 +0,0 @@ -## Copyright (C) 2012 Rik Wehbring -## Copyright (C) 1995-2016 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} poisspdf (@var{x}, @var{lambda}) -## For each element of @var{x}, compute the probability density function (PDF) -## at @var{x} of the Poisson distribution with parameter @var{lambda}. -## @end deftypefn - -## Author: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: PDF of the Poisson distribution - -function pdf = poisspdf (x, lambda) - - if (nargin != 2) - print_usage (); - endif - - if (! isscalar (lambda)) - [retval, x, lambda] = common_size (x, lambda); - if (retval > 0) - error ("poisspdf: X and LAMBDA must be of common size or scalars"); - endif - endif - - if (iscomplex (x) || iscomplex (lambda)) - error ("poisspdf: X and LAMBDA must not be complex"); - endif - - if (isa (x, "single") || isa (lambda, "single")) - pdf = zeros (size (x), "single"); - else - pdf = zeros (size (x)); - endif - - k = isnan (x) | !(lambda > 0); - pdf(k) = NaN; - - k = (x >= 0) & (x < Inf) & (x == fix (x)) & (lambda > 0); - if (isscalar (lambda)) - pdf(k) = exp (x(k) * log (lambda) - lambda - gammaln (x(k) + 1)); - else - pdf(k) = exp (x(k) .* log (lambda(k)) - lambda(k) - gammaln (x(k) + 1)); - endif - -endfunction - - -%!shared x,y -%! x = [-1 0 1 2 Inf]; -%! y = [0, exp(-1)*[1 1 0.5], 0]; -%!assert (poisspdf (x, ones (1,5)), y, eps) -%!assert (poisspdf (x, 1), y, eps) -%!assert (poisspdf (x, [1 0 NaN 1 1]), [y(1) NaN NaN y(4:5)], eps) -%!assert (poisspdf ([x, NaN], 1), [y, NaN], eps) - -## Test class of input preserved -%!assert (poisspdf (single ([x, NaN]), 1), single ([y, NaN]), eps ("single")) -%!assert (poisspdf ([x, NaN], single (1)), single ([y, NaN]), eps ("single")) - -## Test input validation -%!error poisspdf () -%!error poisspdf (1) -%!error poisspdf (1,2,3) -%!error poisspdf (ones (3), ones (2)) -%!error poisspdf (ones (2), ones (3)) -%!error poisspdf (i, 2) -%!error poisspdf (2, i)
--- a/scripts/statistics/distributions/poissrnd.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,119 +0,0 @@ -## Copyright (C) 2012 Rik Wehbring -## Copyright (C) 1995-2016 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} poissrnd (@var{lambda}) -## @deftypefnx {} {} poissrnd (@var{lambda}, @var{r}) -## @deftypefnx {} {} poissrnd (@var{lambda}, @var{r}, @var{c}, @dots{}) -## @deftypefnx {} {} poissrnd (@var{lambda}, [@var{sz}]) -## Return a matrix of random samples from the Poisson distribution with -## parameter @var{lambda}. -## -## When called with a single size argument, return a square matrix with -## the dimension specified. When called with more than one scalar argument the -## first two arguments are taken as the number of rows and columns and any -## further arguments specify additional matrix dimensions. The size may also -## be specified with a vector of dimensions @var{sz}. -## -## If no size arguments are given then the result matrix is the size of -## @var{lambda}. -## @end deftypefn - -## Author: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: Random deviates from the Poisson distribution - -function rnd = poissrnd (lambda, varargin) - - if (nargin < 1) - print_usage (); - endif - - if (nargin == 1) - sz = size (lambda); - elseif (nargin == 2) - if (isscalar (varargin{1}) && varargin{1} >= 0) - sz = [varargin{1}, varargin{1}]; - elseif (isrow (varargin{1}) && all (varargin{1} >= 0)) - sz = varargin{1}; - else - error ("poissrnd: dimension vector must be row vector of non-negative integers"); - endif - elseif (nargin > 2) - if (any (cellfun (@(x) (! isscalar (x) || x < 0), varargin))) - error ("poissrnd: dimensions must be non-negative integers"); - endif - sz = [varargin{:}]; - endif - - if (! isscalar (lambda) && ! isequal (size (lambda), sz)) - error ("poissrnd: LAMBDA must be scalar or of size SZ"); - endif - - if (iscomplex (lambda)) - error ("poissrnd: LAMBDA must not be complex"); - endif - - if (isa (lambda, "single")) - cls = "single"; - else - cls = "double"; - endif - - if (isscalar (lambda)) - if (lambda >= 0 && lambda < Inf) - rnd = randp (lambda, sz, cls); - else - rnd = NaN (sz, cls); - endif - else - rnd = NaN (sz, cls); - - k = (lambda >= 0) & (lambda < Inf); - rnd(k) = randp (lambda(k), cls); - endif - -endfunction - - -%!assert (size (poissrnd (2)), [1, 1]) -%!assert (size (poissrnd (ones (2,1))), [2, 1]) -%!assert (size (poissrnd (ones (2,2))), [2, 2]) -%!assert (size (poissrnd (1, 3)), [3, 3]) -%!assert (size (poissrnd (1, [4 1])), [4, 1]) -%!assert (size (poissrnd (1, 4, 1)), [4, 1]) - -## Test class of input preserved -%!assert (class (poissrnd (2)), "double") -%!assert (class (poissrnd (single (2))), "single") -%!assert (class (poissrnd (single ([2 2]))), "single") - -## Test input validation -%!error poissrnd () -%!error poissrnd (1, -1) -%!error poissrnd (1, ones (2)) -%!error poissrnd (1, 2, ones (2)) -%!error poissrnd (i) -%!error poissrnd (1, 2, -1) -%!error poissrnd (1, [2 -1 2]) -%!error poissrnd (ones (2,2), 3) -%!error poissrnd (ones (2,2), [3, 2]) -%!error poissrnd (ones (2,2), 2, 3) - -%!assert (poissrnd (0, 1, 1), 0) -%!assert (poissrnd ([0, 0, 0], [1, 3]), [0 0 0])
--- a/scripts/statistics/distributions/stdnormal_cdf.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,56 +0,0 @@ -## Copyright (C) 2012 Rik Wehbring -## Copyright (C) 1995-2016 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} stdnormal_cdf (@var{x}) -## For each element of @var{x}, compute the cumulative distribution function -## (CDF) at @var{x} of the standard normal distribution -## (mean = 0, standard deviation = 1). -## @end deftypefn - -## Author: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: CDF of the standard normal distribution - -function cdf = stdnormal_cdf (x) - - if (nargin != 1) - print_usage (); - endif - - if (iscomplex (x)) - error ("stdnormal_cdf: X must not be complex"); - endif - - cdf = erfc (x / (-sqrt(2))) / 2; - -endfunction - - -%!shared x,y -%! x = [-Inf 0 1 Inf]; -%! y = [0, 0.5, 1/2*(1+erf(1/sqrt(2))), 1]; -%!assert (stdnormal_cdf ([x, NaN]), [y, NaN]) - -## Test class of input preserved -%!assert (stdnormal_cdf (single ([x, NaN])), single ([y, NaN]), eps ("single")) - -## Test input validation -%!error stdnormal_cdf () -%!error stdnormal_cdf (1,2) -%!error stdnormal_cdf (i)
--- a/scripts/statistics/distributions/stdnormal_inv.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,56 +0,0 @@ -## Copyright (C) 2012 Rik Wehbring -## Copyright (C) 1995-2016 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} stdnormal_inv (@var{x}) -## For each element of @var{x}, compute the quantile (the -## inverse of the CDF) at @var{x} of the standard normal distribution -## (mean = 0, standard deviation = 1). -## @end deftypefn - -## Author: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: Quantile function of the standard normal distribution - -function inv = stdnormal_inv (x) - - if (nargin != 1) - print_usage (); - endif - - if (iscomplex (x)) - error ("stdnormal_inv: X must not be complex"); - endif - - inv = - sqrt (2) * erfcinv (2 * x); - -endfunction - - -%!shared x -%! x = [-1 0 0.5 1 2]; -%!assert (stdnormal_inv (x), [NaN -Inf 0 Inf NaN]) - -## Test class of input preserved -%!assert (stdnormal_inv ([x, NaN]), [NaN -Inf 0 Inf NaN NaN]) -%!assert (stdnormal_inv (single ([x, NaN])), single ([NaN -Inf 0 Inf NaN NaN])) - -## Test input validation -%!error stdnormal_inv () -%!error stdnormal_inv (1,2) -%!error stdnormal_inv (i)
--- a/scripts/statistics/distributions/stdnormal_pdf.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,56 +0,0 @@ -## Copyright (C) 2012 Rik Wehbring -## Copyright (C) 1995-2016 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} stdnormal_pdf (@var{x}) -## For each element of @var{x}, compute the probability density function (PDF) -## at @var{x} of the standard normal distribution -## (mean = 0, standard deviation = 1). -## @end deftypefn - -## Author: TT <Teresa.Twaroch@ci.tuwien.ac.at> -## Description: PDF of the standard normal distribution - -function pdf = stdnormal_pdf (x) - - if (nargin != 1) - print_usage (); - endif - - if (iscomplex (x)) - error ("stdnormal_pdf: X must not be complex"); - endif - - pdf = (2 * pi)^(- 1/2) * exp (- x .^ 2 / 2); - -endfunction - - -%!shared x,y -%! x = [-Inf 0 1 Inf]; -%! y = 1/sqrt(2*pi)*exp (-x.^2/2); -%!assert (stdnormal_pdf ([x, NaN]), [y, NaN], eps) - -## Test class of input preserved -%!assert (stdnormal_pdf (single ([x, NaN])), single ([y, NaN]), eps ("single")) - -## Test input validation -%!error stdnormal_pdf () -%!error stdnormal_pdf (1,2) -%!error stdnormal_pdf (i)
--- a/scripts/statistics/distributions/stdnormal_rnd.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,73 +0,0 @@ -## Copyright (C) 2012 Rik Wehbring -## Copyright (C) 1995-2016 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} stdnormal_rnd (@var{r}) -## @deftypefnx {} {} stdnormal_rnd (@var{r}, @var{c}, @dots{}) -## @deftypefnx {} {} stdnormal_rnd ([@var{sz}]) -## Return a matrix of random samples from the standard normal distribution -## (mean = 0, standard deviation = 1). -## -## When called with a single size argument, return a square matrix with -## the dimension specified. When called with more than one scalar argument the -## first two arguments are taken as the number of rows and columns and any -## further arguments specify additional matrix dimensions. The size may also -## be specified with a vector of dimensions @var{sz}. -## @end deftypefn - -## Author: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: Random deviates from the standard normal distribution - -function rnd = stdnormal_rnd (varargin) - - if (nargin < 1) - print_usage (); - endif - - if (nargin == 1) - if (isscalar (varargin{1}) && varargin{1} >= 0) - sz = [varargin{1}, varargin{1}]; - elseif (isrow (varargin{1}) && all (varargin{1} >= 0)) - sz = varargin{1}; - else - error ("stdnormal_rnd: dimension vector must be row vector of non-negative integers"); - endif - elseif (nargin > 1) - if (any (cellfun (@(x) (! isscalar (x) || x < 0), varargin))) - error ("stdnormal_rnd: dimensions must be non-negative integers"); - endif - sz = [varargin{:}]; - endif - - rnd = randn (sz); - -endfunction - - -%!assert (size (stdnormal_rnd (3)), [3, 3]) -%!assert (size (stdnormal_rnd ([4 1])), [4, 1]) -%!assert (size (stdnormal_rnd (4,1)), [4, 1]) - -## Test input validation -%!error stdnormal_rnd () -%!error stdnormal_rnd (-1) -%!error stdnormal_rnd (ones (2)) -%!error stdnormal_rnd ([2 -1 2]) -%!error stdnormal_rnd (1, ones (2)) -%!error stdnormal_rnd (1, -1)
--- a/scripts/statistics/distributions/tcdf.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,159 +0,0 @@ -## Copyright (C) 2013-2017 Julien Bect -## Copyright (C) 2012 Rik Wehbring -## Copyright (C) 1995-2016 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} tcdf (@var{x}, @var{n}) -## For each element of @var{x}, compute the cumulative distribution function -## (CDF) at @var{x} of the t (Student) distribution with -## @var{n} degrees of freedom. -## @end deftypefn - -## Author: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: CDF of the t distribution - -function cdf = tcdf (x, n) - - if (nargin != 2) - print_usage (); - endif - - if (! isscalar (n)) - [retval, x, n] = common_size (x, n); - if (retval > 0) - error ("tcdf: X and N must be of common size or scalars"); - endif - endif - - if (iscomplex (x) || iscomplex (n)) - error ("tcdf: X and N must not be complex"); - endif - - if (isa (x, "single") || isa (n, "single")) - cdf = zeros (size (x), "single"); - else - cdf = zeros (size (x)); - endif - - k = ! isinf (x) & (n > 0); - - xx = x .^ 2; - x_big_abs = (xx > n); - - ## deal with the case "abs(x) big" - kk = k & x_big_abs; - if (isscalar (n)) - cdf(kk) = betainc (n ./ (n + xx(kk)), n/2, 1/2) / 2; - else - cdf(kk) = betainc (n(kk) ./ (n(kk) + xx(kk)), n(kk)/2, 1/2) / 2; - endif - - ## deal with the case "abs(x) small" - kk = k & ! x_big_abs; - if (isscalar (n)) - cdf(kk) = 0.5 * (1 - betainc (xx(kk) ./ (n + xx(kk)), 1/2, n/2)); - else - cdf(kk) = 0.5 * (1 - betainc (xx(kk) ./ (n(kk) + xx(kk)), 1/2, n(kk)/2)); - endif - - k &= (x > 0); - if (any (k(:))) - cdf(k) = 1 - cdf(k); - endif - - k = isnan (x) | !(n > 0); - cdf(k) = NaN; - - k = (x == Inf) & (n > 0); - cdf(k) = 1; - -endfunction - - -%!shared x,y -%! x = [-Inf 0 1 Inf]; -%! y = [0 1/2 3/4 1]; -%!assert (tcdf (x, ones (1,4)), y, eps) -%!assert (tcdf (x, 1), y, eps) -%!assert (tcdf (x, [0 1 NaN 1]), [NaN 1/2 NaN 1], eps) -%!assert (tcdf ([x(1:2) NaN x(4)], 1), [y(1:2) NaN y(4)], eps) - -## Test class of input preserved -%!assert (tcdf ([x, NaN], 1), [y, NaN], eps) -%!assert (tcdf (single ([x, NaN]), 1), single ([y, NaN]), eps ("single")) -%!assert (tcdf ([x, NaN], single (1)), single ([y, NaN]), eps ("single")) - -## Test input validation -%!error tcdf () -%!error tcdf (1) -%!error tcdf (1,2,3) -%!error tcdf (ones (3), ones (2)) -%!error tcdf (ones (2), ones (3)) -%!error tcdf (i, 2) -%!error tcdf (2, i) - -## Check some reference values - -%!shared tol_rel -%! tol_rel = 10 * eps; - -## check accuracy for small positive values -%!assert (tcdf (10^(-10), 2.5), 0.50000000003618087, -tol_rel) -%!assert (tcdf (10^(-11), 2.5), 0.50000000000361809, -tol_rel) -%!assert (tcdf (10^(-12), 2.5), 0.50000000000036181, -tol_rel) -%!assert (tcdf (10^(-13), 2.5), 0.50000000000003618, -tol_rel) -%!assert (tcdf (10^(-14), 2.5), 0.50000000000000362, -tol_rel) -%!assert (tcdf (10^(-15), 2.5), 0.50000000000000036, -tol_rel) -%!assert (tcdf (10^(-16), 2.5), 0.50000000000000004, -tol_rel) - -## check accuracy for large negative values -%!assert (tcdf (-10^1, 2.5), 2.2207478836537124e-03, -tol_rel) -%!assert (tcdf (-10^2, 2.5), 7.1916492116661878e-06, -tol_rel) -%!assert (tcdf (-10^3, 2.5), 2.2747463948307452e-08, -tol_rel) -%!assert (tcdf (-10^4, 2.5), 7.1933970159922115e-11, -tol_rel) -%!assert (tcdf (-10^5, 2.5), 2.2747519231756221e-13, -tol_rel) - -## # Reference values obtained using Python 2.7.4 and mpmath 0.17 -## -## from mpmath import * -## -## mp.dps = 100 -## -## def F(x_in, nu_in): -## x = mpf(x_in); -## nu = mpf(nu_in); -## t = nu / (nu + x*x) -## a = nu / 2 -## b = mpf(0.5) -## F = betainc(a, b, 0, t, regularized=True) / 2 -## if (x > 0): -## F = 1 - F -## return F -## -## nu = 2.5 -## -## for i in range(1, 6): -## x = - power(mpf(10), mpf(i)) -## print "%%!assert (tcdf (-10^%d, 2.5), %s, -eps)" \ -## % (i, nstr(F(x, nu), 17)) -## -## for i in range(10, 17): -## x = power(mpf(10), -mpf(i)) -## print "%%!assert (tcdf (10^(-%d), 2.5), %s, -eps)" \ -## % (i, nstr(F(x, nu), 17))
--- a/scripts/statistics/distributions/tinv.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,109 +0,0 @@ -## Copyright (C) 2012 Rik Wehbring -## Copyright (C) 1995-2016 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} tinv (@var{x}, @var{n}) -## For each element of @var{x}, compute the quantile (the inverse of the CDF) -## at @var{x} of the t (Student) distribution with @var{n} -## degrees of freedom. -## -## This function is analogous to looking in a table for the t-value of a -## single-tailed distribution. -## @end deftypefn - -## For very large n, the "correct" formula does not really work well, -## and the quantiles of the standard normal distribution are used -## directly. - -## Author: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: Quantile function of the t distribution - -function inv = tinv (x, n) - - if (nargin != 2) - print_usage (); - endif - - if (! isscalar (n)) - [retval, x, n] = common_size (x, n); - if (retval > 0) - error ("tinv: X and N must be of common size or scalars"); - endif - endif - - if (iscomplex (x) || iscomplex (n)) - error ("tinv: X and N must not be complex"); - endif - - if (isa (x, "single") || isa (n, "single")) - inv = NaN (size (x), "single"); - else - inv = NaN (size (x)); - endif - - k = (x == 0) & (n > 0); - inv(k) = -Inf; - - k = (x == 1) & (n > 0); - inv(k) = Inf; - - if (isscalar (n)) - k = (x > 0) & (x < 1); - if ((n > 0) && (n < 10000)) - inv(k) = (sign (x(k) - 1/2) - .* sqrt (n * (1 ./ betainv (2*min (x(k), 1 - x(k)), - n/2, 1/2) - 1))); - elseif (n >= 10000) - ## For large n, use the quantiles of the standard normal - inv(k) = stdnormal_inv (x(k)); - endif - else - k = (x > 0) & (x < 1) & (n > 0) & (n < 10000); - inv(k) = (sign (x(k) - 1/2) - .* sqrt (n(k) .* (1 ./ betainv (2*min (x(k), 1 - x(k)), - n(k)/2, 1/2) - 1))); - - ## For large n, use the quantiles of the standard normal - k = (x > 0) & (x < 1) & (n >= 10000); - inv(k) = stdnormal_inv (x(k)); - endif - -endfunction - - -%!shared x -%! x = [-1 0 0.5 1 2]; -%!assert (tinv (x, ones (1,5)), [NaN -Inf 0 Inf NaN]) -%!assert (tinv (x, 1), [NaN -Inf 0 Inf NaN], eps) -%!assert (tinv (x, [1 0 NaN 1 1]), [NaN NaN NaN Inf NaN], eps) -%!assert (tinv ([x(1:2) NaN x(4:5)], 1), [NaN -Inf NaN Inf NaN]) - -## Test class of input preserved -%!assert (tinv ([x, NaN], 1), [NaN -Inf 0 Inf NaN NaN], eps) -%!assert (tinv (single ([x, NaN]), 1), single ([NaN -Inf 0 Inf NaN NaN]), eps ("single")) -%!assert (tinv ([x, NaN], single (1)), single ([NaN -Inf 0 Inf NaN NaN]), eps ("single")) - -## Test input validation -%!error tinv () -%!error tinv (1) -%!error tinv (1,2,3) -%!error tinv (ones (3), ones (2)) -%!error tinv (ones (2), ones (3)) -%!error tinv (i, 2) -%!error tinv (2, i)
--- a/scripts/statistics/distributions/tpdf.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,92 +0,0 @@ -## Copyright (C) 2012 Rik Wehbring -## Copyright (C) 1995-2016 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} tpdf (@var{x}, @var{n}) -## For each element of @var{x}, compute the probability density function (PDF) -## at @var{x} of the @var{t} (Student) distribution with -## @var{n} degrees of freedom. -## @end deftypefn - -## Author: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: PDF of the t distribution - -function pdf = tpdf (x, n) - - if (nargin != 2) - print_usage (); - endif - - if (! isscalar (n)) - [retval, x, n] = common_size (x, n); - if (retval > 0) - error ("tpdf: X and N must be of common size or scalars"); - endif - endif - - if (iscomplex (x) || iscomplex (n)) - error ("tpdf: X and N must not be complex"); - endif - - if (isa (x, "single") || isa (n, "single")) - pdf = zeros (size (x), "single"); - else - pdf = zeros (size (x)); - endif - - k = isnan (x) | !(n > 0) | !(n < Inf); - pdf(k) = NaN; - - k = isfinite (x) & (n > 0) & (n < Inf); - if (isscalar (n)) - pdf(k) = (exp (- (n + 1) * log (1 + x(k) .^ 2 / n)/2) - / (sqrt (n) * beta (n/2, 1/2))); - else - pdf(k) = (exp (- (n(k) + 1) .* log (1 + x(k) .^ 2 ./ n(k))/2) - ./ (sqrt (n(k)) .* beta (n(k)/2, 1/2))); - endif - -endfunction - - -%!test -%! x = rand (10,1); -%! y = 1./(pi * (1 + x.^2)); -%! assert (tpdf (x, 1), y, 5*eps); - -%!shared x,y -%! x = [-Inf 0 0.5 1 Inf]; -%! y = 1./(pi * (1 + x.^2)); -%!assert (tpdf (x, ones (1,5)), y, eps) -%!assert (tpdf (x, 1), y, eps) -%!assert (tpdf (x, [0 NaN 1 1 1]), [NaN NaN y(3:5)], eps) - -## Test class of input preserved -%!assert (tpdf ([x, NaN], 1), [y, NaN], eps) -%!assert (tpdf (single ([x, NaN]), 1), single ([y, NaN]), eps ("single")) -%!assert (tpdf ([x, NaN], single (1)), single ([y, NaN]), eps ("single")) - -## Test input validation -%!error tpdf () -%!error tpdf (1) -%!error tpdf (1,2,3) -%!error tpdf (ones (3), ones (2)) -%!error tpdf (ones (2), ones (3)) -%!error tpdf (i, 2) -%!error tpdf (2, i)
--- a/scripts/statistics/distributions/trnd.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,117 +0,0 @@ -## Copyright (C) 2012 Rik Wehbring -## Copyright (C) 1995-2016 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} trnd (@var{n}) -## @deftypefnx {} {} trnd (@var{n}, @var{r}) -## @deftypefnx {} {} trnd (@var{n}, @var{r}, @var{c}, @dots{}) -## @deftypefnx {} {} trnd (@var{n}, [@var{sz}]) -## Return a matrix of random samples from the t (Student) distribution with -## @var{n} degrees of freedom. -## -## When called with a single size argument, return a square matrix with -## the dimension specified. When called with more than one scalar argument the -## first two arguments are taken as the number of rows and columns and any -## further arguments specify additional matrix dimensions. The size may also -## be specified with a vector of dimensions @var{sz}. -## -## If no size arguments are given then the result matrix is the size of -## @var{n}. -## @end deftypefn - -## Author: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: Random deviates from the t distribution - -function rnd = trnd (n, varargin) - - if (nargin < 1) - print_usage (); - endif - - if (nargin == 1) - sz = size (n); - elseif (nargin == 2) - if (isscalar (varargin{1}) && varargin{1} >= 0) - sz = [varargin{1}, varargin{1}]; - elseif (isrow (varargin{1}) && all (varargin{1} >= 0)) - sz = varargin{1}; - else - error ("trnd: dimension vector must be row vector of non-negative integers"); - endif - elseif (nargin > 2) - if (any (cellfun (@(x) (! isscalar (x) || x < 0), varargin))) - error ("trnd: dimensions must be non-negative integers"); - endif - sz = [varargin{:}]; - endif - - if (! isscalar (n) && ! isequal (size (n), sz)) - error ("trnd: N must be scalar or of size SZ"); - endif - - if (iscomplex (n)) - error ("trnd: N must not be complex"); - endif - - if (isa (n, "single")) - cls = "single"; - else - cls = "double"; - endif - - if (isscalar (n)) - if ((n > 0) && (n < Inf)) - rnd = randn (sz, cls) ./ sqrt (2*randg (n/2, sz, cls) / n); - else - rnd = NaN (sz, cls); - endif - else - rnd = NaN (sz, cls); - - k = (n > 0) & (n < Inf); - rnd(k) = randn (sum (k(:)), 1, cls) ... - ./ sqrt (2*randg (n(k)/2, cls) ./ n(k))(:); - endif - -endfunction - - -%!assert (size (trnd (2)), [1, 1]) -%!assert (size (trnd (ones (2,1))), [2, 1]) -%!assert (size (trnd (ones (2,2))), [2, 2]) -%!assert (size (trnd (1, 3)), [3, 3]) -%!assert (size (trnd (1, [4 1])), [4, 1]) -%!assert (size (trnd (1, 4, 1)), [4, 1]) - -## Test class of input preserved -%!assert (class (trnd (1)), "double") -%!assert (class (trnd (single (1))), "single") -%!assert (class (trnd (single ([1 1]))), "single") - -## Test input validation -%!error trnd () -%!error trnd (1, -1) -%!error trnd (1, ones (2)) -%!error trnd (i) -%!error trnd (1, [2 -1 2]) -%!error trnd (1, 2, ones (2)) -%!error trnd (1, 2, -1) -%!error trnd (ones (2,2), 3) -%!error trnd (ones (2,2), [3, 2]) -%!error trnd (ones (2,2), 2, 3)
--- a/scripts/statistics/distributions/unidcdf.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,88 +0,0 @@ -## Copyright (C) 2012 Rik Wehbring -## Copyright (C) 2007-2016 David Bateman -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} unidcdf (@var{x}, @var{n}) -## For each element of @var{x}, compute the cumulative distribution function -## (CDF) at @var{x} of a discrete uniform distribution which assumes -## the integer values 1--@var{n} with equal probability. -## @end deftypefn - -function cdf = unidcdf (x, n) - - if (nargin != 2) - print_usage (); - endif - - if (! isscalar (n)) - [retval, x, n] = common_size (x, n); - if (retval > 0) - error ("unidcdf: X and N must be of common size or scalars"); - endif - endif - - if (iscomplex (x) || iscomplex (n)) - error ("unidcdf: X and N must not be complex"); - endif - - if (isa (x, "single") || isa (n, "single")) - cdf = zeros (size (x), "single"); - else - cdf = zeros (size (x)); - endif - - knan = isnan (x) | ! (n > 0 & n == fix (n)); - if (any (knan(:))) - cdf(knan) = NaN; - endif - - k = (x >= n) & ! knan; - cdf(k) = 1; - - k = (x >= 1) & (x < n) & ! knan; - if (isscalar (n)) - cdf(k) = floor (x(k)) / n; - else - cdf(k) = floor (x(k)) ./ n(k); - endif - -endfunction - - -%!shared x,y -%! x = [0 1 2.5 10 11]; -%! y = [0, 0.1 0.2 1.0 1.0]; -%!assert (unidcdf (x, 10*ones (1,5)), y) -%!assert (unidcdf (x, 10), y) -%!assert (unidcdf (x, 10*[0 1 NaN 1 1]), [NaN 0.1 NaN y(4:5)]) -%!assert (unidcdf ([x(1:2) NaN Inf x(5)], 10), [y(1:2) NaN 1 y(5)]) - -## Test class of input preserved -%!assert (unidcdf ([x, NaN], 10), [y, NaN]) -%!assert (unidcdf (single ([x, NaN]), 10), single ([y, NaN])) -%!assert (unidcdf ([x, NaN], single (10)), single ([y, NaN])) - -## Test input validation -%!error unidcdf () -%!error unidcdf (1) -%!error unidcdf (1,2,3) -%!error unidcdf (ones (3), ones (2)) -%!error unidcdf (ones (2), ones (3)) -%!error unidcdf (i, 2) -%!error unidcdf (2, i)
--- a/scripts/statistics/distributions/unidinv.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,80 +0,0 @@ -## Copyright (C) 2012 Rik Wehbring -## Copyright (C) 2007-2016 David Bateman -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} unidinv (@var{x}, @var{n}) -## For each element of @var{x}, compute the quantile (the inverse of the CDF) -## at @var{x} of the discrete uniform distribution which assumes -## the integer values 1--@var{n} with equal probability. -## @end deftypefn - -function inv = unidinv (x, n) - - if (nargin != 2) - print_usage (); - endif - - if (! isscalar (n)) - [retval, x, n] = common_size (x, n); - if (retval > 0) - error ("unidcdf: X and N must be of common size or scalars"); - endif - endif - - if (iscomplex (x) || iscomplex (n)) - error ("unidinv: X and N must not be complex"); - endif - - if (isa (x, "single") || isa (n, "single")) - inv = NaN (size (x), "single"); - else - inv = NaN (size (x)); - endif - - ## For Matlab compatibility, unidinv(0) = NaN - k = (x > 0) & (x <= 1) & (n > 0 & n == fix (n)); - if (isscalar (n)) - inv(k) = floor (x(k) * n); - else - inv(k) = floor (x(k) .* n(k)); - endif - -endfunction - - -%!shared x -%! x = [-1 0 0.5 1 2]; -%!assert (unidinv (x, 10*ones (1,5)), [NaN NaN 5 10 NaN], eps) -%!assert (unidinv (x, 10), [NaN NaN 5 10 NaN], eps) -%!assert (unidinv (x, 10*[0 1 NaN 1 1]), [NaN NaN NaN 10 NaN], eps) -%!assert (unidinv ([x(1:2) NaN x(4:5)], 10), [NaN NaN NaN 10 NaN], eps) - -## Test class of input preserved -%!assert (unidinv ([x, NaN], 10), [NaN NaN 5 10 NaN NaN], eps) -%!assert (unidinv (single ([x, NaN]), 10), single ([NaN NaN 5 10 NaN NaN]), eps) -%!assert (unidinv ([x, NaN], single (10)), single ([NaN NaN 5 10 NaN NaN]), eps) - -## Test input validation -%!error unidinv () -%!error unidinv (1) -%!error unidinv (1,2,3) -%!error unidinv (ones (3), ones (2)) -%!error unidinv (ones (2), ones (3)) -%!error unidinv (i, 2) -%!error unidinv (2, i)
--- a/scripts/statistics/distributions/unidpdf.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,86 +0,0 @@ -## Copyright (C) 2012 Rik Wehbring -## Copyright (C) 2007-2016 David Bateman -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} unidpdf (@var{x}, @var{n}) -## For each element of @var{x}, compute the probability density function (PDF) -## at @var{x} of a discrete uniform distribution which assumes -## the integer values 1--@var{n} with equal probability. -## -## Warning: The underlying implementation uses the double class and will only -## be accurate for @var{n} < @code{flintmax} (@w{@math{2^{53}}} on -## IEEE 754 compatible systems). -## @end deftypefn - -function pdf = unidpdf (x, n) - - if (nargin != 2) - print_usage (); - endif - - if (! isscalar (n)) - [retval, x, n] = common_size (x, n); - if (retval > 0) - error ("unidpdf: X and N must be of common size or scalars"); - endif - endif - - if (iscomplex (x) || iscomplex (n)) - error ("unidpdf: X and N must not be complex"); - endif - - if (isa (x, "single") || isa (n, "single")) - pdf = zeros (size (x), "single"); - else - pdf = zeros (size (x)); - endif - - k = isnan (x) | ! (n > 0 & n == fix (n)); - pdf(k) = NaN; - - k = ! k & (x >= 1) & (x <= n) & (x == fix (x)); - if (isscalar (n)) - pdf(k) = 1 / n; - else - pdf(k) = 1 ./ n(k); - endif - -endfunction - - -%!shared x,y -%! x = [-1 0 1 2 10 11]; -%! y = [0 0 0.1 0.1 0.1 0]; -%!assert (unidpdf (x, 10*ones (1,6)), y) -%!assert (unidpdf (x, 10), y) -%!assert (unidpdf (x, 10*[0 NaN 1 1 1 1]), [NaN NaN y(3:6)]) -%!assert (unidpdf ([x, NaN], 10), [y, NaN]) - -## Test class of input preserved -%!assert (unidpdf (single ([x, NaN]), 10), single ([y, NaN])) -%!assert (unidpdf ([x, NaN], single (10)), single ([y, NaN])) - -## Test input validation -%!error unidpdf () -%!error unidpdf (1) -%!error unidpdf (1,2,3) -%!error unidpdf (ones (3), ones (2)) -%!error unidpdf (ones (2), ones (3)) -%!error unidpdf (i, 2) -%!error unidpdf (2, i)
--- a/scripts/statistics/distributions/unidrnd.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,111 +0,0 @@ -## Copyright (C) 2012 Rik Wehbring -## Copyright (C) 2005-2016 John W. Eaton -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} unidrnd (@var{n}) -## @deftypefnx {} {} unidrnd (@var{n}, @var{r}) -## @deftypefnx {} {} unidrnd (@var{n}, @var{r}, @var{c}, @dots{}) -## @deftypefnx {} {} unidrnd (@var{n}, [@var{sz}]) -## Return a matrix of random samples from the discrete uniform distribution -## which assumes the integer values 1--@var{n} with equal probability. -## -## @var{n} may be a scalar or a multi-dimensional array. -## -## When called with a single size argument, return a square matrix with -## the dimension specified. When called with more than one scalar argument the -## first two arguments are taken as the number of rows and columns and any -## further arguments specify additional matrix dimensions. The size may also -## be specified with a vector of dimensions @var{sz}. -## -## If no size arguments are given then the result matrix is the size of -## @var{n}. -## @end deftypefn - -## Author: jwe - -function rnd = unidrnd (n, varargin) - - if (nargin < 1) - print_usage (); - endif - - if (nargin == 1) - sz = size (n); - elseif (nargin == 2) - if (isscalar (varargin{1}) && varargin{1} >= 0) - sz = [varargin{1}, varargin{1}]; - elseif (isrow (varargin{1}) && all (varargin{1} >= 0)) - sz = varargin{1}; - else - error ("unidrnd: dimension vector must be row vector of non-negative integers"); - endif - elseif (nargin > 2) - if (any (cellfun (@(x) (! isscalar (x) || x < 0), varargin))) - error ("unidrnd: dimensions must be non-negative integers"); - endif - sz = [varargin{:}]; - endif - - if (! isscalar (n) && ! isequal (size (n), sz)) - error ("unidrnd: N must be scalar or of size SZ"); - endif - - if (iscomplex (n)) - error ("unidrnd: N must not be complex"); - endif - - if (isa (n, "single")) - cls = "single"; - else - cls = "double"; - endif - - if (isscalar (n)) - if (n > 0 && n == fix (n)) - rnd = ceil (rand (sz, cls) * n); - else - rnd = NaN (sz, cls); - endif - else - rnd = ceil (rand (sz, cls) .* n); - - k = ! (n > 0 & n == fix (n)); - rnd(k) = NaN; - endif - -endfunction - - -%!assert (size (unidrnd (2)), [1, 1]) -%!assert (size (unidrnd (ones (2,1))), [2, 1]) -%!assert (size (unidrnd (ones (2,2))), [2, 2]) -%!assert (size (unidrnd (10, [4 1])), [4, 1]) -%!assert (size (unidrnd (10, 4, 1)), [4, 1]) - -## Test class of input preserved -%!assert (class (unidrnd (2)), "double") -%!assert (class (unidrnd (single (2))), "single") -%!assert (class (unidrnd (single ([2 2]))), "single") - -## Test input validation -%!error unidrnd () -%!error unidrnd (10, [1;2;3]) -%!error unidrnd (10, 2, ones (2)) -%!error unidrnd (10*ones (2), 2, 1) -%!error unidrnd (i)
--- a/scripts/statistics/distributions/unifcdf.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,97 +0,0 @@ -## Copyright (C) 2012 Rik Wehbring -## Copyright (C) 1995-2016 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} unifcdf (@var{x}) -## @deftypefnx {} {} unifcdf (@var{x}, @var{a}, @var{b}) -## For each element of @var{x}, compute the cumulative distribution function -## (CDF) at @var{x} of the uniform distribution on the interval -## [@var{a}, @var{b}]. -## -## Default values are @var{a} = 0, @var{b} = 1. -## @end deftypefn - -## Author: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: CDF of the uniform distribution - -function cdf = unifcdf (x, a = 0, b = 1) - - if (nargin != 1 && nargin != 3) - print_usage (); - endif - - if (! isscalar (a) || ! isscalar (b)) - [retval, x, a, b] = common_size (x, a, b); - if (retval > 0) - error ("unifcdf: X, A, and B must be of common size or scalars"); - endif - endif - - if (iscomplex (x) || iscomplex (a) || iscomplex (b)) - error ("unifcdf: X, A, and B must not be complex"); - endif - - if (isa (x, "single") || isa (a, "single") || isa (b, "single")) - cdf = zeros (size (x), "single"); - else - cdf = zeros (size (x)); - endif - - k = isnan (x) | !(a < b); - cdf(k) = NaN; - - k = (x >= b) & (a < b); - cdf(k) = 1; - - k = (x > a) & (x < b); - if (isscalar (a) && isscalar (b)) - cdf(k) = (x(k) < b) .* (x(k) - a) / (b - a); - else - cdf(k) = (x(k) < b(k)) .* (x(k) - a(k)) ./ (b(k) - a(k)); - endif - -endfunction - - -%!shared x,y -%! x = [-1 0 0.5 1 2] + 1; -%! y = [0 0 0.5 1 1]; -%!assert (unifcdf (x, ones (1,5), 2*ones (1,5)), y) -%!assert (unifcdf (x, 1, 2*ones (1,5)), y) -%!assert (unifcdf (x, ones (1,5), 2), y) -%!assert (unifcdf (x, [2 1 NaN 1 1], 2), [NaN 0 NaN 1 1]) -%!assert (unifcdf (x, 1, 2*[0 1 NaN 1 1]), [NaN 0 NaN 1 1]) -%!assert (unifcdf ([x(1:2) NaN x(4:5)], 1, 2), [y(1:2) NaN y(4:5)]) - -## Test class of input preserved -%!assert (unifcdf ([x, NaN], 1, 2), [y, NaN]) -%!assert (unifcdf (single ([x, NaN]), 1, 2), single ([y, NaN])) -%!assert (unifcdf ([x, NaN], single (1), 2), single ([y, NaN])) -%!assert (unifcdf ([x, NaN], 1, single (2)), single ([y, NaN])) - -## Test input validation -%!error unifcdf () -%!error unifcdf (1,2) -%!error unifcdf (1,2,3,4) -%!error unifcdf (ones (3), ones (2), ones (2)) -%!error unifcdf (ones (2), ones (3), ones (2)) -%!error unifcdf (ones (2), ones (2), ones (3)) -%!error unifcdf (i, 2, 2) -%!error unifcdf (2, i, 2) -%!error unifcdf (2, 2, i)
--- a/scripts/statistics/distributions/unifinv.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,89 +0,0 @@ -## Copyright (C) 2012 Rik Wehbring -## Copyright (C) 1995-2016 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} unifinv (@var{x}) -## @deftypefnx {} {} unifinv (@var{x}, @var{a}, @var{b}) -## For each element of @var{x}, compute the quantile (the inverse of the CDF) -## at @var{x} of the uniform distribution on the interval [@var{a}, @var{b}]. -## -## Default values are @var{a} = 0, @var{b} = 1. -## @end deftypefn - -## Author: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: Quantile function of the uniform distribution - -function inv = unifinv (x, a = 0, b = 1) - - if (nargin != 1 && nargin != 3) - print_usage (); - endif - - if (! isscalar (a) || ! isscalar (b)) - [retval, x, a, b] = common_size (x, a, b); - if (retval > 0) - error ("unifinv: X, A, and B must be of common size or scalars"); - endif - endif - - if (iscomplex (x) || iscomplex (a) || iscomplex (b)) - error ("unifinv: X, A, and B must not be complex"); - endif - - if (isa (x, "single") || isa (a, "single") || isa (b, "single")) - inv = NaN (size (x), "single"); - else - inv = NaN (size (x)); - endif - - k = (x >= 0) & (x <= 1) & (a < b); - if (isscalar (a) && isscalar (b)) - inv(k) = a + x(k) * (b - a); - else - inv(k) = a(k) + x(k) .* (b(k) - a(k)); - endif - -endfunction - - -%!shared x -%! x = [-1 0 0.5 1 2]; -%!assert (unifinv (x, ones (1,5), 2*ones (1,5)), [NaN 1 1.5 2 NaN]) -%!assert (unifinv (x, 1, 2*ones (1,5)), [NaN 1 1.5 2 NaN]) -%!assert (unifinv (x, ones (1,5), 2), [NaN 1 1.5 2 NaN]) -%!assert (unifinv (x, [1 2 NaN 1 1], 2), [NaN NaN NaN 2 NaN]) -%!assert (unifinv (x, 1, 2*[1 0 NaN 1 1]), [NaN NaN NaN 2 NaN]) -%!assert (unifinv ([x(1:2) NaN x(4:5)], 1, 2), [NaN 1 NaN 2 NaN]) - -## Test class of input preserved -%!assert (unifinv ([x, NaN], 1, 2), [NaN 1 1.5 2 NaN NaN]) -%!assert (unifinv (single ([x, NaN]), 1, 2), single ([NaN 1 1.5 2 NaN NaN])) -%!assert (unifinv ([x, NaN], single (1), 2), single ([NaN 1 1.5 2 NaN NaN])) -%!assert (unifinv ([x, NaN], 1, single (2)), single ([NaN 1 1.5 2 NaN NaN])) - -## Test input validation -%!error unifinv () -%!error unifinv (1,2) -%!error unifinv (1,2,3,4) -%!error unifinv (ones (3), ones (2), ones (2)) -%!error unifinv (ones (2), ones (3), ones (2)) -%!error unifinv (ones (2), ones (2), ones (3)) -%!error unifinv (i, 2, 2) -%!error unifinv (2, i, 2) -%!error unifinv (2, 2, i)
--- a/scripts/statistics/distributions/unifpdf.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,92 +0,0 @@ -## Copyright (C) 2012 Rik Wehbring -## Copyright (C) 1995-2016 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} unifpdf (@var{x}) -## @deftypefnx {} {} unifpdf (@var{x}, @var{a}, @var{b}) -## For each element of @var{x}, compute the probability density function (PDF) -## at @var{x} of the uniform distribution on the interval [@var{a}, @var{b}]. -## -## Default values are @var{a} = 0, @var{b} = 1. -## @end deftypefn - -## Author: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: PDF of the uniform distribution - -function pdf = unifpdf (x, a = 0, b = 1) - - if (nargin != 1 && nargin != 3) - print_usage (); - endif - - if (! isscalar (a) || ! isscalar (b)) - [retval, x, a, b] = common_size (x, a, b); - if (retval > 0) - error ("unifpdf: X, A, and B must be of common size or scalars"); - endif - endif - - if (iscomplex (x) || iscomplex (a) || iscomplex (b)) - error ("unifpdf: X, A, and B must not be complex"); - endif - - if (isa (x, "single") || isa (a, "single") || isa (b, "single")) - pdf = zeros (size (x), "single"); - else - pdf = zeros (size (x)); - endif - - k = isnan (x) | !(a < b); - pdf(k) = NaN; - - k = (x >= a) & (x <= b) & (a < b); - if (isscalar (a) && isscalar (b)) - pdf(k) = 1 / (b - a); - else - pdf(k) = 1 ./ (b(k) - a(k)); - endif - -endfunction - - -%!shared x,y -%! x = [-1 0 0.5 1 2] + 1; -%! y = [0 1 1 1 0]; -%!assert (unifpdf (x, ones (1,5), 2*ones (1,5)), y) -%!assert (unifpdf (x, 1, 2*ones (1,5)), y) -%!assert (unifpdf (x, ones (1,5), 2), y) -%!assert (unifpdf (x, [2 NaN 1 1 1], 2), [NaN NaN y(3:5)]) -%!assert (unifpdf (x, 1, 2*[0 NaN 1 1 1]), [NaN NaN y(3:5)]) -%!assert (unifpdf ([x, NaN], 1, 2), [y, NaN]) - -## Test class of input preserved -%!assert (unifpdf (single ([x, NaN]), 1, 2), single ([y, NaN])) -%!assert (unifpdf (single ([x, NaN]), single (1), 2), single ([y, NaN])) -%!assert (unifpdf ([x, NaN], 1, single (2)), single ([y, NaN])) - -## Test input validation -%!error unifpdf () -%!error unifpdf (1,2) -%!error unifpdf (1,2,3,4) -%!error unifpdf (ones (3), ones (2), ones (2)) -%!error unifpdf (ones (2), ones (3), ones (2)) -%!error unifpdf (ones (2), ones (2), ones (3)) -%!error unifpdf (i, 2, 2) -%!error unifpdf (2, i, 2) -%!error unifpdf (2, 2, i)
--- a/scripts/statistics/distributions/unifrnd.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,131 +0,0 @@ -## Copyright (C) 2012 Rik Wehbring -## Copyright (C) 1995-2016 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} unifrnd (@var{a}, @var{b}) -## @deftypefnx {} {} unifrnd (@var{a}, @var{b}, @var{r}) -## @deftypefnx {} {} unifrnd (@var{a}, @var{b}, @var{r}, @var{c}, @dots{}) -## @deftypefnx {} {} unifrnd (@var{a}, @var{b}, [@var{sz}]) -## Return a matrix of random samples from the uniform distribution on -## [@var{a}, @var{b}]. -## -## When called with a single size argument, return a square matrix with -## the dimension specified. When called with more than one scalar argument the -## first two arguments are taken as the number of rows and columns and any -## further arguments specify additional matrix dimensions. The size may also -## be specified with a vector of dimensions @var{sz}. -## -## If no size arguments are given then the result matrix is the common size of -## @var{a} and @var{b}. -## @end deftypefn - -## Author: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: Random deviates from the uniform distribution - -function rnd = unifrnd (a, b, varargin) - - if (nargin < 2) - print_usage (); - endif - - if (! isscalar (a) || ! isscalar (b)) - [retval, a, b] = common_size (a, b); - if (retval > 0) - error ("unifrnd: A and B must be of common size or scalars"); - endif - endif - - if (iscomplex (a) || iscomplex (b)) - error ("unifrnd: A and B must not be complex"); - endif - - if (nargin == 2) - sz = size (a); - elseif (nargin == 3) - if (isscalar (varargin{1}) && varargin{1} >= 0) - sz = [varargin{1}, varargin{1}]; - elseif (isrow (varargin{1}) && all (varargin{1} >= 0)) - sz = varargin{1}; - else - error ("unifrnd: dimension vector must be row vector of non-negative integers"); - endif - elseif (nargin > 3) - if (any (cellfun (@(x) (! isscalar (x) || x < 0), varargin))) - error ("unifrnd: dimensions must be non-negative integers"); - endif - sz = [varargin{:}]; - endif - - if (! isscalar (a) && ! isequal (size (a), sz)) - error ("unifrnd: A and B must be scalar or of size SZ"); - endif - - if (isa (a, "single") || isa (b, "single")) - cls = "single"; - else - cls = "double"; - endif - - if (isscalar (a) && isscalar (b)) - if ((-Inf < a) && (a < b) && (b < Inf)) - rnd = a + (b - a) * rand (sz, cls); - else - rnd = NaN (sz, cls); - endif - else - rnd = a + (b - a) .* rand (sz, cls); - - k = !(-Inf < a) | !(a < b) | !(b < Inf); - rnd(k) = NaN; - endif - -endfunction - - -%!assert (size (unifrnd (1,2)), [1, 1]) -%!assert (size (unifrnd (ones (2,1), 2)), [2, 1]) -%!assert (size (unifrnd (ones (2,2), 2)), [2, 2]) -%!assert (size (unifrnd (1, 2*ones (2,1))), [2, 1]) -%!assert (size (unifrnd (1, 2*ones (2,2))), [2, 2]) -%!assert (size (unifrnd (1, 2, 3)), [3, 3]) -%!assert (size (unifrnd (1, 2, [4 1])), [4, 1]) -%!assert (size (unifrnd (1, 2, 4, 1)), [4, 1]) - -## Test class of input preserved -%!assert (class (unifrnd (1, 2)), "double") -%!assert (class (unifrnd (single (1), 2)), "single") -%!assert (class (unifrnd (single ([1 1]), 2)), "single") -%!assert (class (unifrnd (1, single (2))), "single") -%!assert (class (unifrnd (1, single ([2 2]))), "single") - -## Test input validation -%!error unifrnd () -%!error unifrnd (1) -%!error unifrnd (ones (3), ones (2)) -%!error unifrnd (ones (2), ones (3)) -%!error unifrnd (i, 2) -%!error unifrnd (2, i) -%!error unifrnd (1,2, -1) -%!error unifrnd (1,2, ones (2)) -%!error unifrnd (1, 2, [2 -1 2]) -%!error unifrnd (1,2, 1, ones (2)) -%!error unifrnd (1,2, 1, -1) -%!error unifrnd (ones (2,2), 2, 3) -%!error unifrnd (ones (2,2), 2, [3, 2]) -%!error unifrnd (ones (2,2), 2, 2, 3)
--- a/scripts/statistics/distributions/wblcdf.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,114 +0,0 @@ -## Copyright (C) 2012 Rik Wehbring -## Copyright (C) 1995-2016 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} wblcdf (@var{x}) -## @deftypefnx {} {} wblcdf (@var{x}, @var{scale}) -## @deftypefnx {} {} wblcdf (@var{x}, @var{scale}, @var{shape}) -## Compute the cumulative distribution function (CDF) at @var{x} of the -## Weibull distribution with scale parameter @var{scale} and shape -## parameter @var{shape}. -## -## This is defined as -## @tex -## $$ 1 - e^{-({x \over scale})^{shape}} $$ -## for $x \geq 0$. -## @end tex -## @ifnottex -## -## @example -## 1 - exp (-(x/scale)^shape) -## @end example -## -## @noindent -## for @var{x} @geq{} 0. -## -## Default values are @var{scale} = 1, @var{shape} = 1. -## @end ifnottex -## @end deftypefn - -## Author: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: CDF of the Weibull distribution - -function cdf = wblcdf (x, scale = 1, shape = 1) - - if (nargin < 1 || nargin > 3) - print_usage (); - endif - - if (! isscalar (shape) || ! isscalar (scale)) - [retval, x, shape, scale] = common_size (x, shape, scale); - if (retval > 0) - error ("wblcdf: X, SCALE, and SHAPE must be of common size or scalars"); - endif - endif - - if (iscomplex (x) || iscomplex (scale) || iscomplex (shape)) - error ("wblcdf: X, SCALE, and SHAPE must not be complex"); - endif - - if (isa (x, "single") || isa (scale, "single") || isa (shape, "single")) - cdf = NaN (size (x), "single"); - else - cdf = NaN (size (x)); - endif - - ok = (shape > 0) & (shape < Inf) & (scale > 0) & (scale < Inf); - - k = (x <= 0) & ok; - cdf(k) = 0; - - k = (x == Inf) & ok; - cdf(k) = 1; - - k = (x > 0) & (x < Inf) & ok; - if (isscalar (shape) && isscalar (scale)) - cdf(k) = 1 - exp (- (x(k) / scale) .^ shape); - else - cdf(k) = 1 - exp (- (x(k) ./ scale(k)) .^ shape(k)); - endif - -endfunction - - -%!shared x,y -%! x = [-1 0 0.5 1 Inf]; -%! y = [0, 1-exp(-x(2:4)), 1]; -%!assert (wblcdf (x, ones (1,5), ones (1,5)), y) -%!assert (wblcdf (x, 1, ones (1,5)), y) -%!assert (wblcdf (x, ones (1,5), 1), y) -%!assert (wblcdf (x, [0 1 NaN Inf 1], 1), [NaN 0 NaN NaN 1]) -%!assert (wblcdf (x, 1, [0 1 NaN Inf 1]), [NaN 0 NaN NaN 1]) -%!assert (wblcdf ([x(1:2) NaN x(4:5)], 1, 1), [y(1:2) NaN y(4:5)]) - -## Test class of input preserved -%!assert (wblcdf ([x, NaN], 1, 1), [y, NaN]) -%!assert (wblcdf (single ([x, NaN]), 1, 1), single ([y, NaN])) -%!assert (wblcdf ([x, NaN], single (1), 1), single ([y, NaN])) -%!assert (wblcdf ([x, NaN], 1, single (1)), single ([y, NaN])) - -## Test input validation -%!error wblcdf () -%!error wblcdf (1,2,3,4) -%!error wblcdf (ones (3), ones (2), ones (2)) -%!error wblcdf (ones (2), ones (3), ones (2)) -%!error wblcdf (ones (2), ones (2), ones (3)) -%!error wblcdf (i, 2, 2) -%!error wblcdf (2, i, 2) -%!error wblcdf (2, 2, i)
--- a/scripts/statistics/distributions/wblinv.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,98 +0,0 @@ -## Copyright (C) 2012 Rik Wehbring -## Copyright (C) 1995-2016 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} wblinv (@var{x}) -## @deftypefnx {} {} wblinv (@var{x}, @var{scale}) -## @deftypefnx {} {} wblinv (@var{x}, @var{scale}, @var{shape}) -## Compute the quantile (the inverse of the CDF) at @var{x} of the -## Weibull distribution with scale parameter @var{scale} and -## shape parameter @var{shape}. -## -## Default values are @var{scale} = 1, @var{shape} = 1. -## @end deftypefn - -## Author: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: Quantile function of the Weibull distribution - -function inv = wblinv (x, scale = 1, shape = 1) - - if (nargin < 1 || nargin > 3) - print_usage (); - endif - - if (! isscalar (scale) || ! isscalar (shape)) - [retval, x, scale, shape] = common_size (x, scale, shape); - if (retval > 0) - error ("wblinv: X, SCALE, and SHAPE must be of common size or scalars"); - endif - endif - - if (iscomplex (x) || iscomplex (scale) || iscomplex (shape)) - error ("wblinv: X, SCALE, and SHAPE must not be complex"); - endif - - if (isa (x, "single") || isa (scale, "single") || isa (shape, "single")) - inv = NaN (size (x), "single"); - else - inv = NaN (size (x)); - endif - - ok = (scale > 0) & (scale < Inf) & (shape > 0) & (shape < Inf); - - k = (x == 0) & ok; - inv(k) = 0; - - k = (x == 1) & ok; - inv(k) = Inf; - - k = (x > 0) & (x < 1) & ok; - if (isscalar (scale) && isscalar (shape)) - inv(k) = scale * (- log (1 - x(k))) .^ (1 / shape); - else - inv(k) = scale(k) .* (- log (1 - x(k))) .^ (1 ./ shape(k)); - endif - -endfunction - - -%!shared x -%! x = [-1 0 0.63212055882855778 1 2]; -%!assert (wblinv (x, ones (1,5), ones (1,5)), [NaN 0 1 Inf NaN], eps) -%!assert (wblinv (x, 1, ones (1,5)), [NaN 0 1 Inf NaN], eps) -%!assert (wblinv (x, ones (1,5), 1), [NaN 0 1 Inf NaN], eps) -%!assert (wblinv (x, [1 -1 NaN Inf 1], 1), [NaN NaN NaN NaN NaN]) -%!assert (wblinv (x, 1, [1 -1 NaN Inf 1]), [NaN NaN NaN NaN NaN]) -%!assert (wblinv ([x(1:2) NaN x(4:5)], 1, 1), [NaN 0 NaN Inf NaN]) - -## Test class of input preserved -%!assert (wblinv ([x, NaN], 1, 1), [NaN 0 1 Inf NaN NaN], eps) -%!assert (wblinv (single ([x, NaN]), 1, 1), single ([NaN 0 1 Inf NaN NaN]), eps ("single")) -%!assert (wblinv ([x, NaN], single (1), 1), single ([NaN 0 1 Inf NaN NaN]), eps ("single")) -%!assert (wblinv ([x, NaN], 1, single (1)), single ([NaN 0 1 Inf NaN NaN]), eps ("single")) - -## Test input validation -%!error wblinv () -%!error wblinv (1,2,3,4) -%!error wblinv (ones (3), ones (2), ones (2)) -%!error wblinv (ones (2), ones (3), ones (2)) -%!error wblinv (ones (2), ones (2), ones (3)) -%!error wblinv (i, 2, 2) -%!error wblinv (2, i, 2) -%!error wblinv (2, 2, i)
--- a/scripts/statistics/distributions/wblpdf.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,113 +0,0 @@ -## Copyright (C) 2012 Rik Wehbring -## Copyright (C) 1995-2016 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} wblpdf (@var{x}) -## @deftypefnx {} {} wblpdf (@var{x}, @var{scale}) -## @deftypefnx {} {} wblpdf (@var{x}, @var{scale}, @var{shape}) -## Compute the probability density function (PDF) at @var{x} of the -## Weibull distribution with scale parameter @var{scale} and -## shape parameter @var{shape}. -## -## This is given by -## @tex -## $$ {shape \over scale^{shape}} \cdot x^{shape-1} \cdot e^{-({x \over scale})^{shape}} $$ -## @end tex -## @ifnottex -## -## @example -## shape * scale^(-shape) * x^(shape-1) * exp (-(x/scale)^shape) -## @end example -## -## @end ifnottex -## @noindent -## for @var{x} @geq{} 0. -## -## Default values are @var{scale} = 1, @var{shape} = 1. -## @end deftypefn - -## Author: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: PDF of the Weibull distribution - -function pdf = wblpdf (x, scale = 1, shape = 1) - - if (nargin < 1 || nargin > 3) - print_usage (); - endif - - if (! isscalar (scale) || ! isscalar (shape)) - [retval, x, scale, shape] = common_size (x, scale, shape); - if (retval > 0) - error ("wblpdf: X, SCALE, and SHAPE must be of common size or scalars"); - endif - endif - - if (iscomplex (x) || iscomplex (scale) || iscomplex (shape)) - error ("wblpdf: X, SCALE, and SHAPE must not be complex"); - endif - - if (isa (x, "single") || isa (scale, "single") || isa (shape, "single")) - pdf = NaN (size (x), "single"); - else - pdf = NaN (size (x)); - endif - - ok = ((scale > 0) & (scale < Inf) & (shape > 0) & (shape < Inf)); - - k = (x < 0) & ok; - pdf(k) = 0; - - k = (x >= 0) & (x < Inf) & ok; - if (isscalar (scale) && isscalar (shape)) - pdf(k) = (shape * (scale .^ -shape) - .* (x(k) .^ (shape - 1)) - .* exp (- (x(k) / scale) .^ shape)); - else - pdf(k) = (shape(k) .* (scale(k) .^ -shape(k)) - .* (x(k) .^ (shape(k) - 1)) - .* exp (- (x(k) ./ scale(k)) .^ shape(k))); - endif - -endfunction - - -%!shared x,y -%! x = [-1 0 0.5 1 Inf]; -%! y = [0, exp(-x(2:4)), NaN]; -%!assert (wblpdf (x, ones (1,5), ones (1,5)), y) -%!assert (wblpdf (x, 1, ones (1,5)), y) -%!assert (wblpdf (x, ones (1,5), 1), y) -%!assert (wblpdf (x, [0 NaN Inf 1 1], 1), [NaN NaN NaN y(4:5)]) -%!assert (wblpdf (x, 1, [0 NaN Inf 1 1]), [NaN NaN NaN y(4:5)]) -%!assert (wblpdf ([x, NaN], 1, 1), [y, NaN]) - -## Test class of input preserved -%!assert (wblpdf (single ([x, NaN]), 1, 1), single ([y, NaN])) -%!assert (wblpdf ([x, NaN], single (1), 1), single ([y, NaN])) -%!assert (wblpdf ([x, NaN], 1, single (1)), single ([y, NaN])) - -## Test input validation -%!error wblpdf () -%!error wblpdf (1,2,3,4) -%!error wblpdf (ones (3), ones (2), ones (2)) -%!error wblpdf (ones (2), ones (3), ones (2)) -%!error wblpdf (ones (2), ones (2), ones (3)) -%!error wblpdf (i, 2, 2) -%!error wblpdf (2, i, 2) -%!error wblpdf (2, 2, i)
--- a/scripts/statistics/distributions/wblrnd.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,131 +0,0 @@ -## Copyright (C) 2012 Rik Wehbring -## Copyright (C) 1995-2016 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} wblrnd (@var{scale}, @var{shape}) -## @deftypefnx {} {} wblrnd (@var{scale}, @var{shape}, @var{r}) -## @deftypefnx {} {} wblrnd (@var{scale}, @var{shape}, @var{r}, @var{c}, @dots{}) -## @deftypefnx {} {} wblrnd (@var{scale}, @var{shape}, [@var{sz}]) -## Return a matrix of random samples from the Weibull distribution with -## parameters @var{scale} and @var{shape}. -## -## When called with a single size argument, return a square matrix with -## the dimension specified. When called with more than one scalar argument the -## first two arguments are taken as the number of rows and columns and any -## further arguments specify additional matrix dimensions. The size may also -## be specified with a vector of dimensions @var{sz}. -## -## If no size arguments are given then the result matrix is the common size of -## @var{scale} and @var{shape}. -## @end deftypefn - -## Author: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: Random deviates from the Weibull distribution - -function rnd = wblrnd (scale, shape, varargin) - - if (nargin < 2) - print_usage (); - endif - - if (! isscalar (scale) || ! isscalar (shape)) - [retval, scale, shape] = common_size (scale, shape); - if (retval > 0) - error ("wblrnd: SCALE and SHAPE must be of common size or scalars"); - endif - endif - - if (iscomplex (scale) || iscomplex (shape)) - error ("wblrnd: SCALE and SHAPE must not be complex"); - endif - - if (nargin == 2) - sz = size (scale); - elseif (nargin == 3) - if (isscalar (varargin{1}) && varargin{1} >= 0) - sz = [varargin{1}, varargin{1}]; - elseif (isrow (varargin{1}) && all (varargin{1} >= 0)) - sz = varargin{1}; - else - error ("wblrnd: dimension vector must be row vector of non-negative integers"); - endif - elseif (nargin > 3) - if (any (cellfun (@(x) (! isscalar (x) || x < 0), varargin))) - error ("wblrnd: dimensions must be non-negative integers"); - endif - sz = [varargin{:}]; - endif - - if (! isscalar (scale) && ! isequal (size (scale), sz)) - error ("wblrnd: SCALE and SHAPE must be scalar or of size SZ"); - endif - - if (isa (scale, "single") || isa (shape, "single")) - cls = "single"; - else - cls = "double"; - endif - - if (isscalar (scale) && isscalar (shape)) - if ((scale > 0) && (scale < Inf) && (shape > 0) && (shape < Inf)) - rnd = scale * rande (sz, cls) .^ (1/shape); - else - rnd = NaN (sz, cls); - endif - else - rnd = scale .* rande (sz, cls) .^ (1./shape); - - k = (scale <= 0) | (scale == Inf) | (shape <= 0) | (shape == Inf); - rnd(k) = NaN; - endif - -endfunction - - -%!assert (size (wblrnd (1,2)), [1, 1]) -%!assert (size (wblrnd (ones (2,1), 2)), [2, 1]) -%!assert (size (wblrnd (ones (2,2), 2)), [2, 2]) -%!assert (size (wblrnd (1, 2*ones (2,1))), [2, 1]) -%!assert (size (wblrnd (1, 2*ones (2,2))), [2, 2]) -%!assert (size (wblrnd (1, 2, 3)), [3, 3]) -%!assert (size (wblrnd (1, 2, [4 1])), [4, 1]) -%!assert (size (wblrnd (1, 2, 4, 1)), [4, 1]) - -## Test class of input preserved -%!assert (class (wblrnd (1, 2)), "double") -%!assert (class (wblrnd (single (1), 2)), "single") -%!assert (class (wblrnd (single ([1 1]), 2)), "single") -%!assert (class (wblrnd (1, single (2))), "single") -%!assert (class (wblrnd (1, single ([2 2]))), "single") - -## Test input validation -%!error wblrnd () -%!error wblrnd (1) -%!error wblrnd (ones (3), ones (2)) -%!error wblrnd (ones (2), ones (3)) -%!error wblrnd (i, 2) -%!error wblrnd (2, i) -%!error wblrnd (1,2, -1) -%!error wblrnd (1,2, ones (2)) -%!error wblrnd (1, 2, [2 -1 2]) -%!error wblrnd (1,2, 1, ones (2)) -%!error wblrnd (1,2, 1, -1) -%!error wblrnd (ones (2,2), 2, 3) -%!error wblrnd (ones (2,2), 2, [3, 2]) -%!error wblrnd (ones (2,2), 2, 2, 3)
--- a/scripts/statistics/distributions/wienrnd.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,56 +0,0 @@ -## Copyright (C) 1995-2017 Friedrich Leisch -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} wienrnd (@var{t}, @var{d}, @var{n}) -## Return a simulated realization of the @var{d}-dimensional Wiener Process -## on the interval [0, @var{t}]. -## -## If @var{d} is omitted, @var{d} = 1 is used. The first column of the -## return matrix contains time, the remaining columns contain the Wiener -## process. -## -## The optional parameter @var{n} defines the number of summands used for -## simulating the process over an interval of length 1. If @var{n} is -## omitted, @var{n} = 1000 is used. -## @end deftypefn - -## Author: FL <Friedrich.Leisch@ci.tuwien.ac.at> -## Description: Simulate a Wiener process - -function retval = wienrnd (t, d, n) - - if (nargin == 1) - d = 1; - n = 1000; - elseif (nargin == 2) - n = 1000; - elseif (nargin > 3) - print_usage (); - endif - - if (! isscalar (t) || ! isscalar (d) || ! isscalar (n)) - error ("wienrnd: T, D and N must all be positive integers"); - endif - - retval = randn (n * t, d); - retval = cumsum (retval) / sqrt (n); - - retval = [((1: n*t)' / n), retval]; - -endfunction
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/scripts/statistics/empirical_cdf.m Sun Jan 07 17:13:23 2018 -0800 @@ -0,0 +1,61 @@ +## Copyright (C) 2012 Rik Wehbring +## Copyright (C) 1996-2016 Kurt Hornik +## +## This file is part of Octave. +## +## Octave is free software: you can redistribute it and/or modify it +## under the terms of the GNU General Public License as published by +## the Free Software Foundation, either version 3 of the License, or +## (at your option) any later version. +## +## Octave is distributed in the hope that it will be useful, but +## WITHOUT ANY WARRANTY; without even the implied warranty of +## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +## GNU General Public License for more details. +## +## You should have received a copy of the GNU General Public License +## along with Octave; see the file COPYING. If not, see +## <https://www.gnu.org/licenses/>. + +## -*- texinfo -*- +## @deftypefn {} {} empirical_cdf (@var{x}, @var{data}) +## For each element of @var{x}, compute the cumulative distribution function +## (CDF) at @var{x} of the empirical distribution obtained from +## the univariate sample @var{data}. +## @end deftypefn + +## Author: KH <Kurt.Hornik@wu-wien.ac.at> +## Description: CDF of the empirical distribution + +function cdf = empirical_cdf (x, data) + + if (nargin != 2) + print_usage (); + endif + + if (! isvector (data)) + error ("empirical_cdf: DATA must be a vector"); + endif + + cdf = discrete_cdf (x, data, ones (size (data))); + +endfunction + + +%!shared x,v,y +%! x = [-1 0.1 1.1 1.9 3]; +%! v = 0.1:0.2:1.9; +%! y = [0 0.1 0.6 1 1]; +%!assert (empirical_cdf (x, v), y, eps) +%!assert (empirical_cdf ([x(1) NaN x(3:5)], v), [0 NaN 0.6 1 1], eps) + +## Test class of input preserved +%!assert (empirical_cdf ([x, NaN], v), [y, NaN], eps) +%!assert (empirical_cdf (single ([x, NaN]), v), single ([y, NaN]), eps) +%!assert (empirical_cdf ([x, NaN], single (v)), single ([y, NaN]), eps) + +## Test input validation +%!error empirical_cdf () +%!error empirical_cdf (1) +%!error empirical_cdf (1,2,3) +%!error empirical_cdf (1, ones (2))
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/scripts/statistics/empirical_inv.m Sun Jan 07 17:13:23 2018 -0800 @@ -0,0 +1,60 @@ +## Copyright (C) 2012 Rik Wehbring +## Copyright (C) 1996-2016 Kurt Hornik +## +## This file is part of Octave. +## +## Octave is free software: you can redistribute it and/or modify it +## under the terms of the GNU General Public License as published by +## the Free Software Foundation, either version 3 of the License, or +## (at your option) any later version. +## +## Octave is distributed in the hope that it will be useful, but +## WITHOUT ANY WARRANTY; without even the implied warranty of +## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +## GNU General Public License for more details. +## +## You should have received a copy of the GNU General Public License +## along with Octave; see the file COPYING. If not, see +## <https://www.gnu.org/licenses/>. + +## -*- texinfo -*- +## @deftypefn {} {} empirical_inv (@var{x}, @var{data}) +## For each element of @var{x}, compute the quantile (the inverse of the CDF) +## at @var{x} of the empirical distribution obtained from the +## univariate sample @var{data}. +## @end deftypefn + +## Author: KH <Kurt.Hornik@wu-wien.ac.at> +## Description: Quantile function of the empirical distribution + +function inv = empirical_inv (x, data) + + if (nargin != 2) + print_usage (); + endif + + if (! isvector (data)) + error ("empirical_inv: DATA must be a vector"); + endif + + inv = discrete_inv (x, data, ones (size (data))); + +endfunction + + +%!shared x,v,y +%! x = [-1 0 0.1 0.5 1 2]; +%! v = 0.1:0.2:1.9; +%! y = [NaN v(1) v(1) v(end/2) v(end) NaN]; +%!assert (empirical_inv (x, v), y, eps) + +## Test class of input preserved +%!assert (empirical_inv ([x, NaN], v), [y, NaN], eps) +%!assert (empirical_inv (single ([x, NaN]), v), single ([y, NaN]), eps) +%!assert (empirical_inv ([x, NaN], single (v)), single ([y, NaN]), eps) + +## Test input validation +%!error empirical_inv () +%!error empirical_inv (1) +%!error empirical_inv (1,2,3) +%!error empirical_inv (1, ones (2))
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/scripts/statistics/empirical_pdf.m Sun Jan 07 17:13:23 2018 -0800 @@ -0,0 +1,71 @@ +## Copyright (C) 2012 Rik Wehbring +## Copyright (C) 1996-2016 Kurt Hornik +## +## This file is part of Octave. +## +## Octave is free software: you can redistribute it and/or modify it +## under the terms of the GNU General Public License as published by +## the Free Software Foundation, either version 3 of the License, or +## (at your option) any later version. +## +## Octave is distributed in the hope that it will be useful, but +## WITHOUT ANY WARRANTY; without even the implied warranty of +## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +## GNU General Public License for more details. +## +## You should have received a copy of the GNU General Public License +## along with Octave; see the file COPYING. If not, see +## <https://www.gnu.org/licenses/>. + +## -*- texinfo -*- +## @deftypefn {} {} empirical_pdf (@var{x}, @var{data}) +## For each element of @var{x}, compute the probability density function (PDF) +## at @var{x} of the empirical distribution obtained from the +## univariate sample @var{data}. +## @end deftypefn + +## Author: KH <Kurt.Hornik@wu-wien.ac.at> +## Description: PDF of the empirical distribution + +function pdf = empirical_pdf (x, data) + + if (nargin != 2) + print_usage (); + endif + + if (! isvector (data)) + error ("empirical_pdf: DATA must be a vector"); + endif + + uniq_vals = unique (data); + if (numel (data) != numel (uniq_vals)) + ## Handle ties, multiple elements with same value + p = histc (data, uniq_vals); + data = uniq_vals; + else + p = ones (size (data)); + endif + + pdf = discrete_pdf (x, data, p); + +endfunction + + +%!shared x,v,y +%! x = [-1 0.1 1.1 1.9 3]; +%! v = 0.1:0.2:1.9; +%! y = [0 0.1 0.1 0.1 0]; +%!assert (empirical_pdf (x, v), y) + +## Test class of input preserved +%!assert (empirical_pdf (single (x), v), single (y)) +%!assert (empirical_pdf (x, single (v)), single (y)) + +## Test distribution with ties +%!assert (empirical_pdf (2, [1 2 3 2]), 0.5) + +## Test input validation +%!error empirical_pdf () +%!error empirical_pdf (1) +%!error empirical_pdf (1,2,3) +%!error empirical_inv (1, ones (2))
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/scripts/statistics/empirical_rnd.m Sun Jan 07 17:13:23 2018 -0800 @@ -0,0 +1,67 @@ +## Copyright (C) 2012 Rik Wehbring +## Copyright (C) 1996-2016 Kurt Hornik +## +## This file is part of Octave. +## +## Octave is free software: you can redistribute it and/or modify it +## under the terms of the GNU General Public License as published by +## the Free Software Foundation, either version 3 of the License, or +## (at your option) any later version. +## +## Octave is distributed in the hope that it will be useful, but +## WITHOUT ANY WARRANTY; without even the implied warranty of +## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +## GNU General Public License for more details. +## +## You should have received a copy of the GNU General Public License +## along with Octave; see the file COPYING. If not, see +## <https://www.gnu.org/licenses/>. + +## -*- texinfo -*- +## @deftypefn {} {} empirical_rnd (@var{data}) +## @deftypefnx {} {} empirical_rnd (@var{data}, @var{r}) +## @deftypefnx {} {} empirical_rnd (@var{data}, @var{r}, @var{c}, @dots{}) +## @deftypefnx {} {} empirical_rnd (@var{data}, [@var{sz}]) +## Return a matrix of random samples from the empirical distribution obtained +## from the univariate sample @var{data}. +## +## When called with a single size argument, return a square matrix with +## the dimension specified. When called with more than one scalar argument the +## first two arguments are taken as the number of rows and columns and any +## further arguments specify additional matrix dimensions. The size may also +## be specified with a vector of dimensions @var{sz}. +## +## If no size arguments are given then the result matrix is a random ordering +## of the sample @var{data}. +## @end deftypefn + +## Author: KH <Kurt.Hornik@wu-wien.ac.at> +## Description: Bootstrap samples from the empirical distribution + +function rnd = empirical_rnd (data, varargin) + + if (nargin < 1) + print_usage (); + endif + + if (! isvector (data)) + error ("empirical_rnd: DATA must be a vector"); + endif + + rnd = discrete_rnd (data, ones (size (data)), varargin{:}); + +endfunction + + +%!assert (size (empirical_rnd (ones (3, 1))), [3, 1]) +%!assert (size (empirical_rnd (1:2, [4 1])), [4, 1]) +%!assert (size (empirical_rnd (1:2, 4, 1)), [4, 1]) + +## Test class of input preserved +%!assert (class (empirical_rnd (1:2, 1)), "double") +%!assert (class (empirical_rnd (single (1:2), 1)), "single") + +## Test input validation +%!error empirical_rnd () +%!error empirical_rnd (ones (2), 1) +%!error empirical_rnd (ones (2), 1, 1)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/scripts/statistics/histc.m Sun Jan 07 17:13:23 2018 -0800 @@ -0,0 +1,190 @@ +## Copyright (C) 2009-2017 Søren Hauberg +## Copyright (C) 2009 VZLU Prague +## +## This file is part of Octave. +## +## Octave is free software: you can redistribute it and/or modify it +## under the terms of the GNU General Public License as published by +## the Free Software Foundation, either version 3 of the License, or +## (at your option) any later version. +## +## Octave is distributed in the hope that it will be useful, but +## WITHOUT ANY WARRANTY; without even the implied warranty of +## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +## GNU General Public License for more details. +## +## You should have received a copy of the GNU General Public License +## along with Octave; see the file COPYING. If not, see +## <https://www.gnu.org/licenses/>. + +## -*- texinfo -*- +## @deftypefn {} {@var{n} =} histc (@var{x}, @var{edges}) +## @deftypefnx {} {@var{n} =} histc (@var{x}, @var{edges}, @var{dim}) +## @deftypefnx {} {[@var{n}, @var{idx}] =} histc (@dots{}) +## Compute histogram counts. +## +## When @var{x} is a vector, the function counts the number of elements of +## @var{x} that fall in the histogram bins defined by @var{edges}. This +## must be a vector of monotonically increasing values that define the edges +## of the histogram bins. +## @tex +## $n(k)$ +## @end tex +## @ifnottex +## @code{@var{n}(k)} +## @end ifnottex +## contains the number of elements in @var{x} for which +## @tex +## $@var{edges}(k) <= @var{x} < @var{edges}(k+1)$. +## @end tex +## @ifnottex +## @code{@var{edges}(k) <= @var{x} < @var{edges}(k+1)}. +## @end ifnottex +## The final element of @var{n} contains the number of elements of @var{x} +## exactly equal to the last element of @var{edges}. +## +## When @var{x} is an @math{N}-dimensional array, the computation is carried +## out along dimension @var{dim}. If not specified @var{dim} defaults to the +## first non-singleton dimension. +## +## When a second output argument is requested an index matrix is also returned. +## The @var{idx} matrix has the same size as @var{x}. Each element of +## @var{idx} contains the index of the histogram bin in which the +## corresponding element of @var{x} was counted. +## @seealso{hist} +## @end deftypefn + +function [n, idx] = histc (x, edges, dim) + + if (nargin < 2 || nargin > 3) + print_usage (); + endif + + if (! isreal (x)) + error ("histc: X argument must be real-valued, not complex"); + endif + + num_edges = numel (edges); + if (num_edges == 0) + warning ("histc: empty EDGES specified\n"); + n = idx = []; + return; + endif + + if (! isreal (edges)) + error ("histc: EDGES must be real-valued, not complex"); + else + ## Make sure 'edges' is sorted + edges = edges(:); + if (! issorted (edges) || edges(1) > edges(end)) + warning ("histc: edge values not sorted on input"); + edges = sort (edges); + endif + endif + + nd = ndims (x); + sz = size (x); + if (nargin < 3) + ## Find the first non-singleton dimension. + (dim = find (sz > 1, 1)) || (dim = 1); + else + if (!(isscalar (dim) && dim == fix (dim)) + || !(1 <= dim && dim <= nd)) + error ("histc: DIM must be an integer and a valid dimension"); + endif + endif + + nsz = sz; + nsz(dim) = num_edges; + + ## the splitting point is 3 bins + + if (num_edges <= 3) + + ## This is the O(M*N) algorithm. + + ## Allocate the histogram + n = zeros (nsz); + + ## Allocate 'idx' + if (nargout > 1) + idx = zeros (sz); + endif + + ## Prepare indices + idx1 = cell (1, dim-1); + for k = 1:length (idx1) + idx1{k} = 1:sz(k); + endfor + idx2 = cell (length (sz) - dim); + for k = 1:length (idx2) + idx2{k} = 1:sz(k+dim); + endfor + + ## Compute the histograms + for k = 1:num_edges-1 + b = (edges(k) <= x & x < edges(k+1)); + n(idx1{:}, k, idx2{:}) = sum (b, dim); + if (nargout > 1) + idx(b) = k; + endif + endfor + b = (x == edges(end)); + n(idx1{:}, num_edges, idx2{:}) = sum (b, dim); + if (nargout > 1) + idx(b) = num_edges; + endif + + else + + ## This is the O(M*log(N) + N) algorithm. + + ## Look-up indices. + idx = lookup (edges, x); + ## Zero invalid ones (including NaNs). x < edges(1) are already zero. + idx(! (x <= edges(end))) = 0; + + iidx = idx; + + ## In case of matrix input, we adjust the indices. + if (! isvector (x)) + nl = prod (sz(1:dim-1)); + nn = sz(dim); + nu = prod (sz(dim+1:end)); + if (nl != 1) + iidx = (iidx-1) * nl; + iidx += reshape (kron (ones (1, nn*nu), 1:nl), sz); + endif + if (nu != 1) + ne =length (edges); + iidx += reshape (kron (nl*ne*(0:nu-1), ones (1, nl*nn)), sz); + endif + endif + + ## Select valid elements. + iidx = iidx(idx != 0); + + ## Call accumarray to sum the indexed elements. + n = accumarray (iidx(:), 1, nsz); + + endif + +endfunction + + +%!test +%! x = linspace (0, 10, 1001); +%! n = histc (x, 0:10); +%! assert (n, [repmat(100, 1, 10), 1]); + +%!test +%! x = repmat (linspace (0, 10, 1001), [2, 1, 3]); +%! n = histc (x, 0:10, 2); +%! assert (n, repmat ([repmat(100, 1, 10), 1], [2, 1, 3])); + +%!error histc () +%!error histc (1) +%!error histc (1, 2, 3, 4) +%!error histc ([1:10 1+i], 2) +%!warning <empty EDGES specified> histc (1:10, []); +%!error histc (1, 1, 3)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/scripts/statistics/iqr.m Sun Jan 07 17:13:23 2018 -0800 @@ -0,0 +1,100 @@ +## Copyright (C) 1995-2017 Kurt Hornik +## +## This file is part of Octave. +## +## Octave is free software: you can redistribute it and/or modify it +## under the terms of the GNU General Public License as published by +## the Free Software Foundation, either version 3 of the License, or +## (at your option) any later version. +## +## Octave is distributed in the hope that it will be useful, but +## WITHOUT ANY WARRANTY; without even the implied warranty of +## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +## GNU General Public License for more details. +## +## You should have received a copy of the GNU General Public License +## along with Octave; see the file COPYING. If not, see +## <https://www.gnu.org/licenses/>. + +## -*- texinfo -*- +## @deftypefn {} {} iqr (@var{x}) +## @deftypefnx {} {} iqr (@var{x}, @var{dim}) +## Return the interquartile range, i.e., the difference between the upper +## and lower quartile of the input data. +## +## If @var{x} is a matrix, do the above for first non-singleton dimension of +## @var{x}. +## +## If the optional argument @var{dim} is given, operate along this dimension. +## +## As a measure of dispersion, the interquartile range is less affected by +## outliers than either @code{range} or @code{std}. +## @seealso{range, std} +## @end deftypefn + +## Author KH <Kurt.Hornik@wu-wien.ac.at> +## Description: Interquartile range + +function y = iqr (x, dim) + + if (nargin != 1 && nargin != 2) + print_usage (); + endif + + if (! (isnumeric (x) || islogical (x))) + error ("iqr: X must be a numeric vector or matrix"); + endif + + nd = ndims (x); + sz = size (x); + nel = numel (x); + if (nargin != 2) + ## Find the first non-singleton dimension. + (dim = find (sz > 1, 1)) || (dim = 1); + else + if (!(isscalar (dim) && dim == fix (dim)) + || !(1 <= dim && dim <= nd)) + error ("iqr: DIM must be an integer and a valid dimension"); + endif + endif + + ## This code is a bit heavy, but is needed until empirical_inv + ## can take a matrix, rather than just a vector argument. + n = sz(dim); + sz(dim) = 1; + if (isa (x, "single")) + y = zeros (sz, "single"); + else + y = zeros (sz); + endif + stride = prod (sz(1:dim-1)); + for i = 1 : nel / n; + offset = i; + offset2 = 0; + while (offset > stride) + offset -= stride; + offset2 += 1; + endwhile + offset += offset2 * stride * n; + rng = [0 : n-1] * stride + offset; + + y(i) = diff (empirical_inv ([1/4, 3/4], x(rng))); + endfor + +endfunction + + +%!assert (iqr (1:101), 50) +%!assert (iqr (single (1:101)), single (50)) + +## FIXME: iqr throws horrible error when running across a dimension that is 1. +%!test +%! x = [1:100]'; +%! assert (iqr (x, 1), 50); +%! assert (iqr (x', 2), 50); + +%!error iqr () +%!error iqr (1, 2, 3) +%!error iqr (1) +%!error iqr (['A'; 'B']) +%!error iqr (1:10, 3)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/scripts/statistics/kendall.m Sun Jan 07 17:13:23 2018 -0800 @@ -0,0 +1,153 @@ +## Copyright (C) 1995-2017 Kurt Hornik +## +## This file is part of Octave. +## +## Octave is free software: you can redistribute it and/or modify it +## under the terms of the GNU General Public License as published by +## the Free Software Foundation, either version 3 of the License, or +## (at your option) any later version. +## +## Octave is distributed in the hope that it will be useful, but +## WITHOUT ANY WARRANTY; without even the implied warranty of +## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +## GNU General Public License for more details. +## +## You should have received a copy of the GNU General Public License +## along with Octave; see the file COPYING. If not, see +## <https://www.gnu.org/licenses/>. + +## -*- texinfo -*- +## @deftypefn {} {} kendall (@var{x}) +## @deftypefnx {} {} kendall (@var{x}, @var{y}) +## @cindex Kendall's Tau +## Compute Kendall's +## @tex +## $\tau$. +## @end tex +## @ifnottex +## @var{tau}. +## @end ifnottex +## +## For two data vectors @var{x}, @var{y} of common length @math{N}, Kendall's +## @tex +## $\tau$ +## @end tex +## @ifnottex +## @var{tau} +## @end ifnottex +## is the correlation of the signs of all rank differences of +## @var{x} and @var{y}; i.e., if both @var{x} and @var{y} have distinct +## entries, then +## +## @tex +## $$ \tau = {1 \over N(N-1)} \sum_{i,j} {\rm sign}(q_i-q_j) \, {\rm sign}(r_i-r_j) $$ +## @end tex +## @ifnottex +## +## @example +## @group +## 1 +## @var{tau} = ------- SUM sign (@var{q}(i) - @var{q}(j)) * sign (@var{r}(i) - @var{r}(j)) +## N (N-1) i,j +## @end group +## @end example +## +## @end ifnottex +## @noindent +## in which the +## @tex +## $q_i$ and $r_i$ +## @end tex +## @ifnottex +## @var{q}(i) and @var{r}(i) +## @end ifnottex +## are the ranks of @var{x} and @var{y}, respectively. +## +## If @var{x} and @var{y} are drawn from independent distributions, +## Kendall's +## @tex +## $\tau$ +## @end tex +## @ifnottex +## @var{tau} +## @end ifnottex +## is asymptotically normal with mean 0 and variance +## @tex +## ${2 (2N+5) \over 9N(N-1)}$. +## @end tex +## @ifnottex +## @code{(2 * (2N+5)) / (9 * N * (N-1))}. +## @end ifnottex +## +## @code{kendall (@var{x})} is equivalent to @code{kendall (@var{x}, +## @var{x})}. +## @seealso{ranks, spearman} +## @end deftypefn + +## Author: KH <Kurt.Hornik@wu-wien.ac.at> +## Description: Kendall's rank correlation tau + +function tau = kendall (x, y = []) + + if (nargin < 1 || nargin > 2) + print_usage (); + endif + + if ( ! (isnumeric (x) || islogical (x)) + || ! (isnumeric (y) || islogical (y))) + error ("kendall: X and Y must be numeric matrices or vectors"); + endif + + if (ndims (x) != 2 || ndims (y) != 2) + error ("kendall: X and Y must be 2-D matrices or vectors"); + endif + + if (isrow (x)) + x = x.'; + endif + [n, c] = size (x); + + if (nargin == 2) + if (isrow (y)) + y = y.'; + endif + if (rows (y) != n) + error ("kendall: X and Y must have the same number of observations"); + else + x = [x, y]; + endif + endif + + if (isa (x, "single") || isa (y, "single")) + cls = "single"; + else + cls = "double"; + endif + r = ranks (x); + m = sign (kron (r, ones (n, 1, cls)) - kron (ones (n, 1, cls), r)); + tau = corr (m); + + if (nargin == 2) + tau = tau(1 : c, (c + 1) : columns (x)); + endif + +endfunction + + +%!test +%! x = [1:2:10]; +%! y = [100:10:149]; +%! assert (kendall (x,y), 1, 5*eps); +%! assert (kendall (x,fliplr (y)), -1, 5*eps); + +%!assert (kendall (logical (1)), 1) +%!assert (kendall (single (1)), single (1)) + +## Test input validation +%!error kendall () +%!error kendall (1, 2, 3) +%!error kendall (['A'; 'B']) +%!error kendall (ones (2,1), ['A'; 'B']) +%!error kendall (ones (2,2,2)) +%!error kendall (ones (2,2), ones (2,2,2)) +%!error kendall (ones (2,2), ones (3,2))
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/scripts/statistics/kurtosis.m Sun Jan 07 17:13:23 2018 -0800 @@ -0,0 +1,170 @@ +## Copyright (C) 2013-2017 Julien Bect +## Copyright (C) 1996-2016 John W. Eaton +## +## This file is part of Octave. +## +## Octave is free software: you can redistribute it and/or modify it +## under the terms of the GNU General Public License as published by +## the Free Software Foundation, either version 3 of the License, or +## (at your option) any later version. +## +## Octave is distributed in the hope that it will be useful, but +## WITHOUT ANY WARRANTY; without even the implied warranty of +## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +## GNU General Public License for more details. +## +## You should have received a copy of the GNU General Public License +## along with Octave; see the file COPYING. If not, see +## <https://www.gnu.org/licenses/>. + +## -*- texinfo -*- +## @deftypefn {} {} kurtosis (@var{x}) +## @deftypefnx {} {} kurtosis (@var{x}, @var{flag}) +## @deftypefnx {} {} kurtosis (@var{x}, @var{flag}, @var{dim}) +## Compute the sample kurtosis of the elements of @var{x}. +## +## The sample kurtosis is defined as +## @tex +## $$ +## \kappa_1 = {{{1\over N}\, +## \sum_{i=1}^N (x_i - \bar{x})^4} \over \sigma^4}, +## $$ +## where $N$ is the length of @var{x}, $\bar{x}$ its mean, and $\sigma$ +## its (uncorrected) standard deviation. +## @end tex +## @ifnottex +## +## @example +## @group +## mean ((@var{x} - mean (@var{x})).^4) +## k1 = ------------------------ +## std (@var{x}).^4 +## @end group +## @end example +## +## @end ifnottex +## +## @noindent +## The optional argument @var{flag} controls which normalization is used. +## If @var{flag} is equal to 1 (default value, used when @var{flag} is omitted +## or empty), return the sample kurtosis as defined above. If @var{flag} is +## equal to 0, return the @w{"bias-corrected"} kurtosis coefficient instead: +## @tex +## $$ +## \kappa_0 = 3 + {\scriptstyle N - 1 \over \scriptstyle (N - 2)(N - 3)} \, +## \left( (N + 1)\, \kappa_1 - 3 (N - 1) \right) +## $$ +## @end tex +## @ifnottex +## +## @example +## @group +## N - 1 +## k0 = 3 + -------------- * ((N + 1) * k1 - 3 * (N - 1)) +## (N - 2)(N - 3) +## @end group +## @end example +## +## where @math{N} is the length of the @var{x} vector. +## +## @end ifnottex +## The bias-corrected kurtosis coefficient is obtained by replacing the sample +## second and fourth central moments by their unbiased versions. It is an +## unbiased estimate of the population kurtosis for normal populations. +## +## If @var{x} is a matrix, or more generally a multi-dimensional array, return +## the kurtosis along the first non-singleton dimension. If the optional +## @var{dim} argument is given, operate along this dimension. +## +## @seealso{var, skewness, moment} +## @end deftypefn + +## Author: KH <Kurt.Hornik@wu-wien.ac.at> +## Created: 29 July 1994 +## Adapted-By: jwe + +function y = kurtosis (x, flag, dim) + + if (nargin < 1) || (nargin > 3) + print_usage (); + endif + + if (! (isnumeric (x) || islogical (x))) + error ("kurtosis: X must be a numeric vector or matrix"); + endif + + if (nargin < 2 || isempty (flag)) + flag = 1; # default: do not use the "bias corrected" version + else + if (! isscalar (flag) || (flag != 0 && flag != 1)) + error ("kurtosis: FLAG must be 0 or 1"); + endif + endif + + nd = ndims (x); + sz = size (x); + if (nargin < 3) + ## Find the first non-singleton dimension. + (dim = find (sz > 1, 1)) || (dim = 1); + else + if (! (isscalar (dim) && dim == fix (dim) && dim > 0)) + error ("kurtosis: DIM must be an integer and a valid dimension"); + endif + endif + + n = size (x, dim); + sz(dim) = 1; + + x = center (x, dim); # center also promotes integer, logical to double + v = var (x, 1, dim); # normalize with 1/N + y = sum (x .^ 4, dim); + idx = (v != 0); + y(idx) = y(idx) ./ (n * v(idx) .^ 2); + y(! idx) = NaN; + + ## Apply bias correction to the second and fourth central sample moment + if (flag == 0) + if (n > 3) + C = (n - 1) / ((n - 2) * (n - 3)); + y = 3 + C * ((n + 1) * y - 3 * (n - 1)); + else + y(:) = NaN; + endif + endif + +endfunction + + +%!test +%! x = [-1; 0; 0; 0; 1]; +%! y = [x, 2*x]; +%! assert (kurtosis (y), [2.5, 2.5], sqrt (eps)); + +%!assert (kurtosis ([-3, 0, 1]) == kurtosis ([-1, 0, 3])) +%!assert (kurtosis (ones (3, 5)), NaN (1, 5)) +%!assert (kurtosis (1, [], 3), NaN) + +%!assert (kurtosis ([1:5 10; 1:5 10], 0, 2), 5.4377317925288901 * [1; 1], 8 * eps) +%!assert (kurtosis ([1:5 10; 1:5 10], 1, 2), 2.9786509002956195 * [1; 1], 8 * eps) +%!assert (kurtosis ([1:5 10; 1:5 10], [], 2), 2.9786509002956195 * [1; 1], 8 * eps) + +## Test behavior on single input +%!assert (kurtosis (single ([1:5 10])), single (2.9786513), eps ("single")) +%!assert (kurtosis (single ([1 2]), 0), single (NaN)) + +## Verify no "divide-by-zero" warnings +%!test +%! warning ("on", "Octave:divide-by-zero", "local"); +%! lastwarn (""); # clear last warning +%! kurtosis (1); +%! assert (lastwarn (), ""); + +## Test input validation +%!error kurtosis () +%!error kurtosis (1, 2, 3) +%!error <X must be a numeric vector or matrix> kurtosis (['A'; 'B']) +%!error <FLAG must be 0 or 1> kurtosis (1, 2) +%!error <FLAG must be 0 or 1> kurtosis (1, [1 0]) +%!error <DIM must be an integer> kurtosis (1, [], ones (2,2)) +%!error <DIM must be an integer> kurtosis (1, [], 1.5) +%!error <DIM must be .* a valid dimension> kurtosis (1, [], 0)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/scripts/statistics/mean.m Sun Jan 07 17:13:23 2018 -0800 @@ -0,0 +1,164 @@ +## Copyright (C) 1995-2017 Kurt Hornik +## +## This file is part of Octave. +## +## Octave is free software: you can redistribute it and/or modify it +## under the terms of the GNU General Public License as published by +## the Free Software Foundation, either version 3 of the License, or +## (at your option) any later version. +## +## Octave is distributed in the hope that it will be useful, but +## WITHOUT ANY WARRANTY; without even the implied warranty of +## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +## GNU General Public License for more details. +## +## You should have received a copy of the GNU General Public License +## along with Octave; see the file COPYING. If not, see +## <https://www.gnu.org/licenses/>. + +## -*- texinfo -*- +## @deftypefn {} {} mean (@var{x}) +## @deftypefnx {} {} mean (@var{x}, @var{dim}) +## @deftypefnx {} {} mean (@var{x}, @var{opt}) +## @deftypefnx {} {} mean (@var{x}, @var{dim}, @var{opt}) +## Compute the mean of the elements of the vector @var{x}. +## +## The mean is defined as +## +## @tex +## $$ {\rm mean}(x) = \bar{x} = {1\over N} \sum_{i=1}^N x_i $$ +## where $N$ is the number of elements of @var{x}. +## +## @end tex +## @ifnottex +## +## @example +## mean (@var{x}) = SUM_i @var{x}(i) / N +## @end example +## +## where @math{N} is the length of the @var{x} vector. +## +## @end ifnottex +## If @var{x} is a matrix, compute the mean for each column and return them +## in a row vector. +## +## If the optional argument @var{dim} is given, operate along this dimension. +## +## The optional argument @var{opt} selects the type of mean to compute. +## The following options are recognized: +## +## @table @asis +## @item @qcode{"a"} +## Compute the (ordinary) arithmetic mean. [default] +## +## @item @qcode{"g"} +## Compute the geometric mean. +## +## @item @qcode{"h"} +## Compute the harmonic mean. +## @end table +## +## Both @var{dim} and @var{opt} are optional. If both are supplied, either +## may appear first. +## @seealso{median, mode} +## @end deftypefn + +## Author: KH <Kurt.Hornik@wu-wien.ac.at> +## Description: Compute arithmetic, geometric, and harmonic mean + +function y = mean (x, opt1, opt2) + + if (nargin < 1 || nargin > 3) + print_usage (); + endif + + if (! (isnumeric (x) || islogical (x))) + error ("mean: X must be a numeric vector or matrix"); + endif + + need_dim = false; + + if (nargin == 1) + opt = "a"; + need_dim = true; + elseif (nargin == 2) + if (ischar (opt1)) + opt = opt1; + need_dim = true; + else + dim = opt1; + opt = "a"; + endif + elseif (nargin == 3) + if (ischar (opt1)) + opt = opt1; + dim = opt2; + elseif (ischar (opt2)) + opt = opt2; + dim = opt1; + else + error ("mean: OPT must be a string"); + endif + else + print_usage (); + endif + + nd = ndims (x); + sz = size (x); + if (need_dim) + ## Find the first non-singleton dimension. + (dim = find (sz > 1, 1)) || (dim = 1); + else + if (! (isscalar (dim) && dim == fix (dim) && dim > 0)) + error ("mean: DIM must be an integer and a valid dimension"); + endif + endif + + n = size (x, dim); + + if (strcmp (opt, "a")) + y = sum (x, dim) / n; + elseif (strcmp (opt, "g")) + if (all (x(:) >= 0)) + y = exp (sum (log (x), dim) ./ n); + else + error ("mean: X must not contain any negative values"); + endif + elseif (strcmp (opt, "h")) + y = n ./ sum (1 ./ x, dim); + else + error ("mean: option '%s' not recognized", opt); + endif + +endfunction + + +%!test +%! x = -10:10; +%! y = x'; +%! z = [y, y+10]; +%! assert (mean (x), 0); +%! assert (mean (y), 0); +%! assert (mean (z), [0, 10]); + +## Test small numbers +%!assert (mean (repmat (0.1,1,1000), "g"), 0.1, 20*eps) + +%!assert (mean (magic (3), 1), [5, 5, 5]) +%!assert (mean (magic (3), 2), [5; 5; 5]) +%!assert (mean ([2 8], "g"), 4) +%!assert (mean ([4 4 2], "h"), 3) +%!assert (mean (logical ([1 0 1 1])), 0.75) +%!assert (mean (single ([1 0 1 1])), single (0.75)) +%!assert (mean ([1 2], 3), [1 2]) + +## Test input validation +%!error mean () +%!error mean (1, 2, 3, 4) +%!error <X must be a numeric> mean ({1:5}) +%!error <OPT must be a string> mean (1, 2, 3) +%!error <DIM must be an integer> mean (1, ones (2,2)) +%!error <DIM must be an integer> mean (1, 1.5) +%!error <DIM must be .* a valid dimension> mean (1, 0) +%!error <X must not contain any negative values> mean ([1 -1], "g") +%!error <option 'b' not recognized> mean (1, "b")
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/scripts/statistics/meansq.m Sun Jan 07 17:13:23 2018 -0800 @@ -0,0 +1,92 @@ +## Copyright (C) 1995-2017 Kurt Hornik +## Copyright (C) 2009 Jaroslav Hajek +## +## This file is part of Octave. +## +## Octave is free software: you can redistribute it and/or modify it +## under the terms of the GNU General Public License as published by +## the Free Software Foundation, either version 3 of the License, or +## (at your option) any later version. +## +## Octave is distributed in the hope that it will be useful, but +## WITHOUT ANY WARRANTY; without even the implied warranty of +## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +## GNU General Public License for more details. +## +## You should have received a copy of the GNU General Public License +## along with Octave; see the file COPYING. If not, see +## <https://www.gnu.org/licenses/>. + +## -*- texinfo -*- +## @deftypefn {} {} meansq (@var{x}) +## @deftypefnx {} {} meansq (@var{x}, @var{dim}) +## Compute the mean square of the elements of the vector @var{x}. +## +## The mean square is defined as +## @tex +## $$ +## {\rm meansq} (x) = {\sum_{i=1}^N {x_i}^2 \over N} +## $$ +## where $N$ is the number of elements of @var{x}. +## +## @end tex +## @ifnottex +## +## @example +## @group +## meansq (@var{x}) = 1/N SUM_i @var{x}(i)^2 +## @end group +## @end example +## +## where @math{N} is the length of the @var{x} vector. +## +## @end ifnottex +## If @var{x} is a matrix, return a row vector containing the mean square +## of each column. +## +## If the optional argument @var{dim} is given, operate along this dimension. +## @seealso{var, std, moment} +## @end deftypefn + +## Author: KH <Kurt.Hornik@wu-wien.ac.at> +## Description: Compute mean square + +function y = meansq (x, dim) + + if (nargin != 1 && nargin != 2) + print_usage (); + endif + + if (! (isnumeric (x) || islogical (x))) + error ("mean: X must be a numeric vector or matrix"); + endif + + nd = ndims (x); + sz = size (x); + if (nargin < 2) + ## Find the first non-singleton dimension. + (dim = find (sz > 1, 1)) || (dim = 1); + else + if (! (isscalar (dim) && dim == fix (dim) && dim > 0)) + error ("mean: DIM must be an integer and a valid dimension"); + endif + endif + + y = sumsq (x, dim) / size (x, dim); + +endfunction + + +%!assert (meansq (1:5), 11) +%!assert (meansq (single (1:5)), single (11)) +%!assert (meansq (magic (4)), [94.5, 92.5, 92.5, 94.5]) +%!assert (meansq (magic (4), 2), [109.5; 77.5; 77.5; 109.5]) +%!assert (meansq ([1 2], 3), [1 4]) + +## Test input validation +%!error meansq () +%!error meansq (1, 2, 3) +%!error <X must be a numeric> meansq (['A'; 'B']) +%!error <DIM must be an integer> meansq (1, ones (2,2)) +%!error <DIM must be an integer> meansq (1, 1.5) +%!error <DIM must be .* a valid dimension> meansq (1, 0)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/scripts/statistics/median.m Sun Jan 07 17:13:23 2018 -0800 @@ -0,0 +1,141 @@ +## Copyright (C) 1996-2017 John W. Eaton +## Copyright (C) 2009-2010 VZLU Prague +## +## This file is part of Octave. +## +## Octave is free software: you can redistribute it and/or modify it +## under the terms of the GNU General Public License as published by +## the Free Software Foundation, either version 3 of the License, or +## (at your option) any later version. +## +## Octave is distributed in the hope that it will be useful, but +## WITHOUT ANY WARRANTY; without even the implied warranty of +## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +## GNU General Public License for more details. +## +## You should have received a copy of the GNU General Public License +## along with Octave; see the file COPYING. If not, see +## <https://www.gnu.org/licenses/>. + +## -*- texinfo -*- +## @deftypefn {} {} median (@var{x}) +## @deftypefnx {} {} median (@var{x}, @var{dim}) +## Compute the median value of the elements of the vector @var{x}. +## +## When the elements of @var{x} are sorted, say @code{@var{s} = sort (@var{x})}, +## the median is defined as +## @tex +## $$ +## {\rm median} (x) = +## \cases{s(\lceil N/2\rceil), & $N$ odd;\cr +## (s(N/2)+s(N/2+1))/2, & $N$ even.} +## $$ +## where $N$ is the number of elements of @var{x}. +## +## @end tex +## @ifnottex +## +## @example +## @group +## | @var{s}(ceil(N/2)) N odd +## median (@var{x}) = | +## | (@var{s}(N/2) + @var{s}(N/2+1))/2 N even +## @end group +## @end example +## +## @end ifnottex +## If @var{x} is of a discrete type such as integer or logical, then +## the case of even @math{N} rounds up (or toward @code{true}). +## +## If @var{x} is a matrix, compute the median value for each column and +## return them in a row vector. +## +## If the optional @var{dim} argument is given, operate along this dimension. +## @seealso{mean, mode} +## @end deftypefn + +## Author: jwe + +function retval = median (x, dim) + + if (nargin != 1 && nargin != 2) + print_usage (); + endif + + if (! (isnumeric (x) || islogical (x))) + error ("median: X must be a numeric vector or matrix"); + endif + + if (isempty (x)) + error ("median: X cannot be an empty matrix"); + endif + + nd = ndims (x); + sz = size (x); + if (nargin < 2) + ## Find the first non-singleton dimension. + (dim = find (sz > 1, 1)) || (dim = 1); + else + if (! (isscalar (dim) && dim == fix (dim) && dim > 0)) + error ("median: DIM must be an integer and a valid dimension"); + endif + endif + + n = size (x, dim); + k = floor ((n+1) / 2); + if (mod (n, 2) == 1) + retval = nth_element (x, k, dim); + else + retval = sum (nth_element (x, k:k+1, dim), dim, "native") / 2; + if (islogical (x)) + retval = logical (retval); + endif + endif + ## Inject NaNs where needed, to be consistent with Matlab. + if (isfloat (x)) + retval(any (isnan (x), dim)) = NaN; + endif + +endfunction + + +%!test +%! x = [1, 2, 3, 4, 5, 6]; +%! x2 = x'; +%! y = [1, 2, 3, 4, 5, 6, 7]; +%! y2 = y'; +%! +%! assert (median (x) == median (x2) && median (x) == 3.5); +%! assert (median (y) == median (y2) && median (y) == 4); +%! assert (median ([x2, 2*x2]), [3.5, 7]); +%! assert (median ([y2, 3*y2]), [4, 12]); + +%!assert (median (single ([1,2,3])), single (2)) +%!assert (median ([1,2,NaN;4,5,6;NaN,8,9]), [NaN, 5, NaN]) +%!assert (median ([1,2], 3), [1,2]) + +## Test multidimensional arrays +%!shared a, b, x, y +%! rand ("seed", 2); +%! a = rand (2,3,4,5); +%! b = rand (3,4,6,5); +%! x = sort (a, 4); +%! y = sort (b, 3); +%!assert <*35679> (median (a, 4), x(:, :, :, 3)) +%!assert <*35679> (median (b, 3), (y(:, :, 3, :) + y(:, :, 4, :))/2) + +## Test non-floating point types +%!assert (median ([true, false]), true) +%!assert (median (uint8 ([1, 3])), uint8 (2)) +%!assert (median (int8 ([1, 3, 4])), int8 (3)) +%!assert (median (single ([1, 3, 4])), single (3)) +%!assert (median (single ([1, 3, NaN])), single (NaN)) + +## Test input validation +%!error median () +%!error median (1, 2, 3) +%!error <X must be a numeric> median ({1:5}) +%!error <X cannot be an empty matrix> median ([]) +%!error <DIM must be an integer> median (1, ones (2,2)) +%!error <DIM must be an integer> median (1, 1.5) +%!error <DIM must be .* a valid dimension> median (1, 0)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/scripts/statistics/mode.m Sun Jan 07 17:13:23 2018 -0800 @@ -0,0 +1,183 @@ +## Copyright (C) 2007-2017 David Bateman +## +## This file is part of Octave. +## +## Octave is free software: you can redistribute it and/or modify it +## under the terms of the GNU General Public License as published by +## the Free Software Foundation, either version 3 of the License, or +## (at your option) any later version. +## +## Octave is distributed in the hope that it will be useful, but +## WITHOUT ANY WARRANTY; without even the implied warranty of +## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +## GNU General Public License for more details. +## +## You should have received a copy of the GNU General Public License +## along with Octave; see the file COPYING. If not, see +## <https://www.gnu.org/licenses/>. + +## -*- texinfo -*- +## @deftypefn {} {} mode (@var{x}) +## @deftypefnx {} {} mode (@var{x}, @var{dim}) +## @deftypefnx {} {[@var{m}, @var{f}, @var{c}] =} mode (@dots{}) +## Compute the most frequently occurring value in a dataset (mode). +## +## @code{mode} determines the frequency of values along the first non-singleton +## dimension and returns the value with the highest frequency. If two, or +## more, values have the same frequency @code{mode} returns the smallest. +## +## If the optional argument @var{dim} is given, operate along this dimension. +## +## The return variable @var{f} is the number of occurrences of the mode in +## the dataset. +## +## The cell array @var{c} contains all of the elements with the maximum +## frequency. +## @seealso{mean, median} +## @end deftypefn + +function [m, f, c] = mode (x, dim) + + if (nargin < 1 || nargin > 2) + print_usage (); + endif + + if (! (isnumeric (x) || islogical (x))) + error ("mode: X must be a numeric vector or matrix"); + endif + + nd = ndims (x); + sz = size (x); + if (nargin < 2) + ## Find the first non-singleton dimension. + (dim = find (sz > 1, 1)) || (dim = 1); + else + if (! (isscalar (dim) && dim == fix (dim) && dim > 0)) + error ("mode: DIM must be an integer and a valid dimension"); + endif + endif + + if (dim > nd) + ## Special case of mode over non-existent dimension. + m = x; + f = ones (size (x)); + c = num2cell (x); + return; + endif + + sz2 = sz; + sz2(dim) = 1; + sz3 = ones (1, nd); + sz3(dim) = sz(dim); + + if (issparse (x)) + t2 = sparse (sz(1), sz(2)); + else + t2 = zeros (sz); + endif + + if (dim != 1) + perm = [dim, 1:dim-1, dim+1:nd]; + t2 = permute (t2, perm); + endif + + xs = sort (x, dim); + t = cat (dim, true (sz2), diff (xs, 1, dim) != 0); + + if (dim != 1) + t2(permute (t != 0, perm)) = diff ([find(permute (t, perm))(:); prod(sz)+1]); + f = max (ipermute (t2, perm), [], dim); + xs = permute (xs, perm); + else + t2(t) = diff ([find(t)(:); prod(sz)+1]); + f = max (t2, [], dim); + endif + + c = cell (sz2); + if (issparse (x)) + m = sparse (sz2(1), sz2(2)); + else + m = zeros (sz2, class (x)); + endif + for i = 1 : prod (sz2) + c{i} = xs(t2(:, i) == f(i), i); + m(i) = c{i}(1); + endfor + +endfunction + + +%!test +%! [m, f, c] = mode (toeplitz (1:5)); +%! assert (m, [1,2,2,2,1]); +%! assert (f, [1,2,2,2,1]); +%! assert (c, {[1;2;3;4;5],[2],[2;3],[2],[1;2;3;4;5]}); +%!test +%! [m, f, c] = mode (toeplitz (1:5), 2); +%! assert (m, [1;2;2;2;1]); +%! assert (f, [1;2;2;2;1]); +%! assert (c, {[1;2;3;4;5];[2];[2;3];[2];[1;2;3;4;5]}); +%!test +%! a = sprandn (32, 32, 0.05); +%! sp0 = sparse (0); +%! [m, f, c] = mode (a); +%! [m2, f2, c2] = mode (full (a)); +%! assert (m, sparse (m2)); +%! assert (f, sparse (f2)); +%! c_exp(1:length (a)) = { sp0 }; +%! assert (c ,c_exp); +%! assert (c2,c_exp); + +%!assert (mode ([2,3,1,2,3,4],1),[2,3,1,2,3,4]) +%!assert (mode ([2,3,1,2,3,4],2),2) +%!assert (mode ([2,3,1,2,3,4]),2) +%!assert (mode (single ([2,3,1,2,3,4])), single (2)) +%!assert (mode (int8 ([2,3,1,2,3,4])), int8 (2)) + +%!assert (mode ([2;3;1;2;3;4],1),2) +%!assert (mode ([2;3;1;2;3;4],2),[2;3;1;2;3;4]) +%!assert (mode ([2;3;1;2;3;4]),2) + +%!test +%! x = magic (3); +%! [m, f, c] = mode (x, 3); +%! assert (m, x); +%! assert (f, ones (3,3)); +%! assert (c, num2cell (x)); + +%!shared x +%! x(:,:,1) = toeplitz (1:3); +%! x(:,:,2) = circshift (toeplitz (1:3), 1); +%! x(:,:,3) = circshift (toeplitz (1:3), 2); +%!test +%! [m, f, c] = mode (x, 1); +%! assert (reshape (m, [3, 3]), [1 1 1; 2 2 2; 1 1 1]); +%! assert (reshape (f, [3, 3]), [1 1 1; 2 2 2; 1 1 1]); +%! c = reshape (c, [3, 3]); +%! assert (c{1}, [1; 2; 3]); +%! assert (c{2}, 2); +%! assert (c{3}, [1; 2; 3]); +%!test +%! [m, f, c] = mode (x, 2); +%! assert (reshape (m, [3, 3]), [1 1 2; 2 1 1; 1 2 1]); +%! assert (reshape (f, [3, 3]), [1 1 2; 2 1 1; 1 2 1]); +%! c = reshape (c, [3, 3]); +%! assert (c{1}, [1; 2; 3]); +%! assert (c{2}, 2); +%! assert (c{3}, [1; 2; 3]); +%!test +%! [m, f, c] = mode (x, 3); +%! assert (reshape (m, [3, 3]), [1 2 1; 1 2 1; 1 2 1]); +%! assert (reshape (f, [3, 3]), [1 2 1; 1 2 1; 1 2 1]); +%! c = reshape (c, [3, 3]); +%! assert (c{1}, [1; 2; 3]); +%! assert (c{2}, [1; 2; 3]); +%! assert (c{3}, [1; 2; 3]); + +## Test input validation +%!error mode () +%!error mode (1, 2, 3) +%!error <X must be a numeric> mode ({1 2 3}) +%!error <DIM must be an integer> mode (1, ones (2,2)) +%!error <DIM must be an integer> mode (1, 1.5) +%!error <DIM must be .* a valid dimension> mode (1, 0)
--- a/scripts/statistics/models/logistic_regression.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,192 +0,0 @@ -## Copyright (C) 1995-2017 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {[@var{theta}, @var{beta}, @var{dev}, @var{dl}, @var{d2l}, @var{p}] =} logistic_regression (@var{y}, @var{x}, @var{print}, @var{theta}, @var{beta}) -## Perform ordinal logistic regression. -## -## Suppose @var{y} takes values in @var{k} ordered categories, and let -## @code{gamma_i (@var{x})} be the cumulative probability that @var{y} -## falls in one of the first @var{i} categories given the covariate -## @var{x}. Then -## -## @example -## [theta, beta] = logistic_regression (y, x) -## @end example -## -## @noindent -## fits the model -## -## @example -## logit (gamma_i (x)) = theta_i - beta' * x, i = 1 @dots{} k-1 -## @end example -## -## The number of ordinal categories, @var{k}, is taken to be the number -## of distinct values of @code{round (@var{y})}. If @var{k} equals 2, -## @var{y} is binary and the model is ordinary logistic regression. The -## matrix @var{x} is assumed to have full column rank. -## -## Given @var{y} only, @code{theta = logistic_regression (y)} -## fits the model with baseline logit odds only. -## -## The full form is -## -## @example -## @group -## [theta, beta, dev, dl, d2l, gamma] -## = logistic_regression (y, x, print, theta, beta) -## @end group -## @end example -## -## @noindent -## in which all output arguments and all input arguments except @var{y} -## are optional. -## -## Setting @var{print} to 1 requests summary information about the fitted -## model to be displayed. Setting @var{print} to 2 requests information -## about convergence at each iteration. Other values request no -## information to be displayed. The input arguments @var{theta} and -## @var{beta} give initial estimates for @var{theta} and @var{beta}. -## -## The returned value @var{dev} holds minus twice the log-likelihood. -## -## The returned values @var{dl} and @var{d2l} are the vector of first -## and the matrix of second derivatives of the log-likelihood with -## respect to @var{theta} and @var{beta}. -## -## @var{p} holds estimates for the conditional distribution of @var{y} -## given @var{x}. -## @end deftypefn - -## Original for MATLAB written by Gordon K Smyth <gks@maths.uq.oz.au>, -## U of Queensland, Australia, on Nov 19, 1990. Last revision Aug 3, -## 1992. - -## Author: Gordon K Smyth <gks@maths.uq.oz.au>, -## Adapted-By: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: Ordinal logistic regression - -## Uses the auxiliary functions logistic_regression_derivatives and -## logistic_regression_likelihood. - -function [theta, beta, dev, dl, d2l, p] = logistic_regression (y, x, print, theta, beta) - - ## check input - y = round (vec (y)); - [my, ny] = size (y); - if (nargin < 2) - x = zeros (my, 0); - endif; - [mx, nx] = size (x); - if (mx != my) - error ("logistic_regression: X and Y must have the same number of observations"); - endif - - ## initial calculations - x = -x; - tol = 1e-6; incr = 10; decr = 2; - ymin = min (y); ymax = max (y); yrange = ymax - ymin; - z = (y * ones (1, yrange)) == ((y * 0 + 1) * (ymin : (ymax - 1))); - z1 = (y * ones (1, yrange)) == ((y * 0 + 1) * ((ymin + 1) : ymax)); - z = z(:, any (z)); - z1 = z1(:, any(z1)); - [mz, nz] = size (z); - - ## starting values - if (nargin < 3) - print = 0; - endif; - if (nargin < 4) - beta = zeros (nx, 1); - endif; - if (nargin < 5) - g = cumsum (sum (z))' ./ my; - theta = log (g ./ (1 - g)); - endif; - tb = [theta; beta]; - - ## likelihood and derivatives at starting values - [g, g1, p, dev] = logistic_regression_likelihood (y, x, tb, z, z1); - [dl, d2l] = logistic_regression_derivatives (x, z, z1, g, g1, p); - epsilon = std (vec (d2l)) / 1000; - - ## maximize likelihood using Levenberg modified Newton's method - iter = 0; - while (abs (dl' * (d2l \ dl) / length (dl)) > tol) - iter += 1; - tbold = tb; - devold = dev; - tb = tbold - d2l \ dl; - [g, g1, p, dev] = logistic_regression_likelihood (y, x, tb, z, z1); - if ((dev - devold) / (dl' * (tb - tbold)) < 0) - epsilon /= decr; - else - while ((dev - devold) / (dl' * (tb - tbold)) > 0) - epsilon *= incr; - if (epsilon > 1e+15) - error ("logistic_regression: epsilon too large"); - endif - tb = tbold - (d2l - epsilon * eye (size (d2l))) \ dl; - [g, g1, p, dev] = logistic_regression_likelihood (y, x, tb, z, z1); - disp ("epsilon"); disp (epsilon); - endwhile - endif - [dl, d2l] = logistic_regression_derivatives (x, z, z1, g, g1, p); - if (print == 2) - disp ("Iteration"); disp (iter); - disp ("Deviance"); disp (dev); - disp ("First derivative"); disp (dl'); - disp ("Eigenvalues of second derivative"); disp (eig (d2l)'); - endif - endwhile - - ## tidy up output - - theta = tb(1 : nz, 1); - beta = tb((nz + 1) : (nz + nx), 1); - - if (print >= 1) - printf ("\n"); - printf ("Logistic Regression Results:\n"); - printf ("\n"); - printf ("Number of Iterations: %d\n", iter); - printf ("Deviance: %f\n", dev); - printf ("Parameter Estimates:\n"); - printf (" Theta S.E.\n"); - se = sqrt (diag (inv (-d2l))); - for i = 1 : nz - printf (" %8.4f %8.4f\n", tb (i), se (i)); - endfor - if (nx > 0) - printf (" Beta S.E.\n"); - for i = (nz + 1) : (nz + nx) - printf (" %8.4f %8.4f\n", tb (i), se (i)); - endfor - endif - endif - - if (nargout == 6) - if (nx > 0) - e = ((x * beta) * ones (1, nz)) + ((y * 0 + 1) * theta'); - else - e = (y * 0 + 1) * theta'; - endif - gamma = diff ([(y * 0), (exp (e) ./ (1 + exp (e))), (y * 0 + 1)]')'; - endif - -endfunction
--- a/scripts/statistics/models/module.mk Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,26 +0,0 @@ -FCN_FILE_DIRS += \ - scripts/statistics/models \ - %reldir%/private - -%canon_reldir%_PRIVATE_FCN_FILES = \ - %reldir%/private/logistic_regression_derivatives.m \ - %reldir%/private/logistic_regression_likelihood.m - -%canon_reldir%_FCN_FILES = \ - %reldir%/logistic_regression.m - -%canon_reldir%dir = $(fcnfiledir)/statistics/models - -%canon_reldir%_DATA = $(%canon_reldir%_FCN_FILES) - -%canon_reldir%_privatedir = $(fcnfiledir)/statistics/models/private - -%canon_reldir%_private_DATA = $(%canon_reldir%_PRIVATE_FCN_FILES) - -FCN_FILES += \ - $(%canon_reldir%_FCN_FILES) \ - $(%canon_reldir%_PRIVATE_FCN_FILES) - -PKG_ADD_FILES += %reldir%/PKG_ADD - -DIRSTAMP_FILES += %reldir%/$(octave_dirstamp)
--- a/scripts/statistics/models/private/logistic_regression_derivatives.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,44 +0,0 @@ -## Copyright (C) 1995-2017 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {[@var{dl}, @var{d2l}] =} logistic_regression_derivatives (@var{x}, @var{z}, @var{z1}, @var{g}, @var{g1}, @var{p}) -## Calculate derivatives of the log-likelihood for ordinal logistic regression -## model. -## -## Private function called by @code{logistic_regression}. -## @seealso{logistic_regression} -## @end deftypefn - -## Author: Gordon K. Smyth <gks@maths.uq.oz.au> -## Adapted-By: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: Derivates of log-likelihood in logistic regression - -function [dl, d2l] = logistic_regression_derivatives (x, z, z1, g, g1, p) - - ## first derivative - v = g .* (1 - g) ./ p; v1 = g1 .* (1 - g1) ./ p; - dlogp = [(diag (v) * z - diag (v1) * z1), (diag (v - v1) * x)]; - dl = sum (dlogp)'; - - ## second derivative - w = v .* (1 - 2 * g); w1 = v1 .* (1 - 2 * g1); - d2l = [z, x]' * diag (w) * [z, x] - [z1, x]' * diag (w1) * [z1, x] ... - - dlogp' * dlogp; - -endfunction
--- a/scripts/statistics/models/private/logistic_regression_likelihood.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,40 +0,0 @@ -## Copyright (C) 1995-2017 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {[@var{g}, @var{g1}, @var{p}, @var{dev}] =} logistic_regression_likelihood (@var{y}, @var{x}, @var{beta}, @var{z}, @var{z1}) -## Calculate the likelihood for the ordinal logistic regression model. -## -## Private function called by @code{logistic_regression}. -## @seealso{logistic_regression} -## @end deftypefn - -## Author: Gordon K. Smyth <gks@maths.uq.oz.au> -## Adapted-By: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: Likelihood in logistic regression - -function [g, g1, p, dev] = logistic_regression_likelihood (y, x, beta, z, z1) - - e = exp ([z, x] * beta); e1 = exp ([z1, x] * beta); - g = e ./ (1 + e); g1 = e1 ./ (1 + e1); - g = max (y == max (y), g); g1 = min (y > min (y), g1); - - p = g - g1; - dev = -2 * sum (log (p)); - -endfunction
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/scripts/statistics/module.mk Sun Jan 07 17:13:23 2018 -0800 @@ -0,0 +1,48 @@ +FCN_FILE_DIRS += scripts/statistics + +%canon_reldir%_FCN_FILES = \ + %reldir%/center.m \ + %reldir%/corrcoef.m \ + %reldir%/corr.m \ + %reldir%/cov.m \ + %reldir%/discrete_cdf.m \ + %reldir%/discrete_inv.m \ + %reldir%/discrete_pdf.m \ + %reldir%/discrete_rnd.m \ + %reldir%/empirical_cdf.m \ + %reldir%/empirical_inv.m \ + %reldir%/empirical_pdf.m \ + %reldir%/empirical_rnd.m \ + %reldir%/histc.m \ + %reldir%/iqr.m \ + %reldir%/kendall.m \ + %reldir%/kurtosis.m \ + %reldir%/mean.m \ + %reldir%/meansq.m \ + %reldir%/median.m \ + %reldir%/mode.m \ + %reldir%/moment.m \ + %reldir%/prctile.m \ + %reldir%/quantile.m \ + %reldir%/range.m \ + %reldir%/ranks.m \ + %reldir%/run_count.m \ + %reldir%/runlength.m \ + %reldir%/skewness.m \ + %reldir%/spearman.m \ + %reldir%/statistics.m \ + %reldir%/std.m \ + %reldir%/var.m \ + %reldir%/zscore.m + +%canon_reldir%dir = $(fcnfiledir)/statistics + +%canon_reldir%_DATA = $(%canon_reldir%_FCN_FILES) + +FCN_FILES += \ + $(%canon_reldir%_FCN_FILES) \ + $(%canon_reldir%_PRIVATE_FCN_FILES) + +PKG_ADD_FILES += %reldir%/PKG_ADD + +DIRSTAMP_FILES += %reldir%/$(octave_dirstamp)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/scripts/statistics/moment.m Sun Jan 07 17:13:23 2018 -0800 @@ -0,0 +1,211 @@ +## Copyright (C) 1995-2017 Kurt Hornik +## +## This file is part of Octave. +## +## Octave is free software: you can redistribute it and/or modify it +## under the terms of the GNU General Public License as published by +## the Free Software Foundation, either version 3 of the License, or +## (at your option) any later version. +## +## Octave is distributed in the hope that it will be useful, but +## WITHOUT ANY WARRANTY; without even the implied warranty of +## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +## GNU General Public License for more details. +## +## You should have received a copy of the GNU General Public License +## along with Octave; see the file COPYING. If not, see +## <https://www.gnu.org/licenses/>. + +## -*- texinfo -*- +## @deftypefn {} {} moment (@var{x}, @var{p}) +## @deftypefnx {} {} moment (@var{x}, @var{p}, @var{type}) +## @deftypefnx {} {} moment (@var{x}, @var{p}, @var{dim}) +## @deftypefnx {} {} moment (@var{x}, @var{p}, @var{type}, @var{dim}) +## @deftypefnx {} {} moment (@var{x}, @var{p}, @var{dim}, @var{type}) +## Compute the @var{p}-th central moment of the vector @var{x}: +## +## @tex +## $$ +## {\sum_{i=1}^N (x_i - \bar{x})^p \over N} +## $$ +## where $\bar{x}$ is the mean value of @var{x} and $N$ is the number of elements of @var{x}. +## +## +## @end tex +## @ifnottex +## +## @example +## @group +## 1/N SUM_i (@var{x}(i) - mean(@var{x}))^@var{p} +## @end group +## @end example +## +## where @math{N} is the length of the @var{x} vector. +## +## @end ifnottex +## +## If @var{x} is a matrix, return the row vector containing the @var{p}-th +## central moment of each column. +## +## If the optional argument @var{dim} is given, operate along this dimension. +## +## The optional string @var{type} specifies the type of moment to be computed. +## Valid options are: +## +## @table @asis +## @item @qcode{"c"} +## Central Moment (default). +## +## @item @qcode{"a"} +## @itemx @qcode{"ac"} +## Absolute Central Moment. The moment about the mean ignoring sign +## defined as +## @tex +## $$ +## {\sum_{i=1}^N {\left| x_i - \bar{x} \right|}^p \over N} +## $$ +## @end tex +## @ifnottex +## +## @example +## @group +## 1/N SUM_i (abs (@var{x}(i) - mean(@var{x})))^@var{p} +## @end group +## @end example +## +## @end ifnottex +## +## @item @qcode{"r"} +## Raw Moment. The moment about zero defined as +## +## @tex +## $$ +## {\rm moment} (x) = { \sum_{i=1}^N {x_i}^p \over N } +## $$ +## @end tex +## @ifnottex +## +## @example +## @group +## moment (@var{x}) = 1/N SUM_i @var{x}(i)^@var{p} +## @end group +## @end example +## +## @end ifnottex +## +## @item @nospell{@qcode{"ar"}} +## Absolute Raw Moment. The moment about zero ignoring sign defined as +## @tex +## $$ +## {\sum_{i=1}^N {\left| x_i \right|}^p \over N} +## $$ +## @end tex +## @ifnottex +## +## @example +## @group +## 1/N SUM_i ( abs (@var{x}(i)) )^@var{p} +## @end group +## @end example +## +## @end ifnottex +## @end table +## +## If both @var{type} and @var{dim} are given they may appear in any order. +## @seealso{var, skewness, kurtosis} +## @end deftypefn + +## Can easily be made to work for continuous distributions (using quad) +## as well, but how does the general case work? + +## Author: KH <Kurt.Hornik@wu-wien.ac.at> +## Description: Compute moments + +function m = moment (x, p, opt1, opt2) + + if (nargin < 2 || nargin > 4) + print_usage (); + endif + + if (! (isnumeric (x) || islogical (x)) || isempty (x)) + error ("moment: X must be a non-empty numeric matrix or vector"); + endif + + if (! (isnumeric (p) && isscalar (p))) + error ("moment: P must be a numeric scalar"); + endif + + need_dim = false; + + if (nargin == 2) + type = ""; + need_dim = true; + elseif (nargin == 3) + if (ischar (opt1)) + type = opt1; + need_dim = true; + else + dim = opt1; + type = ""; + endif + elseif (nargin == 4) + if (ischar (opt1)) + type = opt1; + dim = opt2; + elseif (ischar (opt2)) + type = opt2; + dim = opt1; + else + error ("moment: TYPE must be a string"); + endif + endif + + nd = ndims (x); + sz = size (x); + if (need_dim) + ## Find the first non-singleton dimension. + (dim = find (sz > 1, 1)) || (dim = 1); + else + if (! (isscalar (dim) && dim == fix (dim) && dim > 0)) + error ("moment: DIM must be an integer and a valid dimension"); + endif + endif + + n = size (x, dim); + + if (! any (type == "r")) + x = center (x, dim); + endif + if (any (type == "a")) + x = abs (x); + endif + + m = sum (x .^ p, dim) / n; + +endfunction + + +%!shared x +%! x = rand (10); +%!assert (moment (x,1), mean (center (x)), eps) +%!assert (moment (x,2), meansq (center (x)), eps) +%!assert (moment (x,1,2), mean (center (x, 2), 2), eps) +%!assert (moment (x,1,"a"), mean (abs (center (x))), eps) +%!assert (moment (x,1,"r"), mean (x), eps) +%!assert (moment (x,1,"ar"), mean (abs (x)), eps) + +%!assert (moment (single ([1 2 3]), 1, "r"), single (2)) + +%!assert (moment (1, 2, 4), 0) + +## Test input validation +%!error moment () +%!error moment (1) +%!error moment (1, 2, 3, 4, 5) +%!error <X must be a non-empty numeric matrix> moment (['A'; 'B'], 2) +%!error <X must be a non-empty numeric matrix> moment (ones (2,0,3), 2) +%!error <P must be a numeric scalar> moment (1, true) +%!error <P must be a numeric scalar> moment (1, ones (2,2)) +%!error <TYPE must be a string> moment (1, 2, 3, 4) +%!error <DIM must be an integer and a valid dimension> moment (1, 2, ones (2,2)) +%!error <DIM must be an integer and a valid dimension> moment (1, 2, 1.5)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/scripts/statistics/prctile.m Sun Jan 07 17:13:23 2018 -0800 @@ -0,0 +1,186 @@ +## Copyright (C) 2008-2017 Ben Abbott +## +## This file is part of Octave. +## +## Octave is free software: you can redistribute it and/or modify it +## under the terms of the GNU General Public License as published by +## the Free Software Foundation, either version 3 of the License, or +## (at your option) any later version. +## +## Octave is distributed in the hope that it will be useful, but +## WITHOUT ANY WARRANTY; without even the implied warranty of +## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +## GNU General Public License for more details. +## +## You should have received a copy of the GNU General Public License +## along with Octave; see the file COPYING. If not, see +## <https://www.gnu.org/licenses/>. + +## -*- texinfo -*- +## @deftypefn {} {@var{q} =} prctile (@var{x}) +## @deftypefnx {} {@var{q} =} prctile (@var{x}, @var{p}) +## @deftypefnx {} {@var{q} =} prctile (@var{x}, @var{p}, @var{dim}) +## For a sample @var{x}, compute the quantiles, @var{q}, corresponding +## to the cumulative probability values, @var{p}, in percent. +## +## If @var{x} is a matrix, compute the percentiles for each column and return +## them in a matrix, such that the i-th row of @var{q} contains the +## @var{p}(i)th percentiles of each column of @var{x}. +## +## If @var{p} is unspecified, return the quantiles for @code{[0 25 50 75 100]}. +## +## The optional argument @var{dim} determines the dimension along which the +## percentiles are calculated. If @var{dim} is omitted it defaults to the +## first non-singleton dimension. +## +## Programming Note: All non-numeric values (NaNs) of @var{x} are ignored. +## @seealso{quantile} +## @end deftypefn + +## Author: Ben Abbott <bpabbott@mac.com> +## Description: Matlab style prctile function. + +function q = prctile (x, p = [], dim) + + if (nargin < 1 || nargin > 3) + print_usage (); + endif + + if (! (isnumeric (x) || islogical (x))) + error ("prctile: X must be a numeric vector or matrix"); + endif + + if (isempty (p)) + p = [0, 25, 50, 75, 100]; + endif + + if (! (isnumeric (p) && isvector (p))) + error ("prctile: P must be a numeric vector"); + endif + + nd = ndims (x); + sz = size (x); + if (nargin < 3) + ## Find the first non-singleton dimension. + (dim = find (sz > 1, 1)) || (dim = 1); + else + if (!(isscalar (dim) && dim == fix (dim)) + || !(1 <= dim && dim <= nd)) + error ("prctile: DIM must be an integer and a valid dimension"); + endif + endif + + ## Convert from percent to decimal. + p /= 100; + + q = quantile (x, p, dim); + +endfunction + + +%!test +%! pct = 50; +%! q = prctile (1:4, pct); +%! qa = 2.5; +%! assert (q, qa); +%! q = prctile (1:4, pct, 1); +%! qa = [1, 2, 3, 4]; +%! assert (q, qa); +%! q = prctile (1:4, pct, 2); +%! qa = 2.5; +%! assert (q, qa); + +%!test +%! pct = [50 75]; +%! q = prctile (1:4, pct); +%! qa = [2.5 3.5]; +%! assert (q, qa); +%! q = prctile (1:4, pct, 1); +%! qa = [1, 2, 3, 4; 1, 2, 3, 4]; +%! assert (q, qa); +%! q = prctile (1:4, pct, 2); +%! qa = [2.5 3.5]; +%! assert (q, qa); + +%!test +%! pct = 50; +%! x = [0.1126, 0.1148, 0.0521, 0.2364, 0.1393 +%! 0.1718, 0.7273, 0.2041, 0.4531, 0.1585 +%! 0.2795, 0.7978, 0.3296, 0.5567, 0.7307 +%! 0.4288, 0.8753, 0.6477, 0.6287, 0.8165 +%! 0.9331, 0.9312, 0.9635, 0.7796, 0.8461]; +%! tol = 0.0001; +%! q = prctile (x, pct, 1); +%! qa = [0.2795, 0.7978, 0.3296, 0.5567, 0.7307]; +%! assert (q, qa, tol); +%! q = prctile (x, pct, 2); +%! qa = [0.1148; 0.2041; 0.5567; 0.6477; 0.9312]; +%! assert (q, qa, tol); + +%!test +%! pct = 50; +%! tol = 0.0001; +%! x = [0.1126, 0.1148, 0.0521, 0.2364, 0.1393 +%! 0.1718, 0.7273, 0.2041, 0.4531, 0.1585 +%! 0.2795, 0.7978, 0.3296, 0.5567, 0.7307 +%! 0.4288, 0.8753, 0.6477, 0.6287, 0.8165 +%! 0.9331, 0.9312, 0.9635, 0.7796, 0.8461]; +%! x(5,5) = Inf; +%! q = prctile (x, pct, 1); +%! qa = [0.2795, 0.7978, 0.3296, 0.5567, 0.7307]; +%! assert (q, qa, tol); +%! x(5,5) = -Inf; +%! q = prctile (x, pct, 1); +%! qa = [0.2795, 0.7978, 0.3296, 0.5567, 0.1585]; +%! assert (q, qa, tol); +%! x(1,1) = Inf; +%! q = prctile (x, pct, 1); +%! qa = [0.4288, 0.7978, 0.3296, 0.5567, 0.1585]; +%! assert (q, qa, tol); + +%!test +%! pct = 50; +%! tol = 0.0001; +%! x = [0.1126, 0.1148, 0.0521, 0.2364, 0.1393 +%! 0.1718, 0.7273, 0.2041, 0.4531, 0.1585 +%! 0.2795, 0.7978, 0.3296, 0.5567, 0.7307 +%! 0.4288, 0.8753, 0.6477, 0.6287, 0.8165 +%! 0.9331, 0.9312, 0.9635, 0.7796, 0.8461]; +%! x(3,3) = Inf; +%! q = prctile (x, pct, 1); +%! qa = [0.2795, 0.7978, 0.6477, 0.5567, 0.7307]; +%! assert (q, qa, tol); +%! q = prctile (x, pct, 2); +%! qa = [0.1148; 0.2041; 0.7307; 0.6477; 0.9312]; +%! assert (q, qa, tol); + +%!test +%! pct = 50; +%! tol = 0.0001; +%! x = [0.1126, 0.1148, 0.0521, 0.2364, 0.1393 +%! 0.1718, 0.7273, 0.2041, 0.4531, 0.1585 +%! 0.2795, 0.7978, 0.3296, 0.5567, 0.7307 +%! 0.4288, 0.8753, 0.6477, 0.6287, 0.8165 +%! 0.9331, 0.9312, 0.9635, 0.7796, 0.8461]; +%! x(5,5) = NaN; +%! q = prctile (x, pct, 2); +%! qa = [0.1148; 0.2041; 0.5567; 0.6477; 0.9322]; +%! assert (q, qa, tol); +%! x(1,1) = NaN; +%! q = prctile (x, pct, 2); +%! qa = [0.1270; 0.2041; 0.5567; 0.6477; 0.9322]; +%! assert (q, qa, tol); +%! x(3,3) = NaN; +%! q = prctile (x, pct, 2); +%! qa = [0.1270; 0.2041; 0.6437; 0.6477; 0.9322]; +%! assert (q, qa, tol); + +## Test input validation +%!error prctile () +%!error prctile (1, 2, 3, 4) +%!error prctile (['A'; 'B'], 10) +%!error prctile (1:10, [true, false]) +%!error prctile (1:10, ones (2,2)) +%!error prctile (1, 1, 1.5) +%!error prctile (1, 1, 0) +%!error prctile (1, 1, 3)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/scripts/statistics/quantile.m Sun Jan 07 17:13:23 2018 -0800 @@ -0,0 +1,490 @@ +## Copyright (C) 2008-2017 Ben Abbott and Jaroslav Hajek +## +## This file is part of Octave. +## +## Octave is free software: you can redistribute it and/or modify it +## under the terms of the GNU General Public License as published by +## the Free Software Foundation, either version 3 of the License, or +## (at your option) any later version. +## +## Octave is distributed in the hope that it will be useful, but +## WITHOUT ANY WARRANTY; without even the implied warranty of +## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +## GNU General Public License for more details. +## +## You should have received a copy of the GNU General Public License +## along with Octave; see the file COPYING. If not, see +## <https://www.gnu.org/licenses/>. + +## -*- texinfo -*- +## @deftypefn {} {@var{q} =} quantile (@var{x}) +## @deftypefnx {} {@var{q} =} quantile (@var{x}, @var{p}) +## @deftypefnx {} {@var{q} =} quantile (@var{x}, @var{p}, @var{dim}) +## @deftypefnx {} {@var{q} =} quantile (@var{x}, @var{p}, @var{dim}, @var{method}) +## For a sample, @var{x}, calculate the quantiles, @var{q}, corresponding to +## the cumulative probability values in @var{p}. All non-numeric values (NaNs) +## of @var{x} are ignored. +## +## If @var{x} is a matrix, compute the quantiles for each column and +## return them in a matrix, such that the i-th row of @var{q} contains +## the @var{p}(i)th quantiles of each column of @var{x}. +## +## If @var{p} is unspecified, return the quantiles for +## @code{[0.00 0.25 0.50 0.75 1.00]}. +## The optional argument @var{dim} determines the dimension along which +## the quantiles are calculated. If @var{dim} is omitted it defaults to +## the first non-singleton dimension. +## +## The methods available to calculate sample quantiles are the nine methods +## used by R (@url{http://www.r-project.org/}). The default value is +## @w{@var{method} = 5}. +## +## Discontinuous sample quantile methods 1, 2, and 3 +## +## @enumerate 1 +## @item Method 1: Inverse of empirical distribution function. +## +## @item Method 2: Similar to method 1 but with averaging at discontinuities. +## +## @item Method 3: SAS definition: nearest even order statistic. +## @end enumerate +## +## Continuous sample quantile methods 4 through 9, where +## @tex +## $p(k)$ +## @end tex +## @ifnottex +## @var{p}(k) +## @end ifnottex +## is the linear +## interpolation function respecting each method's representative cdf. +## +## @enumerate 4 +## @item Method 4: +## @tex +## $p(k) = k / N$. +## @end tex +## @ifnottex +## @var{p}(k) = k / N. +## @end ifnottex +## That is, linear interpolation of the empirical cdf, where @math{N} is the +## length of @var{P}. +## +## @item Method 5: +## @tex +## $p(k) = (k - 0.5) / N$. +## @end tex +## @ifnottex +## @var{p}(k) = (k - 0.5) / N. +## @end ifnottex +## That is, a piecewise linear function where the knots are the values midway +## through the steps of the empirical cdf. +## +## @item Method 6: +## @tex +## $p(k) = k / (N + 1)$. +## @end tex +## @ifnottex +## @var{p}(k) = k / (N + 1). +## @end ifnottex +## +## @item Method 7: +## @tex +## $p(k) = (k - 1) / (N - 1)$. +## @end tex +## @ifnottex +## @var{p}(k) = (k - 1) / (N - 1). +## @end ifnottex +## +## @item Method 8: +## @tex +## $p(k) = (k - 1/3) / (N + 1/3)$. +## @end tex +## @ifnottex +## @var{p}(k) = (k - 1/3) / (N + 1/3). +## @end ifnottex +## The resulting quantile estimates are approximately median-unbiased +## regardless of the distribution of @var{x}. +## +## @item Method 9: +## @tex +## $p(k) = (k - 3/8) / (N + 1/4)$. +## @end tex +## @ifnottex +## @var{p}(k) = (k - 3/8) / (N + 1/4). +## @end ifnottex +## The resulting quantile estimates are approximately unbiased for the +## expected order statistics if @var{x} is normally distributed. +## @end enumerate +## +## @nospell{Hyndman and Fan} (1996) recommend method 8. Maxima, S, and R +## (versions prior to 2.0.0) use 7 as their default. Minitab and SPSS +## use method 6. @sc{matlab} uses method 5. +## +## References: +## +## @itemize @bullet +## @item @nospell{Becker, R. A., Chambers, J. M. and Wilks, A. R.} (1988) +## The New S Language. @nospell{Wadsworth & Brooks/Cole}. +## +## @item @nospell{Hyndman, R. J. and Fan, Y.} (1996) Sample quantiles in +## statistical packages, American Statistician, 50, 361--365. +## +## @item R: A Language and Environment for Statistical Computing; +## @url{http://cran.r-project.org/doc/manuals/fullrefman.pdf}. +## @end itemize +## +## Examples: +## @c Set example in small font to prevent overfull line +## +## @smallexample +## @group +## x = randi (1000, [10, 1]); # Create empirical data in range 1-1000 +## q = quantile (x, [0, 1]); # Return minimum, maximum of distribution +## q = quantile (x, [0.25 0.5 0.75]); # Return quartiles of distribution +## @end group +## @end smallexample +## @seealso{prctile} +## @end deftypefn + +## Author: Ben Abbott <bpabbott@mac.com> +## Description: Matlab style quantile function of a discrete/continuous +## distribution. + +function q = quantile (x, p = [], dim, method = 5) + + if (nargin < 1 || nargin > 4) + print_usage (); + endif + + if (! (isnumeric (x) || islogical (x)) || isempty (x)) + error ("quantile: X must be a non-empty numeric vector or matrix"); + endif + + if (isempty (p)) + p = [0.00 0.25, 0.50, 0.75, 1.00]; + endif + + if (! (isnumeric (p) && isvector (p))) + error ("quantile: P must be a numeric vector"); + endif + + if (nargin < 3) + ## Find the first non-singleton dimension. + (dim = find (size (x) > 1, 1)) || (dim = 1); + else + if (!(isscalar (dim) && dim == fix (dim)) + || !(1 <= dim && dim <= ndims (x))) + error ("quantile: DIM must be an integer and a valid dimension"); + endif + endif + + ## Set the permutation vector. + perm = 1:ndims (x); + perm(1) = dim; + perm(dim) = 1; + + ## Permute dim to the 1st index. + x = permute (x, perm); + + ## Save the size of the permuted x N-d array. + sx = size (x); + + ## Reshape to a 2-d array. + x = reshape (x, [sx(1), prod(sx(2:end))]); + + ## Calculate the quantiles. + q = __quantile__ (x, p, method); + + ## Return the shape to the original N-d array. + q = reshape (q, [numel(p), sx(2:end)]); + + ## Permute the 1st index back to dim. + q = ipermute (q, perm); + +endfunction + + +%!test +%! p = 0.50; +%! q = quantile (1:4, p); +%! qa = 2.5; +%! assert (q, qa); +%! q = quantile (1:4, p, 1); +%! qa = [1, 2, 3, 4]; +%! assert (q, qa); +%! q = quantile (1:4, p, 2); +%! qa = 2.5; +%! assert (q, qa); + +%!test +%! p = [0.50 0.75]; +%! q = quantile (1:4, p); +%! qa = [2.5 3.5]; +%! assert (q, qa); +%! q = quantile (1:4, p, 1); +%! qa = [1, 2, 3, 4; 1, 2, 3, 4]; +%! assert (q, qa); +%! q = quantile (1:4, p, 2); +%! qa = [2.5 3.5]; +%! assert (q, qa); + +%!test +%! p = 0.5; +%! x = sort (rand (11)); +%! q = quantile (x, p); +%! assert (q, x(6,:)); +%! x = x.'; +%! q = quantile (x, p, 2); +%! assert (q, x(:,6)); + +%!test +%! p = [0.00, 0.25, 0.50, 0.75, 1.00]; +%! x = [1; 2; 3; 4]; +%! a = [1.0000 1.0000 2.0000 3.0000 4.0000 +%! 1.0000 1.5000 2.5000 3.5000 4.0000 +%! 1.0000 1.0000 2.0000 3.0000 4.0000 +%! 1.0000 1.0000 2.0000 3.0000 4.0000 +%! 1.0000 1.5000 2.5000 3.5000 4.0000 +%! 1.0000 1.2500 2.5000 3.7500 4.0000 +%! 1.0000 1.7500 2.5000 3.2500 4.0000 +%! 1.0000 1.4167 2.5000 3.5833 4.0000 +%! 1.0000 1.4375 2.5000 3.5625 4.0000]; +%! for m = 1:9 +%! q = quantile (x, p, 1, m).'; +%! assert (q, a(m,:), 0.0001); +%! endfor + +%!test +%! p = [0.00, 0.25, 0.50, 0.75, 1.00]; +%! x = [1; 2; 3; 4; 5]; +%! a = [1.0000 2.0000 3.0000 4.0000 5.0000 +%! 1.0000 2.0000 3.0000 4.0000 5.0000 +%! 1.0000 1.0000 2.0000 4.0000 5.0000 +%! 1.0000 1.2500 2.5000 3.7500 5.0000 +%! 1.0000 1.7500 3.0000 4.2500 5.0000 +%! 1.0000 1.5000 3.0000 4.5000 5.0000 +%! 1.0000 2.0000 3.0000 4.0000 5.0000 +%! 1.0000 1.6667 3.0000 4.3333 5.0000 +%! 1.0000 1.6875 3.0000 4.3125 5.0000]; +%! for m = 1:9 +%! q = quantile (x, p, 1, m).'; +%! assert (q, a(m,:), 0.0001); +%! endfor + +%!test +%! p = [0.00, 0.25, 0.50, 0.75, 1.00]; +%! x = [1; 2; 5; 9]; +%! a = [1.0000 1.0000 2.0000 5.0000 9.0000 +%! 1.0000 1.5000 3.5000 7.0000 9.0000 +%! 1.0000 1.0000 2.0000 5.0000 9.0000 +%! 1.0000 1.0000 2.0000 5.0000 9.0000 +%! 1.0000 1.5000 3.5000 7.0000 9.0000 +%! 1.0000 1.2500 3.5000 8.0000 9.0000 +%! 1.0000 1.7500 3.5000 6.0000 9.0000 +%! 1.0000 1.4167 3.5000 7.3333 9.0000 +%! 1.0000 1.4375 3.5000 7.2500 9.0000]; +%! for m = 1:9 +%! q = quantile (x, p, 1, m).'; +%! assert (q, a(m,:), 0.0001); +%! endfor + +%!test +%! p = [0.00, 0.25, 0.50, 0.75, 1.00]; +%! x = [1; 2; 5; 9; 11]; +%! a = [1.0000 2.0000 5.0000 9.0000 11.0000 +%! 1.0000 2.0000 5.0000 9.0000 11.0000 +%! 1.0000 1.0000 2.0000 9.0000 11.0000 +%! 1.0000 1.2500 3.5000 8.0000 11.0000 +%! 1.0000 1.7500 5.0000 9.5000 11.0000 +%! 1.0000 1.5000 5.0000 10.0000 11.0000 +%! 1.0000 2.0000 5.0000 9.0000 11.0000 +%! 1.0000 1.6667 5.0000 9.6667 11.0000 +%! 1.0000 1.6875 5.0000 9.6250 11.0000]; +%! for m = 1:9 +%! q = quantile (x, p, 1, m).'; +%! assert (q, a(m,:), 0.0001); +%! endfor + +%!test +%! p = [0.00, 0.25, 0.50, 0.75, 1.00]; +%! x = [16; 11; 15; 12; 15; 8; 11; 12; 6; 10]; +%! a = [6.0000 10.0000 11.0000 15.0000 16.0000 +%! 6.0000 10.0000 11.5000 15.0000 16.0000 +%! 6.0000 8.0000 11.0000 15.0000 16.0000 +%! 6.0000 9.0000 11.0000 13.5000 16.0000 +%! 6.0000 10.0000 11.5000 15.0000 16.0000 +%! 6.0000 9.5000 11.5000 15.0000 16.0000 +%! 6.0000 10.2500 11.5000 14.2500 16.0000 +%! 6.0000 9.8333 11.5000 15.0000 16.0000 +%! 6.0000 9.8750 11.5000 15.0000 16.0000]; +%! for m = 1:9 +%! q = quantile (x, p, 1, m).'; +%! assert (q, a(m,:), 0.0001); +%! endfor + +%!test +%! p = [0.00, 0.25, 0.50, 0.75, 1.00]; +%! x = [-0.58851; 0.40048; 0.49527; -2.551500; -0.52057; ... +%! -0.17841; 0.057322; -0.62523; 0.042906; 0.12337]; +%! a = [-2.551474 -0.588505 -0.178409 0.123366 0.495271 +%! -2.551474 -0.588505 -0.067751 0.123366 0.495271 +%! -2.551474 -0.625231 -0.178409 0.123366 0.495271 +%! -2.551474 -0.606868 -0.178409 0.090344 0.495271 +%! -2.551474 -0.588505 -0.067751 0.123366 0.495271 +%! -2.551474 -0.597687 -0.067751 0.192645 0.495271 +%! -2.551474 -0.571522 -0.067751 0.106855 0.495271 +%! -2.551474 -0.591566 -0.067751 0.146459 0.495271 +%! -2.551474 -0.590801 -0.067751 0.140686 0.495271]; +%! for m = 1:9 +%! q = quantile (x, p, 1, m).'; +%! assert (q, a(m,:), 0.0001); +%! endfor + +%!test +%! p = 0.5; +%! x = [0.112600, 0.114800, 0.052100, 0.236400, 0.139300 +%! 0.171800, 0.727300, 0.204100, 0.453100, 0.158500 +%! 0.279500, 0.797800, 0.329600, 0.556700, 0.730700 +%! 0.428800, 0.875300, 0.647700, 0.628700, 0.816500 +%! 0.933100, 0.931200, 0.963500, 0.779600, 0.846100]; +%! tol = 0.00001; +%! x(5,5) = NaN; +%! assert (quantile (x, p, 1), [0.27950, 0.79780, 0.32960, 0.55670, 0.44460], tol); +%! x(1,1) = NaN; +%! assert (quantile (x, p, 1), [0.35415, 0.79780, 0.32960, 0.55670, 0.44460], tol); +%! x(3,3) = NaN; +%! assert (quantile (x, p, 1), [0.35415, 0.79780, 0.42590, 0.55670, 0.44460], tol); + +%!test +%! sx = [2, 3, 4]; +%! x = rand (sx); +%! dim = 2; +%! p = 0.5; +%! yobs = quantile (x, p, dim); +%! yexp = median (x, dim); +%! assert (yobs, yexp); + +%!assert <*45455> (quantile ([1 3 2], 0.5, 1), [1 3 2]) + +## Test input validation +%!error quantile () +%!error quantile (1, 2, 3, 4, 5) +%!error quantile (['A'; 'B'], 10) +%!error quantile (1:10, [true, false]) +%!error quantile (1:10, ones (2,2)) +%!error quantile (1, 1, 1.5) +%!error quantile (1, 1, 0) +%!error quantile (1, 1, 3) +%!error quantile ((1:5)', 0.5, 1, 0) +%!error quantile ((1:5)', 0.5, 1, 10) + +## For the cumulative probability values in @var{p}, compute the +## quantiles, @var{q} (the inverse of the cdf), for the sample, @var{x}. +## +## The optional input, @var{method}, refers to nine methods available in R +## (http://www.r-project.org/). The default is @var{method} = 7. +## @seealso{prctile, quantile, statistics} + +## Author: Ben Abbott <bpabbott@mac.com> +## Vectorized version: Jaroslav Hajek <highegg@gmail.com> +## Description: Quantile function of empirical samples + +function inv = __quantile__ (x, p, method = 5) + + if (nargin < 2 || nargin > 3) + print_usage (); + endif + + if (isinteger (x) || islogical (x)) + x = double (x); + endif + + ## set shape of quantiles to column vector. + p = p(:); + + ## Save length and set shape of samples. + x = sort (x, 1); + m = sum (! isnan (x)); + [xr, xc] = size (x); + + ## Initialize output values. + inv = Inf (class (x)) * (-(p < 0) + (p > 1)); + inv = repmat (inv, 1, xc); + + ## Do the work. + if (any (k = find ((p >= 0) & (p <= 1)))) + n = length (k); + p = p(k); + ## Special case of 1 row. + if (xr == 1) + inv(k,:) = repmat (x, n, 1); + return; + endif + + ## The column-distribution indices. + pcd = kron (ones (n, 1), xr*(0:xc-1)); + mm = kron (ones (n, 1), m); + switch (method) + case {1, 2, 3} + switch (method) + case 1 + p = max (ceil (kron (p, m)), 1); + inv(k,:) = x(p + pcd); + + case 2 + p = kron (p, m); + p_lr = max (ceil (p), 1); + p_rl = min (floor (p + 1), mm); + inv(k,:) = (x(p_lr + pcd) + x(p_rl + pcd))/2; + + case 3 + ## Used by SAS, method PCTLDEF=2. + ## http://support.sas.com/onlinedoc/913/getDoc/en/statug.hlp/stdize_sect14.htm + t = max (kron (p, m), 1); + t = roundb (t); + inv(k,:) = x(t + pcd); + endswitch + + otherwise + switch (method) + case 4 + p = kron (p, m); + + case 5 + ## Used by Matlab. + p = kron (p, m) + 0.5; + + case 6 + ## Used by Minitab and SPSS. + p = kron (p, m+1); + + case 7 + ## Used by S and R. + p = kron (p, m-1) + 1; + + case 8 + ## Median unbiased. + p = kron (p, m+1/3) + 1/3; + + case 9 + ## Approximately unbiased respecting order statistics. + p = kron (p, m+0.25) + 0.375; + + otherwise + error ("quantile: Unknown METHOD, '%d'", method); + endswitch + + ## Duplicate single values. + imm1 = (mm(1,:) == 1); + x(2,imm1) = x(1,imm1); + + ## Interval indices. + pi = max (min (floor (p), mm-1), 1); + pr = max (min (p - pi, 1), 0); + pi += pcd; + inv(k,:) = (1-pr) .* x(pi) + pr .* x(pi+1); + endswitch + endif + +endfunction
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/scripts/statistics/range.m Sun Jan 07 17:13:23 2018 -0800 @@ -0,0 +1,63 @@ +## Copyright (C) 1995-2017 Kurt Hornik +## Copyright (C) 2009 Jaroslav Hajek +## +## This file is part of Octave. +## +## Octave is free software: you can redistribute it and/or modify it +## under the terms of the GNU General Public License as published by +## the Free Software Foundation, either version 3 of the License, or +## (at your option) any later version. +## +## Octave is distributed in the hope that it will be useful, but +## WITHOUT ANY WARRANTY; without even the implied warranty of +## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +## GNU General Public License for more details. +## +## You should have received a copy of the GNU General Public License +## along with Octave; see the file COPYING. If not, see +## <https://www.gnu.org/licenses/>. + +## -*- texinfo -*- +## @deftypefn {} {} range (@var{x}) +## @deftypefnx {} {} range (@var{x}, @var{dim}) +## Return the range, i.e., the difference between the maximum and the minimum +## of the input data. +## +## If @var{x} is a vector, the range is calculated over the elements of +## @var{x}. If @var{x} is a matrix, the range is calculated over each column +## of @var{x}. +## +## If the optional argument @var{dim} is given, operate along this dimension. +## +## The range is a quickly computed measure of the dispersion of a data set, but +## is less accurate than @code{iqr} if there are outlying data points. +## @seealso{iqr, std} +## @end deftypefn + +## Author: KH <Kurt.Hornik@wu-wien.ac.at> +## Description: Compute range + +function y = range (x, dim) + + if (nargin < 1 || nargin > 2) + print_usage (); + endif + + if (nargin == 1) + y = max (x) - min (x); + else + y = max (x, [], dim) - min (x, [], dim); + endif + +endfunction + + +%!assert (range (1:10), 9) +%!assert (range (single (1:10)), single (9)) +%!assert (range (magic (3)), [5, 8, 5]) +%!assert (range (magic (3), 2), [7; 4; 7]) +%!assert (range (2), 0) + +## Test input validation +%!error range () +%!error range (1, 2, 3)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/scripts/statistics/ranks.m Sun Jan 07 17:13:23 2018 -0800 @@ -0,0 +1,104 @@ +## Copyright (C) 1995-2017 Kurt Hornik +## +## This file is part of Octave. +## +## Octave is free software: you can redistribute it and/or modify it +## under the terms of the GNU General Public License as published by +## the Free Software Foundation, either version 3 of the License, or +## (at your option) any later version. +## +## Octave is distributed in the hope that it will be useful, but +## WITHOUT ANY WARRANTY; without even the implied warranty of +## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +## GNU General Public License for more details. +## +## You should have received a copy of the GNU General Public License +## along with Octave; see the file COPYING. If not, see +## <https://www.gnu.org/licenses/>. + +## -*- texinfo -*- +## @deftypefn {} {} ranks (@var{x}, @var{dim}) +## Return the ranks of @var{x} along the first non-singleton dimension +## adjusted for ties. +## +## If the optional argument @var{dim} is given, operate along this dimension. +## @seealso{spearman, kendall} +## @end deftypefn + +## Author: KH <Kurt.Hornik@wu-wien.ac.at> +## Description: Compute ranks + +## This code was rather ugly, since it didn't use sort due to the +## fact of how to deal with ties. Now it does use sort and its +## even uglier! At least it handles NDArrays. + +function y = ranks (x, dim) + + if (nargin != 1 && nargin != 2) + print_usage (); + endif + + if (! (isnumeric (x) || islogical (x))) + error ("ranks: X must be a numeric vector or matrix"); + endif + + nd = ndims (x); + sz = size (x); + if (nargin != 2) + ## Find the first non-singleton dimension. + (dim = find (sz > 1, 1)) || (dim = 1); + else + if (!(isscalar (dim) && dim == fix (dim)) + || !(1 <= dim && dim <= nd)) + error ("ranks: DIM must be an integer and a valid dimension"); + endif + endif + + if (sz(dim) == 1) + y = ones (sz); + else + ## The algorithm works only on dim = 1, so permute if necesary. + if (dim != 1) + perm = [1 : nd]; + perm(1) = dim; + perm(dim) = 1; + x = permute (x, perm); + endif + sz = size (x); + infvec = -Inf ([1, sz(2 : end)]); + [xs, xi] = sort (x); + eq_el = find (diff ([xs; infvec]) == 0); + if (isempty (eq_el)) + [eq_el, y] = sort (xi); + else + runs = setdiff (eq_el, eq_el+1); + len = diff (find (diff ([Inf; eq_el; -Inf]) != 1)) + 1; + [eq_el, y] = sort (xi); + for i = 1 : length (runs) + y (xi (runs (i) + [0:(len(i)-1)]) + floor (runs (i) ./ sz(1)) + * sz(1)) = eq_el(runs(i)) + (len(i) - 1) / 2; + endfor + endif + if (dim != 1) + y = permute (y, perm); + endif + endif + +endfunction + + +%!assert (ranks (1:2:10), 1:5) +%!assert (ranks (10:-2:1), 5:-1:1) +%!assert (ranks ([2, 1, 2, 4]), [2.5, 1, 2.5, 4]) +%!assert (ranks (ones (1, 5)), 3*ones (1, 5)) +%!assert (ranks (1e6*ones (1, 5)), 3*ones (1, 5)) +%!assert (ranks (rand (1, 5), 1), ones (1, 5)) + +## Test input validation +%!error ranks () +%!error ranks (1, 2, 3) +%!error ranks ({1, 2}) +%!error ranks (['A'; 'B']) +%!error ranks (1, 1.5) +%!error ranks (1, 0) +%!error ranks (1, 3)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/scripts/statistics/run_count.m Sun Jan 07 17:13:23 2018 -0800 @@ -0,0 +1,112 @@ +## Copyright (C) 1995-2017 Friedrich Leisch +## +## This file is part of Octave. +## +## Octave is free software: you can redistribute it and/or modify it +## under the terms of the GNU General Public License as published by +## the Free Software Foundation, either version 3 of the License, or +## (at your option) any later version. +## +## Octave is distributed in the hope that it will be useful, but +## WITHOUT ANY WARRANTY; without even the implied warranty of +## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +## GNU General Public License for more details. +## +## You should have received a copy of the GNU General Public License +## along with Octave; see the file COPYING. If not, see +## <https://www.gnu.org/licenses/>. + +## -*- texinfo -*- +## @deftypefn {} {} run_count (@var{x}, @var{n}) +## @deftypefnx {} {} run_count (@var{x}, @var{n}, @var{dim}) +## Count the upward runs along the first non-singleton dimension of @var{x} +## of length 1, 2, @dots{}, @var{n}-1 and greater than or equal to @var{n}. +## +## If the optional argument @var{dim} is given then operate along this +## dimension. +## @seealso{runlength} +## @end deftypefn + +## Author: FL <Friedrich.Leisch@ci.tuwien.ac.at> +## Description: Count upward runs + +function retval = run_count (x, n, dim) + + if (nargin != 2 && nargin != 3) + print_usage (); + endif + + if (! (isnumeric (x) || islogical (x))) + error ("run_count: X must be a numeric vector or matrix"); + endif + + if (!(isscalar (n) && n == fix (n) && n > 0)) + error ("run_count: N must be a positive integer"); + endif + + nd = ndims (x); + sz = size (x); + if (nargin != 3) + ## Find the first non-singleton dimension. + (dim = find (sz > 1, 1)) || (dim = 1); + else + if (!(isscalar (dim) && dim == fix (dim)) + || !(1 <= dim && dim <= nd)) + error ("run_count: DIM must be an integer and a valid dimension"); + endif + endif + + ## Algorithm works on rows. Permute array if necessary, ipermute back at end + if (dim != 1) + perm = [1 : nd]; + perm(1) = dim; + perm(dim) = 1; + x = permute (x, perm); + endif + + sz = size (x); + idx = cell (); + for i = 1 : nd + idx{i} = 1 : sz(i); + endfor + c = sz(1); + tmp = zeros ([c + 1, sz(2 : end)]); + infvec = Inf ([1, sz(2 : end)]); + + ind = find (diff ([infvec; x; -infvec]) < 0); + tmp(ind(2:end) - 1) = diff (ind); + tmp = tmp(idx{:}); + + sz(1) = n; + retval = zeros (sz); + for k = 1 : (n-1) + idx{1} = k; + retval(idx{:}) = sum (tmp == k); + endfor + idx{1} = n; + retval(idx{:}) = sum (tmp >= n); + + if (dim != 1) + retval = ipermute (retval, perm); + endif + +endfunction + + +%!assert (run_count (magic (3), 4), [1,0,1;1,0,1;0,1,0;0,0,0]) +%!assert (run_count (magic (3), 4, 2), [1,0,1;1,0,1;0,1,0;0,0,0]') +%!assert (run_count (5:-1:1, 5), [5, 0, 0, 0, 0]) +%!assert (run_count (ones (3), 4), [0,0,0;0,0,0;1,1,1;0,0,0]) + +## Test input validation +%!error run_count () +%!error run_count (1) +%!error run_count (1, 2, 3, 4) +%!error run_count ({1, 2}, 3) +%!error run_count (['A'; 'A'; 'B'], 3) +%!error run_count (1:5, ones (2,2)) +%!error run_count (1:5, 1.5) +%!error run_count (1:5, -2) +%!error run_count (1:5, 3, ones (2,2)) +%!error run_count (1:5, 3, 1.5) +%!error run_count (1:5, 3, 0)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/scripts/statistics/runlength.m Sun Jan 07 17:13:23 2018 -0800 @@ -0,0 +1,72 @@ +## Copyright (C) 2005-2017 Paul Kienzle +## +## This file is part of Octave. +## +## Octave is free software: you can redistribute it and/or modify it +## under the terms of the GNU General Public License as published by +## the Free Software Foundation, either version 3 of the License, or +## (at your option) any later version. +## +## Octave is distributed in the hope that it will be useful, but +## WITHOUT ANY WARRANTY; without even the implied warranty of +## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +## GNU General Public License for more details. +## +## You should have received a copy of the GNU General Public License +## along with Octave; see the file COPYING. If not, see +## <https://www.gnu.org/licenses/>. + +## -*- texinfo -*- +## @deftypefn {} {count =} runlength (@var{x}) +## @deftypefnx {} {[count, value] =} runlength (@var{x}) +## Find the lengths of all sequences of common values. +## +## @var{count} is a vector with the lengths of each repeated value. +## +## The optional output @var{value} contains the value that was repeated in +## the sequence. +## +## @example +## @group +## runlength ([2, 2, 0, 4, 4, 4, 0, 1, 1, 1, 1]) +## @result{} [2, 1, 3, 1, 4] +## @end group +## @end example +## @seealso{run_count} +## @end deftypefn + +function [count, value] = runlength (x) + + if (nargin != 1) + print_usage (); + endif + + if (! (isnumeric (x) || islogical (x)) || ! isvector (x)) + error ("runlength: X must be a numeric vector"); + endif + + if (iscolumn (x)) + x = x.'; + endif + + idx = [find(x(1:end-1) != x(2:end)), length(x)]; + count = diff ([0 idx]); + if (nargout == 2) + value = x(idx); + endif + +endfunction + + +%!assert (runlength ([2 2 0 4 4 4 0 1 1 1 1]), [2 1 3 1 4]) +%!assert (runlength ([2 2 0 4 4 4 0 1 1 1 1]'), [2 1 3 1 4]) +%!test +%! [c, v] = runlength ([2 2 0 4 4 4 0 1 1 1 1]); +%! assert (c, [2 1 3 1 4]); +%! assert (v, [2 0 4 0 1]); + +## Test input validation +%!error runlength () +%!error runlength (1, 2) +%!error runlength (['A'; 'B']) +%!error runlength (ones (2,2))
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/scripts/statistics/skewness.m Sun Jan 07 17:13:23 2018 -0800 @@ -0,0 +1,169 @@ +## Copyright (C) 2013-2017 Julien Bect +## Copyright (C) 1996-2016 John W. Eaton +## +## This file is part of Octave. +## +## Octave is free software: you can redistribute it and/or modify it +## under the terms of the GNU General Public License as published by +## the Free Software Foundation, either version 3 of the License, or +## (at your option) any later version. +## +## Octave is distributed in the hope that it will be useful, but +## WITHOUT ANY WARRANTY; without even the implied warranty of +## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +## GNU General Public License for more details. +## +## You should have received a copy of the GNU General Public License +## along with Octave; see the file COPYING. If not, see +## <https://www.gnu.org/licenses/>. + +## -*- texinfo -*- +## @deftypefn {} {} skewness (@var{x}) +## @deftypefnx {} {} skewness (@var{x}, @var{flag}) +## @deftypefnx {} {} skewness (@var{x}, @var{flag}, @var{dim}) +## Compute the sample skewness of the elements of @var{x}. +## +## The sample skewness is defined as +## @tex +## $$ +## {\rm skewness} (@var{x}) = {{{1\over N}\, +## \sum_{i=1}^N (x_i - \bar{x})^3} \over \sigma^3}, +## $$ +## where $N$ is the length of @var{x}, $\bar{x}$ its mean and $\sigma$ +## its (uncorrected) standard deviation. +## @end tex +## @ifnottex +## +## @example +## @group +## mean ((@var{x} - mean (@var{x})).^3) +## skewness (@var{X}) = ------------------------. +## std (@var{x}).^3 +## @end group +## @end example +## +## @end ifnottex +## +## @noindent +## The optional argument @var{flag} controls which normalization is used. +## If @var{flag} is equal to 1 (default value, used when @var{flag} is omitted +## or empty), return the sample skewness as defined above. If @var{flag} is +## equal to 0, return the adjusted skewness coefficient instead: +## @tex +## $$ +## {\rm skewness} (@var{x}) = {\sqrt{N (N - 1)} \over N - 2} \times \, +## {{{1 \over N} \sum_{i=1}^N (x_i - \bar{x})^3} \over \sigma^3} +## $$ +## @end tex +## @ifnottex +## +## @example +## @group +## sqrt (N*(N-1)) mean ((@var{x} - mean (@var{x})).^3) +## skewness (@var{X}, 0) = -------------- * ------------------------. +## (N - 2) std (@var{x}).^3 +## @end group +## @end example +## +## where @math{N} is the length of the @var{x} vector. +## +## @end ifnottex +## The adjusted skewness coefficient is obtained by replacing the sample second +## and third central moments by their bias-corrected versions. +## +## If @var{x} is a matrix, or more generally a multi-dimensional array, return +## the skewness along the first non-singleton dimension. If the optional +## @var{dim} argument is given, operate along this dimension. +## +## @seealso{var, kurtosis, moment} +## @end deftypefn + +## Author: KH <Kurt.Hornik@wu-wien.ac.at> +## Created: 29 July 1994 +## Adapted-By: jwe + +function y = skewness (x, flag, dim) + + if (nargin < 1) || (nargin > 3) + print_usage (); + endif + + if (! (isnumeric (x) || islogical (x))) + error ("skewness: X must be a numeric vector or matrix"); + endif + + if (nargin < 2 || isempty (flag)) + flag = 1; # default: do not use the "bias corrected" version + elseif (! isscalar (flag) || (flag != 0 && flag != 1)) + error ("skewness: FLAG must be 0 or 1"); + endif + + nd = ndims (x); + sz = size (x); + if (nargin < 3) + ## Find the first non-singleton dimension. + (dim = find (sz > 1, 1)) || (dim = 1); + else + if (! (isscalar (dim) && dim == fix (dim) && dim > 0)) + error ("skewness: DIM must be an integer and a valid dimension"); + endif + endif + + n = size (x, dim); + sz(dim) = 1; + + x = center (x, dim); # center also promotes integer, logical to double + s = std (x, 1, dim); # Normalize with 1/N + y = sum (x .^ 3, dim); + idx = (s != 0); + y(idx) ./= (n * s(idx) .^ 3); + y(! idx) = NaN; + + ## Apply bias correction to the second and third central sample moment + if (flag == 0) + if (n > 2) + y *= sqrt (n * (n - 1)) / (n - 2); + else + y(:) = NaN; + endif + endif + +endfunction + + +%!assert (skewness ([-1, 0, 1]), 0) +%!assert (skewness ([-2, 0, 1]) < 0) +%!assert (skewness ([-1, 0, 2]) > 0) +%!assert (skewness ([-3, 0, 1]) == -1 * skewness ([-1, 0, 3])) +%!assert (skewness (ones (3, 5)), NaN (1, 5)) +%!assert (skewness (1, [], 3), NaN) + +%!test +%! x = [0; 0; 0; 1]; +%! y = [x, 2*x]; +%! assert (skewness (y), 1.154700538379251 * [1 1], 5*eps); + +%!assert (skewness ([1:5 10; 1:5 10], 0, 2), 1.439590274527954 * [1; 1], eps) +%!assert (skewness ([1:5 10; 1:5 10], 1, 2), 1.051328089232020 * [1; 1], 2*eps) +%!assert (skewness ([1:5 10; 1:5 10], [], 2), 1.051328089232020 * [1; 1], 2*eps) + +## Test behavior on single input +%!assert (skewness (single ([1:5 10])), single (1.0513283), eps ("single")) +%!assert (skewness (single ([1 2]), 0), single (NaN)) + +## Verify no "divide-by-zero" warnings +%!test +%! warning ("on", "Octave:divide-by-zero", "local"); +%! lastwarn (""); # clear last warning +%! skewness (1); +%! assert (lastwarn (), ""); + +## Test input validation +%!error skewness () +%!error skewness (1, 2, 3) +%!error <X must be a numeric vector or matrix> skewness (['A'; 'B']) +%!error <FLAG must be 0 or 1> skewness (1, 2) +%!error <FLAG must be 0 or 1> skewness (1, [1 0]) +%!error <DIM must be an integer> skewness (1, [], ones (2,2)) +%!error <DIM must be an integer> skewness (1, [], 1.5) +%!error <DIM must be .* a valid dimension> skewness (1, [], 0)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/scripts/statistics/spearman.m Sun Jan 07 17:13:23 2018 -0800 @@ -0,0 +1,119 @@ +## Copyright (C) 1995-2017 Kurt Hornik +## +## This file is part of Octave. +## +## Octave is free software: you can redistribute it and/or modify it +## under the terms of the GNU General Public License as published by +## the Free Software Foundation, either version 3 of the License, or +## (at your option) any later version. +## +## Octave is distributed in the hope that it will be useful, but +## WITHOUT ANY WARRANTY; without even the implied warranty of +## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +## GNU General Public License for more details. +## +## You should have received a copy of the GNU General Public License +## along with Octave; see the file COPYING. If not, see +## <https://www.gnu.org/licenses/>. + +## -*- texinfo -*- +## @deftypefn {} {} spearman (@var{x}) +## @deftypefnx {} {} spearman (@var{x}, @var{y}) +## @cindex Spearman's Rho +## Compute Spearman's rank correlation coefficient +## @tex +## $\rho$. +## @end tex +## @ifnottex +## @var{rho}. +## @end ifnottex +## +## For two data vectors @var{x} and @var{y}, Spearman's +## @tex +## $\rho$ +## @end tex +## @ifnottex +## @var{rho} +## @end ifnottex +## is the correlation coefficient of the ranks of @var{x} and @var{y}. +## +## If @var{x} and @var{y} are drawn from independent distributions, +## @tex +## $\rho$ +## @end tex +## @ifnottex +## @var{rho} +## @end ifnottex +## has zero mean and variance +## @tex +## $1 / (N - 1)$, +## @end tex +## @ifnottex +## @code{1 / (N - 1)}, +## @end ifnottex +## where @math{N} is the length of the @var{x} and @var{y} vectors, and is +## asymptotically normally distributed. +## +## @code{spearman (@var{x})} is equivalent to +## @code{spearman (@var{x}, @var{x})}. +## @seealso{ranks, kendall} +## @end deftypefn + +## Author: KH <Kurt.Hornik@wu-wien.ac.at> +## Description: Spearman's rank correlation rho + +function rho = spearman (x, y = []) + + if (nargin < 1 || nargin > 2) + print_usage (); + endif + + if ( ! (isnumeric (x) || islogical (x)) + || ! (isnumeric (y) || islogical (y))) + error ("spearman: X and Y must be numeric matrices or vectors"); + endif + + if (ndims (x) != 2 || ndims (y) != 2) + error ("spearman: X and Y must be 2-D matrices or vectors"); + endif + + if (isrow (x)) + x = x.'; + endif + + if (nargin == 1) + rho = corr (ranks (x)); + else + if (isrow (y)) + y = y.'; + endif + if (rows (x) != rows (y)) + error ("spearman: X and Y must have the same number of observations"); + endif + rho = corr (ranks (x), ranks (y)); + endif + + ## Restore class cleared by ranks + if (isa (x, "single") || isa (y, "single")) + rho = single (rho); + endif + +endfunction + + +%!test +%! x = 1:10; +%! y = exp (x); +%! assert (spearman (x,y), 1, 5*eps); +%! assert (spearman (x,-y), -1, 5*eps); + +%!assert (spearman ([1 2 3], [-1 1 -2]), -0.5, 5*eps) + +## Test input validation +%!error spearman () +%!error spearman (1, 2, 3) +%!error spearman (['A'; 'B']) +%!error spearman (ones (1,2), {1, 2}) +%!error spearman (ones (2,2,2)) +%!error spearman (ones (2,2), ones (2,2,2)) +%!error spearman (ones (2,2), ones (3,2))
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/scripts/statistics/statistics.m Sun Jan 07 17:13:23 2018 -0800 @@ -0,0 +1,99 @@ +## Copyright (C) 1995-2017 Kurt Hornik +## +## This file is part of Octave. +## +## Octave is free software: you can redistribute it and/or modify it +## under the terms of the GNU General Public License as published by +## the Free Software Foundation, either version 3 of the License, or +## (at your option) any later version. +## +## Octave is distributed in the hope that it will be useful, but +## WITHOUT ANY WARRANTY; without even the implied warranty of +## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +## GNU General Public License for more details. +## +## You should have received a copy of the GNU General Public License +## along with Octave; see the file COPYING. If not, see +## <https://www.gnu.org/licenses/>. + +## -*- texinfo -*- +## @deftypefn {} {} statistics (@var{x}) +## @deftypefnx {} {} statistics (@var{x}, @var{dim}) +## Return a vector with the minimum, first quartile, median, third quartile, +## maximum, mean, standard deviation, skewness, and kurtosis of the elements of +## the vector @var{x}. +## +## If @var{x} is a matrix, calculate statistics over the first non-singleton +## dimension. +## +## If the optional argument @var{dim} is given, operate along this dimension. +## @seealso{min, max, median, mean, std, skewness, kurtosis} +## @end deftypefn + +## Author: KH <Kurt.Hornik@wu-wien.ac.at> +## Description: Compute basic statistics + +function stats = statistics (x, dim) + + if (nargin != 1 && nargin != 2) + print_usage (); + endif + + if (! (isnumeric (x) || islogical (x))) + error ("statistics: X must be a numeric vector or matrix"); + endif + + nd = ndims (x); + sz = size (x); + if (nargin != 2) + ## Find the first non-singleton dimension. + (dim = find (sz > 1, 1)) || (dim = 1); + else + if (!(isscalar (dim) && dim == fix (dim)) + || !(1 <= dim && dim <= nd)) + error ("statistics: DIM must be an integer and a valid dimension"); + endif + endif + + if (sz(dim) < 2) + error ("statistics: dimension of X is too small (<2)"); + endif + + emp_inv = quantile (x, [0.25; 0.5; 0.75], dim, 7); + + stats = cat (dim, min (x, [], dim), emp_inv, max (x, [], dim), mean (x, dim), + std (x, [], dim), skewness (x, [], dim), kurtosis (x, [], dim)); + +endfunction + + +%!test +%! x = rand (7,5); +%! s = statistics (x); +%! assert (min (x), s(1,:), eps); +%! assert (median (x), s(3,:), eps); +%! assert (max (x), s(5,:), eps); +%! assert (mean (x), s(6,:), eps); +%! assert (std (x), s(7,:), eps); +%! assert (skewness (x), s(8,:), eps); +%! assert (kurtosis (x), s(9,:), eps); + +%! x = rand (7,5); +%! s = statistics (x, 2); +%! assert (min (x, [], 2), s(:,1), eps); +%! assert (median (x, 2), s(:,3), eps); +%! assert (max (x, [], 2), s(:,5), eps); +%! assert (mean (x, 2), s(:,6), eps); +%! assert (std (x, [], 2), s(:,7), eps); +%! assert (skewness (x, [], 2), s(:,8), eps); +%! assert (kurtosis (x, [], 2), s(:,9), eps); + +## Test input validation +%!error statistics () +%!error statistics (1, 2, 3) +%!error statistics (['A'; 'B']) +%!error statistics (1, ones (2,2)) +%!error statistics (1, 1.5) +%!error statistics (1, 0) +%!error statistics (1, 3) +%!error statistics (1)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/scripts/statistics/std.m Sun Jan 07 17:13:23 2018 -0800 @@ -0,0 +1,130 @@ +## Copyright (C) 1996-2017 John W. Eaton +## +## This file is part of Octave. +## +## Octave is free software: you can redistribute it and/or modify it +## under the terms of the GNU General Public License as published by +## the Free Software Foundation, either version 3 of the License, or +## (at your option) any later version. +## +## Octave is distributed in the hope that it will be useful, but +## WITHOUT ANY WARRANTY; without even the implied warranty of +## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +## GNU General Public License for more details. +## +## You should have received a copy of the GNU General Public License +## along with Octave; see the file COPYING. If not, see +## <https://www.gnu.org/licenses/>. + +## -*- texinfo -*- +## @deftypefn {} {} std (@var{x}) +## @deftypefnx {} {} std (@var{x}, @var{opt}) +## @deftypefnx {} {} std (@var{x}, @var{opt}, @var{dim}) +## Compute the standard deviation of the elements of the vector @var{x}. +## +## The standard deviation is defined as +## @tex +## $$ +## {\rm std} (x) = \sigma = \sqrt{{\sum_{i=1}^N (x_i - \bar{x})^2 \over N - 1}} +## $$ +## where $\bar{x}$ is the mean value of @var{x} and $N$ is the number of elements of @var{x}. +## @end tex +## @ifnottex +## +## @example +## @group +## std (@var{x}) = sqrt ( 1/(N-1) SUM_i (@var{x}(i) - mean(@var{x}))^2 ) +## @end group +## @end example +## +## @noindent +## where @math{N} is the number of elements of the @var{x} vector. +## @end ifnottex +## +## If @var{x} is a matrix, compute the standard deviation for each column and +## return them in a row vector. +## +## The argument @var{opt} determines the type of normalization to use. +## Valid values are +## +## @table @asis +## @item 0: +## normalize with @math{N-1}, provides the square root of the best unbiased +## estimator of the variance [default] +## +## @item 1: +## normalize with @math{N}, this provides the square root of the second +## moment around the mean +## @end table +## +## If the optional argument @var{dim} is given, operate along this dimension. +## @seealso{var, range, iqr, mean, median} +## @end deftypefn + +## Author: jwe + +function retval = std (x, opt = 0, dim) + + if (nargin < 1 || nargin > 3) + print_usage (); + endif + + if (! (isnumeric (x) || islogical (x))) + error ("std: X must be a numeric vector or matrix"); + endif + + if (isempty (opt)) + opt = 0; + elseif (! isscalar (opt) || (opt != 0 && opt != 1)) + error ("std: normalization OPT must be 0 or 1"); + endif + + nd = ndims (x); + sz = size (x); + if (nargin < 3) + ## Find the first non-singleton dimension. + (dim = find (sz > 1, 1)) || (dim = 1); + else + if (! (isscalar (dim) && dim == fix (dim) && dim > 0)) + error ("std: DIM must be an integer and a valid dimension"); + endif + endif + + n = size (x, dim); + if (n == 1 || isempty (x)) + if (isa (x, "single")) + retval = zeros (sz, "single"); + else + retval = zeros (sz); + endif + else + retval = sqrt (sumsq (center (x, dim), dim) / (n - 1 + opt)); + endif + +endfunction + + +%!test +%! x = ones (10, 2); +%! y = [1, 3]; +%! assert (std (x), [0, 0]); +%! assert (std (y), sqrt (2), sqrt (eps)); +%! assert (std (x, 0, 2), zeros (10, 1)); + +%!assert (std (ones (3, 1, 2), 0, 2), zeros (3, 1, 2)) +%!assert (std ([1 2], 0), sqrt (2)/2, 5*eps) +%!assert (std ([1 2], 1), 0.5, 5*eps) +%!assert (std (1), 0) +%!assert (std (single (1)), single (0)) +%!assert (std ([]), []) +%!assert (std (ones (1,3,0,2)), ones (1,3,0,2)) +%!assert (std ([1 2 3], [], 3), [0 0 0]) + +## Test input validation +%!error std () +%!error std (1, 2, 3, 4) +%!error <X must be a numeric> std (['A'; 'B']) +%!error <OPT must be 0 or 1> std (1, 2) +%!error <DIM must be an integer> std (1, [], ones (2,2)) +%!error <DIM must be an integer> std (1, [], 1.5) +%!error <DIM must be .* a valid dimension> std (1, [], 0)
--- a/scripts/statistics/tests/anova.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,111 +0,0 @@ -## Copyright (C) 1995-2017 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {[@var{pval}, @var{f}, @var{df_b}, @var{df_w}] =} anova (@var{y}, @var{g}) -## Perform a one-way analysis of variance (ANOVA). -## -## The goal is to test whether the population means of data taken from -## @var{k} different groups are all equal. -## -## Data may be given in a single vector @var{y} with groups specified by a -## corresponding vector of group labels @var{g} (e.g., numbers from 1 to -## @var{k}). This is the general form which does not impose any restriction -## on the number of data in each group or the group labels. -## -## If @var{y} is a matrix and @var{g} is omitted, each column of @var{y} is -## treated as a group. This form is only appropriate for balanced ANOVA in -## which the numbers of samples from each group are all equal. -## -## Under the null of constant means, the statistic @var{f} follows an F -## distribution with @var{df_b} and @var{df_w} degrees of freedom. -## -## The p-value (1 minus the CDF of this distribution at @var{f}) is returned -## in @var{pval}. -## -## If no output argument is given, the standard one-way ANOVA table is printed. -## @seealso{manova} -## @end deftypefn - -## Author: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: One-way analysis of variance (ANOVA) - -function [pval, f, df_b, df_w] = anova (y, g) - - if (nargin < 1 || nargin > 2) - print_usage (); - elseif (nargin == 1) - if (isvector (y)) - error ("anova: for 'anova (Y)', Y must not be a vector"); - endif - [group_count, k] = size (y); - n = group_count * k; - group_mean = mean (y); - else - if (! isvector (y)) - error ("anova: for 'anova (Y, G)', Y must be a vector"); - endif - n = length (y); - if (! isvector (g) || (length (g) != n)) - error ("anova: G must be a vector of the same length as Y"); - endif - s = sort (g); - i = find (s (2 : n) > s(1 : (n-1))); - k = length (i) + 1; - if (k == 1) - error ("anova: there should be at least 2 groups"); - else - group_label = s ([1, (reshape (i, 1, k-1) + 1)]); - endif - for i = 1 : k; - v = y (find (g == group_label (i))); - group_count (i) = length (v); - group_mean (i) = mean (v); - endfor - - endif - - total_mean = mean (y(:)); - SSB = sum (group_count .* (group_mean - total_mean) .^ 2); - SST = sumsq (reshape (y, n, 1) - total_mean); - SSW = SST - SSB; - df_b = k - 1; - df_w = n - k; - v_b = SSB / df_b; - v_w = SSW / df_w; - f = v_b / v_w; - pval = 1 - fcdf (f, df_b, df_w); - - if (nargout == 0) - ## This eventually needs to be done more cleanly ... - printf ("\n"); - printf ("One-way ANOVA Table:\n"); - printf ("\n"); - printf ("Source of Variation Sum of Squares df Empirical Var\n"); - printf ("*********************************************************\n"); - printf ("Between Groups %15.4f %4d %13.4f\n", SSB, df_b, v_b); - printf ("Within Groups %15.4f %4d %13.4f\n", SSW, df_w, v_w); - printf ("---------------------------------------------------------\n"); - printf ("Total %15.4f %4d\n", SST, n - 1); - printf ("\n"); - printf ("Test Statistic f %15.4f\n", f); - printf ("p-value %15.4f\n", pval); - printf ("\n"); - endif - -endfunction
--- a/scripts/statistics/tests/bartlett_test.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,67 +0,0 @@ -## Copyright (C) 1995-2017 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {[@var{pval}, @var{chisq}, @var{df}] =} bartlett_test (@var{x1}, @dots{}) -## Perform a Bartlett test for the homogeneity of variances in the data -## vectors @var{x1}, @var{x2}, @dots{}, @var{xk}, where @var{k} > 1. -## -## Under the null of equal variances, the test statistic @var{chisq} -## approximately follows a chi-square distribution with @var{df} degrees of -## freedom. -## -## The p-value (1 minus the CDF of this distribution at @var{chisq}) is -## returned in @var{pval}. -## -## If no output argument is given, the p-value is displayed. -## @end deftypefn - -## Author: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: Bartlett test for homogeneity of variances - -function [pval, chisq, df] = bartlett_test (varargin) - - k = nargin; - if (k < 2) - print_usage (); - endif - - f = zeros (k, 1); - v = zeros (k, 1); - - for i = 1 : k; - x = varargin{i}; - if (! isvector (x)) - error ("bartlett_test: all arguments must be vectors"); - endif - f(i) = length (x) - 1; - v(i) = var (x); - endfor - - f_tot = sum (f); - v_tot = sum (f .* v) / f_tot; - c = 1 + (sum (1 ./ f) - 1 / f_tot) / (3 * (k - 1)); - chisq = (f_tot * log (v_tot) - sum (f .* log (v))) / c; - df = k; - pval = 1 - chi2cdf (chisq, df); - - if (nargout == 0) - printf (" pval: %g\n", pval); - endif - -endfunction
--- a/scripts/statistics/tests/chisquare_test_homogeneity.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,68 +0,0 @@ -## Copyright (C) 1995-2017 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {[@var{pval}, @var{chisq}, @var{df}] =} chisquare_test_homogeneity (@var{x}, @var{y}, @var{c}) -## Given two samples @var{x} and @var{y}, perform a chisquare test for -## homogeneity of the null hypothesis that @var{x} and @var{y} come from -## the same distribution, based on the partition induced by the -## (strictly increasing) entries of @var{c}. -## -## For large samples, the test statistic @var{chisq} approximately follows a -## chisquare distribution with @var{df} = @code{length (@var{c})} degrees of -## freedom. -## -## The p-value (1 minus the CDF of this distribution at @var{chisq}) is -## returned in @var{pval}. -## -## If no output argument is given, the p-value is displayed. -## @end deftypefn - -## Author: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: Chi-square test for homogeneity - -function [pval, chisq, df] = chisquare_test_homogeneity (x, y, c) - - if (nargin != 3) - print_usage (); - endif - - if (! (isvector (x) && isvector (y) && isvector (c))) - error ("chisquare_test_homogeneity: X, Y and C must be vectors"); - endif - ## Now test c for strictly increasing entries - df = length (c); - if (any ((c(2 : df) - c(1 : (df - 1))) <= 0)) - error ("chisquare_test_homogeneity: C must be increasing"); - endif - - c = [(reshape (c, 1, df)), Inf]; - l_x = length (x); - x = reshape (x, l_x, 1); - n_x = sum (x * ones (1, df+1) < ones (l_x, 1) * c); - l_y = length (y); - y = reshape (y, l_y, 1); - n_y = sum (y * ones (1, df+1) < ones (l_y, 1) * c); - chisq = l_x * l_y * sum ((n_x/l_x - n_y/l_y).^2 ./ (n_x + n_y)); - pval = 1 - chi2cdf (chisq, df); - - if (nargout == 0) - printf (" pval: %g\n", pval); - endif - -endfunction
--- a/scripts/statistics/tests/chisquare_test_independence.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,54 +0,0 @@ -## Copyright (C) 1995-2017 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {[@var{pval}, @var{chisq}, @var{df}] =} chisquare_test_independence (@var{x}) -## Perform a chi-square test for independence based on the contingency table -## @var{x}. -## -## Under the null hypothesis of independence, @var{chisq} approximately has a -## chi-square distribution with @var{df} degrees of freedom. -## -## The p-value (1 minus the CDF of this distribution at chisq) of the test is -## returned in @var{pval}. -## -## If no output argument is given, the p-value is displayed. -## @end deftypefn - -## Author: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: Chi-square test for independence - -function [pval, chisq, df] = chisquare_test_independence (x) - - if (nargin != 1) - print_usage (); - endif - - [r, s] = size (x); - df = (r - 1) * (s - 1); - n = sum (sum (x)); - y = sum (x')' * sum (x) / n; - x = (x - y) .^2 ./ y; - chisq = sum (sum (x)); - pval = 1 - chi2cdf (chisq, df); - - if (nargout == 0) - printf (" pval: %g\n", pval); - endif - -endfunction
--- a/scripts/statistics/tests/cor_test.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,135 +0,0 @@ -## Copyright (C) 1995-2017 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} cor_test (@var{x}, @var{y}, @var{alt}, @var{method}) -## Test whether two samples @var{x} and @var{y} come from uncorrelated -## populations. -## -## The optional argument string @var{alt} describes the alternative -## hypothesis, and can be @qcode{"!="} or @qcode{"<>"} (nonzero), @qcode{">"} -## (greater than 0), or @qcode{"<"} (less than 0). The default is the -## two-sided case. -## -## The optional argument string @var{method} specifies which correlation -## coefficient to use for testing. If @var{method} is @qcode{"pearson"} -## (default), the (usual) Pearson's product moment correlation coefficient is -## used. In this case, the data should come from a bivariate normal -## distribution. Otherwise, the other two methods offer nonparametric -## alternatives. If @var{method} is @qcode{"kendall"}, then Kendall's rank -## correlation tau is used. If @var{method} is @qcode{"spearman"}, then -## Spearman's rank correlation rho is used. Only the first character is -## necessary. -## -## The output is a structure with the following elements: -## -## @table @var -## @item pval -## The p-value of the test. -## -## @item stat -## The value of the test statistic. -## -## @item dist -## The distribution of the test statistic. -## -## @item params -## The parameters of the null distribution of the test statistic. -## -## @item alternative -## The alternative hypothesis. -## -## @item method -## The method used for testing. -## @end table -## -## If no output argument is given, the p-value is displayed. -## @end deftypefn - -## Author: FL <Friedrich.Leisch@ci.tuwien.ac.at> -## Adapted-by: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: Test for zero correlation - -function t = cor_test (x, y, alt, method) - - if (nargin < 2 || nargin > 4) - print_usage (); - endif - - if (! isvector (x) || ! isvector (y) || length (x) != length (y)) - error ("cor_test: X and Y must be vectors of the same length"); - endif - - if (nargin < 3) - alt = "!="; - elseif (! ischar (alt)) - error ("cor_test: ALT must be a string"); - endif - - if (nargin < 4) - method = "pearson"; - elseif (! ischar (method)) - error ("cor_test: METHOD must be a string"); - endif - - n = length (x); - m = method(1); - - if (m == "p") - r = corr (x, y); - df = n - 2; - t.method = "Pearson's product moment correlation"; - t.params = df; - t.stat = sqrt (df) .* r / sqrt (1 - r.^2); - t.dist = "t"; - cdf = tcdf (t.stat, df); - elseif (m == "k") - tau = kendall (x, y); - t.method = "Kendall's rank correlation tau"; - t.params = []; - t.stat = tau / sqrt ((2 * (2*n+5)) / (9*n*(n-1))); - t.dist = "stdnormal"; - cdf = stdnormal_cdf (t.stat); - elseif (m == "s") - rho = spearman (x, y); - t.method = "Spearman's rank correlation rho"; - t.params = []; - t.stat = sqrt (n-1) * (rho - 6/(n^3-n)); - t.dist = "stdnormal"; - cdf = stdnormal_cdf (t.stat); - else - error ("cor_test: METHOD '%s' not recognized", method); - endif - - if (strcmp (alt, "!=") || strcmp (alt, "<>")) - t.pval = 2 * min (cdf, 1 - cdf); - elseif (strcmp (alt, ">")) - t.pval = 1 - cdf; - elseif (strcmp (alt, "<")) - t.pval = cdf; - else - error ("cor_test: alternative '%s' not recognized", alt); - endif - - t.alternative = alt; - - if (nargout == 0) - printf ("pval: %g\n", t.pval); - endif - -endfunction
--- a/scripts/statistics/tests/f_test_regression.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,77 +0,0 @@ -## Copyright (C) 1995-2017 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {[@var{pval}, @var{f}, @var{df_num}, @var{df_den}] =} f_test_regression (@var{y}, @var{x}, @var{rr}, @var{r}) -## Perform an F test for the null hypothesis @nospell{rr * b = r} in a -## classical normal regression model y = X * b + e. -## -## Under the null, the test statistic @var{f} follows an F distribution with -## @var{df_num} and @var{df_den} degrees of freedom. -## -## The p-value (1 minus the CDF of this distribution at @var{f}) is returned -## in @var{pval}. -## -## If not given explicitly, @var{r} = 0. -## -## If no output argument is given, the p-value is displayed. -## @end deftypefn - -## Author: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: Test linear hypotheses in linear regression model - -function [pval, f, df_num, df_den] = f_test_regression (y, x, rr, r) - - if (nargin < 3 || nargin > 4) - print_usage (); - endif - - [T, k] = size (x); - if (! (isvector (y) && (length (y) == T))) - error ("f_test_regression: Y must be a vector of length rows (X)"); - endif - y = reshape (y, T, 1); - - [q, c_R ] = size (rr); - if (c_R != k) - error ("f_test_regression: RR must have as many columns as X"); - endif - - if (nargin == 4) - s_r = size (r); - if ((min (s_r) != 1) || (max (s_r) != q)) - error ("f_test_regression: R must be a vector of length rows (RR)"); - endif - r = reshape (r, q, 1); - else - r = zeros (q, 1); - endif - - df_num = q; - df_den = T - k; - - [b, v] = ols (y, x); - diff = rr * b - r; - f = diff' * inv (rr * inv (x' * x) * rr') * diff / (q * v); - pval = 1 - fcdf (f, df_num, df_den); - - if (nargout == 0) - printf (" pval: %g\n", pval); - endif - -endfunction
--- a/scripts/statistics/tests/hotelling_test.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,72 +0,0 @@ -## Copyright (C) 1996-2017 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {[@var{pval}, @var{tsq}] =} hotelling_test (@var{x}, @var{m}) -## For a sample @var{x} from a multivariate normal distribution with unknown -## mean and covariance matrix, test the null hypothesis that -## @code{mean (@var{x}) == @var{m}}. -## -## Hotelling's @math{T^2} is returned in @var{tsq}. Under the null, -## @math{(n-p) T^2 / (p(n-1))} has an F distribution with @math{p} and -## @math{n-p} degrees of freedom, where @math{n} and @math{p} are the -## numbers of samples and variables, respectively. -## -## The p-value of the test is returned in @var{pval}. -## -## If no output argument is given, the p-value of the test is displayed. -## @end deftypefn - -## Author: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: Test for mean of a multivariate normal - -function [pval, Tsq] = hotelling_test (x, m) - - if (nargin != 2) - print_usage (); - endif - - if (isvector (x)) - if (! isscalar (m)) - error ("hotelling_test: if X is a vector, M must be a scalar"); - endif - n = length (x); - p = 1; - elseif (ismatrix (x)) - [n, p] = size (x); - if (n <= p) - error ("hotelling_test: X must have more rows than columns"); - endif - if (isvector (m) && length (m) == p) - m = reshape (m, 1, p); - else - error ("hotelling_test: if X is a matrix, M must be a vector of length columns (X)"); - endif - else - error ("hotelling_test: X must be a matrix or vector"); - endif - - d = mean (x) - m; - Tsq = n * d * (cov (x) \ d'); - pval = 1 - fcdf ((n-p) * Tsq / (p * (n-1)), p, n-p); - - if (nargout == 0) - printf (" pval: %g\n", pval); - endif - -endfunction
--- a/scripts/statistics/tests/hotelling_test_2.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,86 +0,0 @@ -## Copyright (C) 1996-2017 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {[@var{pval}, @var{tsq}] =} hotelling_test_2 (@var{x}, @var{y}) -## For two samples @var{x} from multivariate normal distributions with -## the same number of variables (columns), unknown means and unknown -## equal covariance matrices, test the null hypothesis @code{mean -## (@var{x}) == mean (@var{y})}. -## -## Hotelling's two-sample @math{T^2} is returned in @var{tsq}. Under the null, -## @tex -## $$ -## {(n_x+n_y-p-1) T^2 \over p(n_x+n_y-2)} -## $$ -## @end tex -## @ifnottex -## -## @example -## (n_x+n_y-p-1) T^2 / (p(n_x+n_y-2)) -## @end example -## -## @end ifnottex -## @noindent -## has an F distribution with @math{p} and @math{n_x+n_y-p-1} degrees of -## freedom, where @math{n_x} and @math{n_y} are the sample sizes and -## @math{p} is the number of variables. -## -## The p-value of the test is returned in @var{pval}. -## -## If no output argument is given, the p-value of the test is displayed. -## @end deftypefn - -## Author: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: Compare means of two multivariate normals - -function [pval, Tsq] = hotelling_test_2 (x, y) - - if (nargin != 2) - print_usage (); - endif - - if (isvector (x)) - n_x = length (x); - if (! isvector (y)) - error ("hotelling_test_2: if X is a vector, Y must also be a vector"); - else - n_y = length (y); - p = 1; - endif - elseif (ismatrix (x)) - [n_x, p] = size (x); - [n_y, q] = size (y); - if (p != q) - error ("hotelling_test_2: X and Y must have the same number of columns"); - endif - else - error ("hotelling_test_2: X and Y must be matrices (or vectors)"); - endif - - d = mean (x) - mean (y); - S = ((n_x - 1) * cov (x) + (n_y - 1) * cov (y)) / (n_x + n_y - 2); - Tsq = (n_x * n_y / (n_x + n_y)) * d * (S \ d'); - pval = 1 - fcdf ((n_x + n_y - p - 1) * Tsq / (p * (n_x + n_y - 2)), - p, n_x + n_y - p - 1); - - if (nargout == 0) - printf (" pval: %g\n", pval); - endif - -endfunction
--- a/scripts/statistics/tests/kolmogorov_smirnov_test.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,127 +0,0 @@ -## Copyright (C) 1995-2017 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {[@var{pval}, @var{ks}] =} kolmogorov_smirnov_test (@var{x}, @var{dist}, @var{params}, @var{alt}) -## Perform a Kolmogorov-Smirnov test of the null hypothesis that the -## sample @var{x} comes from the (continuous) distribution @var{dist}. -## -## if F and G are the CDFs corresponding to the sample and dist, -## respectively, then the null is that F == G. -## -## The optional argument @var{params} contains a list of parameters of -## @var{dist}. For example, to test whether a sample @var{x} comes from -## a uniform distribution on [2,4], use -## -## @example -## kolmogorov_smirnov_test (x, "unif", 2, 4) -## @end example -## -## @noindent -## @var{dist} can be any string for which a function @var{distcdf} -## that calculates the CDF of distribution @var{dist} exists. -## -## With the optional argument string @var{alt}, the alternative of interest -## can be selected. If @var{alt} is @qcode{"!="} or @qcode{"<>"}, the null -## is tested against the two-sided alternative F != G@. In this case, the -## test statistic @var{ks} follows a two-sided Kolmogorov-Smirnov -## distribution. If @var{alt} is @qcode{">"}, the one-sided alternative F > -## G is considered. Similarly for @qcode{"<"}, the one-sided alternative F > -## G is considered. In this case, the test statistic @var{ks} has a -## one-sided Kolmogorov-Smirnov distribution. The default is the two-sided -## case. -## -## The p-value of the test is returned in @var{pval}. -## -## If no output argument is given, the p-value is displayed. -## @end deftypefn - -## Author: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: One-sample Kolmogorov-Smirnov test - -function [pval, ks] = kolmogorov_smirnov_test (x, dist, varargin) - - if (nargin < 2) - print_usage (); - endif - - if (! isvector (x)) - error ("kolmogorov_smirnov_test: X must be a vector"); - endif - - n = length (x); - s = sort (x); - try - f = str2func (sprintf ("%scdf", dist)); - catch - try - f = str2func (sprintf ("%s_cdf", dist)); - catch - error ("kolmogorov_smirnov_test: no %scdf or %s_cdf function found", - dist, dist); - end_try_catch - end_try_catch - - alt = "!="; - - args{1} = s; - nvargs = numel (varargin); - if (nvargs > 0) - if (ischar (varargin{end})) - alt = varargin{end}; - args(2:nvargs) = varargin(1:end-1); - else - args(2:nvargs+1) = varargin; - endif - endif - - z = reshape (feval (f, args{:}), 1, n); - - if (strcmp (alt, "!=") || strcmp (alt, "<>")) - ks = sqrt (n) * max (max ([abs(z - (0:(n-1))/n); abs(z - (1:n)/n)])); - pval = 1 - kolmogorov_smirnov_cdf (ks); - elseif (strcmp (alt, ">")) - ks = sqrt (n) * max (max ([z - (0:(n-1))/n; z - (1:n)/n])); - pval = exp (- 2 * ks^2); - elseif (strcmp (alt, "<")) - ks = - sqrt (n) * min (min ([z - (0:(n-1))/n; z - (1:n)/n])); - pval = exp (- 2 * ks^2); - else - error ("kolmogorov_smirnov_test: alternative %s not recognized", alt); - endif - - if (nargout == 0) - printf ("pval: %g\n", pval); - endif - -endfunction - - -## test for recognition of unifcdf function -%!assert (kolmogorov_smirnov_test (0:100, "unif", 0, 100), 1.0, eps) -## test for recognition of logistic_cdf function -%!assert (kolmogorov_smirnov_test (0:100, "logistic"), 0) -## test for F < G -%!assert (kolmogorov_smirnov_test (50:100, "unif", 0, 50, "<")) - -%!error kolmogorov_smirnov_test (1) -%!error <X must be a vector> kolmogorov_smirnov_test ({}, "unif", 2, 4) -%!error <no not_a_distcdf or not_a_dist_cdf function found> -%! kolmogorov_smirnov_test (1, "not_a_dist"); -%!error <alternative foo not recognized> -%! kolmogorov_smirnov_test (1, "unif", 2, 4, "foo");
--- a/scripts/statistics/tests/kolmogorov_smirnov_test_2.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,104 +0,0 @@ -## Copyright (C) 1995-2017 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {[@var{pval}, @var{ks}, @var{d}] =} kolmogorov_smirnov_test_2 (@var{x}, @var{y}, @var{alt}) -## Perform a 2-sample Kolmogorov-Smirnov test of the null hypothesis that the -## samples @var{x} and @var{y} come from the same (continuous) distribution. -## -## If F and G are the CDFs corresponding to the @var{x} and @var{y} samples, -## respectively, then the null is that F == G. -## -## With the optional argument string @var{alt}, the alternative of interest -## can be selected. If @var{alt} is @qcode{"!="} or @qcode{"<>"}, the null -## is tested against the two-sided alternative F != G@. In this case, the -## test statistic @var{ks} follows a two-sided Kolmogorov-Smirnov -## distribution. If @var{alt} is @qcode{">"}, the one-sided alternative F > -## G is considered. Similarly for @qcode{"<"}, the one-sided alternative F < -## G is considered. In this case, the test statistic @var{ks} has a -## one-sided Kolmogorov-Smirnov distribution. The default is the two-sided -## case. -## -## The p-value of the test is returned in @var{pval}. -## -## The third returned value, @var{d}, is the test statistic, the maximum -## vertical distance between the two cumulative distribution functions. -## -## If no output argument is given, the p-value is displayed. -## @end deftypefn - -## Author: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: Two-sample Kolmogorov-Smirnov test - -function [pval, ks, d] = kolmogorov_smirnov_test_2 (x, y, alt) - - if (nargin < 2 || nargin > 3) - print_usage (); - endif - - if (! (isvector (x) && isvector (y))) - error ("kolmogorov_smirnov_test_2: both X and Y must be vectors"); - endif - - if (nargin == 2) - alt = "!="; - else - if (! ischar (alt)) - error ("kolmogorov_smirnov_test_2: ALT must be a string"); - endif - endif - - n_x = length (x); - n_y = length (y); - n = n_x * n_y / (n_x + n_y); - x = reshape (x, n_x, 1); - y = reshape (y, n_y, 1); - [s, i] = sort ([x; y]); - count (find (i <= n_x)) = 1 / n_x; - count (find (i > n_x)) = - 1 / n_y; - - z = cumsum (count); - ds = diff (s); - if (any (ds == 0)) - ## There are some ties, so keep only those changes. - warning ("kolmogorov_smirnov_test_2: cannot compute correct p-values with ties"); - elems = [find(ds); n_x+n_y]; - z = z(elems); - endif - - if (strcmp (alt, "!=") || strcmp (alt, "<>")) - d = max (abs (z)); - ks = sqrt (n) * d; - pval = 1 - kolmogorov_smirnov_cdf (ks); - elseif (strcmp (alt, ">")) - d = max (z); - ks = sqrt (n) * d; - pval = exp (-2 * ks^2); - elseif (strcmp (alt, "<")) - d = min (z); - ks = -sqrt (n) * d; - pval = exp (-2 * ks^2); - else - error ("kolmogorov_smirnov_test_2: option %s not recognized", alt); - endif - - if (nargout == 0) - printf (" pval: %g\n", pval); - endif - -endfunction
--- a/scripts/statistics/tests/kruskal_wallis_test.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,99 +0,0 @@ -## Copyright (C) 1995-2017 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {[@var{pval}, @var{k}, @var{df}] =} kruskal_wallis_test (@var{x1}, @dots{}) -## Perform a @nospell{Kruskal-Wallis} one-factor analysis of variance. -## -## Suppose a variable is observed for @var{k} > 1 different groups, and let -## @var{x1}, @dots{}, @var{xk} be the corresponding data vectors. -## -## Under the null hypothesis that the ranks in the pooled sample are not -## affected by the group memberships, the test statistic @var{k} is -## approximately chi-square with @var{df} = @var{k} - 1 degrees of freedom. -## -## If the data contains ties (some value appears more than once) -## @var{k} is divided by -## -## 1 - @var{sum_ties} / (@var{n}^3 - @var{n}) -## -## where @var{sum_ties} is the sum of @var{t}^2 - @var{t} over each group of -## ties where @var{t} is the number of ties in the group and @var{n} is the -## total number of values in the input data. For more info on this -## adjustment see @nospell{William H. Kruskal and W. Allen Wallis}, -## @cite{Use of Ranks in One-Criterion Variance Analysis}, -## Journal of the American Statistical Association, Vol. 47, No. 260 (Dec -## 1952). -## -## The p-value (1 minus the CDF of this distribution at @var{k}) is returned -## in @var{pval}. -## -## If no output argument is given, the p-value is displayed. -## @end deftypefn - -## Author: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: Kruskal-Wallis test - -function [pval, k, df] = kruskal_wallis_test (varargin) - - m = nargin; - if (m < 2) - print_usage (); - endif - - n = []; - p = []; - - for i = 1 : m; - x = varargin{i}; - if (! isvector (x)) - error ("kruskal_wallis_test: all arguments must be vectors"); - endif - l = length (x); - n = [n, l]; - p = [p, (reshape (x, 1, l))]; - endfor - - r = ranks (p); - - k = 0; - j = 0; - for i = 1 : m; - k += (sum (r ((j + 1) : (j + n(i))))) ^ 2 / n(i); - j = j + n(i); - endfor - - n = length (p); - k = 12 * k / (n * (n + 1)) - 3 * (n + 1); - - ## Adjust the result to takes ties into account. - sum_ties = sum (polyval ([1, 0, -1, 0], runlength (sort (p)))); - k /= (1 - sum_ties / (n^3 - n)); - - df = m - 1; - pval = 1 - chi2cdf (k, df); - - if (nargout == 0) - printf ("pval: %g\n", pval); - endif - -endfunction - - -## Test with ties -%!assert (abs (kruskal_wallis_test ([86 86], [74]) - 0.157299207050285) < 0.0000000000001)
--- a/scripts/statistics/tests/manova.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,164 +0,0 @@ -## Copyright (C) 1996-2017 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {} manova (@var{x}, @var{g}) -## Perform a one-way multivariate analysis of variance (MANOVA). -## -## The goal is to test whether the p-dimensional population means of data -## taken from @var{k} different groups are all equal. All data are assumed -## drawn independently from p-dimensional normal distributions with the same -## covariance matrix. -## -## The data matrix is given by @var{x}. As usual, rows are observations and -## columns are variables. The vector @var{g} specifies the corresponding -## group labels (e.g., numbers from 1 to @var{k}). -## -## The LR test statistic (@nospell{Wilks' Lambda}) and approximate p-values are -## computed and displayed. -## @seealso{anova} -## @end deftypefn - -## The Hotelling-Lawley and Pillai-Bartlett test statistics are coded. -## However, they are currently disabled until they can be verified by someone -## with sufficient understanding of the algorithms. Please feel free to -## improve this. - -## Author: TF <Thomas.Fuereder@ci.tuwien.ac.at> -## Adapted-By: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: One-way multivariate analysis of variance (MANOVA) - -function manova (x, g) - - if (nargin != 2) - print_usage (); - endif - - if (isvector (x)) - error ("manova: X must not be a vector"); - endif - - [n, p] = size (x); - - if (! isvector (g) || (length (g) != n)) - error ("manova: G must be a vector of length rows (X)"); - endif - - s = sort (g); - i = find (s (2:n) > s(1:(n-1))); - k = length (i) + 1; - - if (k == 1) - error ("manova: there should be at least 2 groups"); - else - group_label = s ([1, (reshape (i, 1, k - 1) + 1)]); - endif - - x -= ones (n, 1) * mean (x); - SST = x' * x; - - s = zeros (1, p); - SSB = zeros (p, p); - for i = 1 : k; - v = x (find (g == group_label (i)), :); - s = sum (v); - SSB += s' * s / rows (v); - endfor - n_b = k - 1; - - SSW = SST - SSB; - n_w = n - k; - - l = real (eig (SSB / SSW)); - - if (isa (l, "single")) - l(l < eps ("single")) = 0; - else - l(l < eps) = 0; - endif - - ## Wilks' Lambda - ## ============= - - Lambda = prod (1 ./ (1 + l)); - - delta = n_w + n_b - (p + n_b + 1) / 2; - df_num = p * n_b; - W_pval_1 = 1 - chi2cdf (- delta * log (Lambda), df_num); - - if (p < 3) - eta = p; - else - eta = sqrt ((p^2 * n_b^2 - 4) / (p^2 + n_b^2 - 5)); - endif - - df_den = delta * eta - df_num / 2 + 1; - - WT = exp (- log (Lambda) / eta) - 1; - W_pval_2 = 1 - fcdf (WT * df_den / df_num, df_num, df_den); - - if (0) - - ## Hotelling-Lawley Test - ## ===================== - - HL = sum (l); - - theta = min (p, n_b); - u = (abs (p - n_b) - 1) / 2; - v = (n_w - p - 1) / 2; - - df_num = theta * (2 * u + theta + 1); - df_den = 2 * (theta * v + 1); - - HL_pval = 1 - fcdf (HL * df_den / df_num, df_num, df_den); - - ## Pillai-Bartlett - ## =============== - - PB = sum (l ./ (1 + l)); - - df_den = theta * (2 * v + theta + 1); - PB_pval = 1 - fcdf (PB * df_den / df_num, df_num, df_den); - - printf ("\n"); - printf ("One-way MANOVA Table:\n"); - printf ("\n"); - printf ("Test Test Statistic Approximate p\n"); - printf ("**************************************************\n"); - printf ("Wilks %10.4f %10.9f \n", Lambda, W_pval_1); - printf (" %10.9f \n", W_pval_2); - printf ("Hotelling-Lawley %10.4f %10.9f \n", HL, HL_pval); - printf ("Pillai-Bartlett %10.4f %10.9f \n", PB, PB_pval); - printf ("\n"); - - endif - - printf ("\n"); - printf ("MANOVA Results:\n"); - printf ("\n"); - printf ("# of groups: %d\n", k); - printf ("# of samples: %d\n", n); - printf ("# of variables: %d\n", p); - printf ("\n"); - printf ("Wilks' Lambda: %5.4f\n", Lambda); - printf ("Approximate p: %10.9f (chisquare approximation)\n", W_pval_1); - printf (" %10.9f (F approximation)\n", W_pval_2); - printf ("\n"); - -endfunction
--- a/scripts/statistics/tests/mcnemar_test.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,64 +0,0 @@ -## Copyright (C) 1996-2017 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {[@var{pval}, @var{chisq}, @var{df}] =} mcnemar_test (@var{x}) -## For a square contingency table @var{x} of data cross-classified on the row -## and column variables, @nospell{McNemar's} test can be used for testing the -## null hypothesis of symmetry of the classification probabilities. -## -## Under the null, @var{chisq} is approximately distributed as chisquare with -## @var{df} degrees of freedom. -## -## The p-value (1 minus the CDF of this distribution at @var{chisq}) is -## returned in @var{pval}. -## -## If no output argument is given, the p-value of the test is displayed. -## @end deftypefn - -## Author: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: McNemar's test for symmetry - -function [pval, chisq, df] = mcnemar_test (x) - - if (nargin != 1) - print_usage (); - endif - - if (! (min (size (x)) > 1) && issquare (x)) - error ("mcnemar_test: X must be a square matrix of size > 1"); - elseif (! (all ((x(:) >= 0)) && all (x(:) == fix (x(:))))) - error ("mcnemar_test: all entries of X must be non-negative integers"); - endif - - r = rows (x); - df = r * (r - 1) / 2; - if (r == 2) - num = max (abs (x - x') - 1, 0) .^ 2; - else - num = abs (x - x') .^ 2; - endif - - chisq = sum (sum (triu (num ./ (x + x'), 1))); - pval = 1 - chi2cdf (chisq, df); - - if (nargout == 0) - printf (" pval: %g\n", pval); - endif - -endfunction
--- a/scripts/statistics/tests/module.mk Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,38 +0,0 @@ -FCN_FILE_DIRS += scripts/statistics/tests - -%canon_reldir%_FCN_FILES = \ - %reldir%/anova.m \ - %reldir%/bartlett_test.m \ - %reldir%/chisquare_test_homogeneity.m \ - %reldir%/chisquare_test_independence.m \ - %reldir%/cor_test.m \ - %reldir%/f_test_regression.m \ - %reldir%/hotelling_test.m \ - %reldir%/hotelling_test_2.m \ - %reldir%/kolmogorov_smirnov_test.m \ - %reldir%/kolmogorov_smirnov_test_2.m \ - %reldir%/kruskal_wallis_test.m \ - %reldir%/manova.m \ - %reldir%/mcnemar_test.m \ - %reldir%/prop_test_2.m \ - %reldir%/run_test.m \ - %reldir%/sign_test.m \ - %reldir%/t_test.m \ - %reldir%/t_test_2.m \ - %reldir%/t_test_regression.m \ - %reldir%/u_test.m \ - %reldir%/var_test.m \ - %reldir%/welch_test.m \ - %reldir%/wilcoxon_test.m \ - %reldir%/z_test.m \ - %reldir%/z_test_2.m - -%canon_reldir%dir = $(fcnfiledir)/statistics/tests - -%canon_reldir%_DATA = $(%canon_reldir%_FCN_FILES) - -FCN_FILES += $(%canon_reldir%_FCN_FILES) - -PKG_ADD_FILES += %reldir%/PKG_ADD - -DIRSTAMP_FILES += %reldir%/$(octave_dirstamp)
--- a/scripts/statistics/tests/prop_test_2.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,81 +0,0 @@ -## Copyright (C) 1996-2017 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {[@var{pval}, @var{z}] =} prop_test_2 (@var{x1}, @var{n1}, @var{x2}, @var{n2}, @var{alt}) -## If @var{x1} and @var{n1} are the counts of successes and trials in one -## sample, and @var{x2} and @var{n2} those in a second one, test the null -## hypothesis that the success probabilities @var{p1} and @var{p2} are the -## same. -## -## Under the null, the test statistic @var{z} approximately follows a -## standard normal distribution. -## -## With the optional argument string @var{alt}, the alternative of interest -## can be selected. If @var{alt} is @qcode{"!="} or @qcode{"<>"}, the null -## is tested against the two-sided alternative @var{p1} != @var{p2}. If -## @var{alt} is @qcode{">"}, the one-sided alternative @var{p1} > @var{p2} is -## used. Similarly for @qcode{"<"}, the one-sided alternative -## @var{p1} < @var{p2} is used. The default is the two-sided case. -## -## The p-value of the test is returned in @var{pval}. -## -## If no output argument is given, the p-value of the test is displayed. -## @end deftypefn - -## Author: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: Compare two proportions - -function [pval, z] = prop_test_2 (x1, n1, x2, n2, alt) - - if (nargin < 4 || nargin > 5) - print_usage (); - endif - - ## Could do sanity checking on x1, n1, x2, n2 here - - p1 = x1 / n1; - p2 = x2 / n2; - pc = (x1 + x2) / (n1 + n2); - - z = (p1 - p2) / sqrt (pc * (1 - pc) * (1/n1 + 1/n2)); - - cdf = stdnormal_cdf (z); - - if (nargin == 4) - alt = "!="; - endif - - if (! ischar (alt)) - error ("prop_test_2: ALT must be a string"); - endif - if (strcmp (alt, "!=") || strcmp (alt, "<>")) - pval = 2 * min (cdf, 1 - cdf); - elseif (strcmp (alt, ">")) - pval = 1 - cdf; - elseif (strcmp (alt, "<")) - pval = cdf; - else - error ("prop_test_2: option %s not recognized", alt); - endif - - if (nargout == 0) - printf (" pval: %g\n", pval); - endif - -endfunction
--- a/scripts/statistics/tests/run_test.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,60 +0,0 @@ -## Copyright (C) 1995-2017 Friedrich Leisch -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {[@var{pval}, @var{chisq}] =} run_test (@var{x}) -## Perform a chi-square test with 6 degrees of freedom based on the upward -## runs in the columns of @var{x}. -## -## @code{run_test} can be used to decide whether @var{x} contains independent -## data. -## -## The p-value of the test is returned in @var{pval}. -## -## If no output argument is given, the p-value is displayed. -## @end deftypefn - -## Author: FL <Friedrich.Leisch@ci.tuwien.ac.at> -## Description: Run test for independence - -function [pval, chisq] = run_test (x) - - if (nargin != 1) - print_usage (); - endif - - A = [4529.4, 9044.9, 13568, 18091, 22615, 27892; - 9044.4, 18097, 27139, 36187, 45234, 55789; - 13568, 27139, 40721, 54281, 67852, 83685; - 18091, 36187, 54281, 72414, 90470, 111580; - 22615, 45234, 67852, 90470, 113262, 139476; - 27892, 55789, 83685, 111580, 139476, 172860]; - - b = [1/6; 5/24; 11/120; 19/720; 29/5040; 1/840]; - - n = rows (x); - r = run_count (x, 6) - n * b * ones (1, columns (x)); - - chisq = diag (r' * A * r)' / n; - pval = chi2cdf (chisq, 6); - - if (nargout == 0) - printf ("pval: %g\n", pval); - endif - -endfunction
--- a/scripts/statistics/tests/sign_test.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,84 +0,0 @@ -## Copyright (C) 1995-2017 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {[@var{pval}, @var{b}, @var{n}] =} sign_test (@var{x}, @var{y}, @var{alt}) -## For two matched-pair samples @var{x} and @var{y}, perform a sign test -## of the null hypothesis -## PROB (@var{x} > @var{y}) == PROB (@var{x} < @var{y}) == 1/2. -## -## Under the null, the test statistic @var{b} roughly follows a -## binomial distribution with parameters -## @code{@var{n} = sum (@var{x} != @var{y})} and @var{p} = 1/2. -## -## With the optional argument @code{alt}, the alternative of interest can be -## selected. If @var{alt} is @qcode{"!="} or @qcode{"<>"}, the null -## hypothesis is tested against the two-sided alternative -## PROB (@var{x} < @var{y}) != 1/2. If @var{alt} is @qcode{">"}, the one-sided -## alternative PROB (@var{x} > @var{y}) > 1/2 ("x is stochastically greater -## than y") is considered. Similarly for @qcode{"<"}, the one-sided -## alternative PROB (@var{x} > @var{y}) < 1/2 ("x is stochastically less than -## y") is considered. The default is the two-sided case. -## -## The p-value of the test is returned in @var{pval}. -## -## If no output argument is given, the p-value of the test is displayed. -## @end deftypefn - -## Author: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: Sign test - -function [pval, b, n] = sign_test (x, y, alt) - - if (nargin < 2 || nargin > 3) - print_usage (); - endif - - if (! (isvector (x) && isvector (y) && (length (x) == length (y)))) - error ("sign_test: X and Y must be vectors of the same length"); - endif - - n = length (x); - x = reshape (x, 1, n); - y = reshape (y, 1, n); - n = sum (x != y); - b = sum (x > y); - cdf = binocdf (b, n, 1/2); - - if (nargin == 2) - alt = "!="; - endif - - if (! ischar (alt)) - error ("sign_test: ALT must be a string"); - endif - if (strcmp (alt, "!=") || strcmp (alt, "<>")) - pval = 2 * min (cdf, 1 - cdf); - elseif (strcmp (alt, ">")) - pval = 1 - cdf; - elseif (strcmp (alt, "<")) - pval = cdf; - else - error ("sign_test: option %s not recognized", alt); - endif - - if (nargout == 0) - printf (" pval: %g\n", pval); - endif - -endfunction
--- a/scripts/statistics/tests/t_test.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,114 +0,0 @@ -## Copyright (C) 1995-2017 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {[@var{pval}, @var{t}, @var{df}] =} t_test (@var{x}, @var{m}, @var{alt}) -## For a sample @var{x} from a normal distribution with unknown mean and -## variance, perform a t-test of the null hypothesis -## @code{mean (@var{x}) == @var{m}}. -## -## Under the null, the test statistic @var{t} follows a Student distribution -## with @code{@var{df} = length (@var{x}) - 1} degrees of freedom. -## -## With the optional argument string @var{alt}, the alternative of interest -## can be selected. If @var{alt} is @qcode{"!="} or @qcode{"<>"}, the null -## is tested against the two-sided alternative @code{mean (@var{x}) != -## @var{m}}. If @var{alt} is @qcode{">"}, the one-sided alternative -## @code{mean (@var{x}) > @var{m}} is considered. Similarly for @var{"<"}, -## the one-sided alternative @code{mean (@var{x}) < @var{m}} is considered. -## The default is the two-sided case. -## -## The p-value of the test is returned in @var{pval}. -## -## If no output argument is given, the p-value of the test is displayed. -## @end deftypefn - -## Author: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: Student's one-sample t test - -function [pval, t, df] = t_test (x, m, alt) - - if (nargin < 2 || nargin > 3) - print_usage (); - endif - - if (! isvector (x)) - error ("t_test: X must be a vector"); - endif - if (! isscalar (m)) - error ("t_test: M must be a scalar"); - endif - - n = length (x); - df = n - 1; - t = sqrt (n) * (sum (x) / n - m) / std (x); - cdf = tcdf (t, df); - - if (nargin == 2) - alt = "!="; - endif - - if (! ischar (alt)) - error ("t_test: ALT must be a string"); - endif - if (strcmp (alt, "!=") || strcmp (alt, "<>")) - pval = 2 * min (cdf, 1 - cdf); - elseif (strcmp (alt, ">")) - pval = 1 - cdf; - elseif (strcmp (alt, "<")) - pval = cdf; - else - error ("t_test: option %s not recognized", alt); - endif - - if (nargout == 0) - printf (" pval: %g\n", pval); - endif - -endfunction - - -%!test -%! ## Two-sided (also the default option) -%! x = rand (10,1); n = length (x); -%! u0 = 0.5; # true mean -%! xbar = mean (x); -%! pval = t_test (x, u0, "!="); -%! if (xbar >= u0) -%! tval = abs (tinv (0.5*pval, n-1)); -%! else -%! tval = -abs (tinv (0.5*pval, n-1)); -%! endif -%! unew = tval * std(x)/sqrt(n) + u0; -%! assert (xbar, unew, 100*eps); - -%!test -%! x = rand (10,1); n = length (x); -%! u0 = 0.5; -%! pval = t_test (x, u0, ">"); -%! tval = tinv (1-pval, n-1); -%! unew = tval * std(x)/sqrt(n) + u0; -%! assert (mean (x), unew, 100*eps); - -%!test -%! x = rand (10,1); n = length (x); -%! u0 = 0.5; -%! pval = t_test (x, u0, "<"); -%! tval = tinv (pval, n-1); -%! unew = tval * std(x)/sqrt(n) + u0; -%! assert (mean (x), unew, 100*eps);
--- a/scripts/statistics/tests/t_test_2.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,84 +0,0 @@ -## Copyright (C) 1995-2017 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {[@var{pval}, @var{t}, @var{df}] =} t_test_2 (@var{x}, @var{y}, @var{alt}) -## For two samples x and y from normal distributions with unknown means and -## unknown equal variances, perform a two-sample t-test of the null -## hypothesis of equal means. -## -## Under the null, the test statistic @var{t} follows a Student distribution -## with @var{df} degrees of freedom. -## -## With the optional argument string @var{alt}, the alternative of interest -## can be selected. If @var{alt} is @qcode{"!="} or @qcode{"<>"}, the null -## is tested against the two-sided alternative @code{mean (@var{x}) != mean -## (@var{y})}. If @var{alt} is @qcode{">"}, the one-sided alternative -## @code{mean (@var{x}) > mean (@var{y})} is used. Similarly for -## @qcode{"<"}, the one-sided alternative @code{mean (@var{x}) < mean -## (@var{y})} is used. The default is the two-sided case. -## -## The p-value of the test is returned in @var{pval}. -## -## If no output argument is given, the p-value of the test is displayed. -## @end deftypefn - -## Author: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: Student's two-sample t test - -function [pval, t, df] = t_test_2 (x, y, alt) - - if (nargin < 2 || nargin > 3) - print_usage (); - endif - - if (! (isvector (x) && isvector (y))) - error ("t_test_2: both X and Y must be vectors"); - endif - - n_x = length (x); - n_y = length (y); - df = n_x + n_y - 2; - mu_x = sum (x) / n_x; - mu_y = sum (y) / n_y; - v = sumsq (x - mu_x) + sumsq (y - mu_y); - t = (mu_x - mu_y) * sqrt ((n_x * n_y * df) / (v * (n_x + n_y))); - cdf = tcdf (t, df); - - if (nargin == 2) - alt = "!="; - endif - - if (! ischar (alt)) - error ("t_test_2: ALT must be a string"); - endif - if (strcmp (alt, "!=") || strcmp (alt, "<>")) - pval = 2 * min (cdf, 1 - cdf); - elseif (strcmp (alt, ">")) - pval = 1 - cdf; - elseif (strcmp (alt, "<")) - pval = cdf; - else - error ("t_test_2: option %s not recognized", alt); - endif - - if (nargout == 0) - printf (" pval: %g\n", pval); - endif - -endfunction
--- a/scripts/statistics/tests/t_test_regression.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,98 +0,0 @@ -## Copyright (C) 1995-2017 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {[@var{pval}, @var{t}, @var{df}] =} t_test_regression (@var{y}, @var{x}, @var{rr}, @var{r}, @var{alt}) -## Perform a t test for the null hypothesis -## @nospell{@code{@var{rr} * @var{b} = @var{r}}} in a classical normal -## regression model @code{@var{y} = @var{x} * @var{b} + @var{e}}. -## -## Under the null, the test statistic @var{t} follows a @var{t} distribution -## with @var{df} degrees of freedom. -## -## If @var{r} is omitted, a value of 0 is assumed. -## -## With the optional argument string @var{alt}, the alternative of interest -## can be selected. If @var{alt} is @qcode{"!="} or @qcode{"<>"}, the null -## is tested against the two-sided alternative @nospell{@code{@var{rr} * -## @var{b} != @var{r}}}. If @var{alt} is @qcode{">"}, the one-sided -## alternative @nospell{@code{@var{rr} * @var{b} > @var{r}}} is used. -## Similarly for @var{"<"}, the one-sided alternative @nospell{@code{@var{rr} -## * @var{b} < @var{r}}} is used. The default is the two-sided case. -## -## The p-value of the test is returned in @var{pval}. -## -## If no output argument is given, the p-value of the test is displayed. -## @end deftypefn - -## Author: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: Test one linear hypothesis in linear regression model - -function [pval, t, df] = t_test_regression (y, x, rr, r, alt) - - if (nargin == 3) - r = 0; - alt = "!="; - elseif (nargin == 4) - if (ischar (r)) - alt = r; - r = 0; - else - alt = "!="; - endif - elseif (! (nargin == 5)) - print_usage (); - endif - - if (! isscalar (r)) - error ("t_test_regression: R must be a scalar"); - elseif (! ischar (alt)) - error ("t_test_regression: ALT must be a string"); - endif - - [T, k] = size (x); - if (! (isvector (y) && (length (y) == T))) - error ("t_test_regression: Y must be a vector of length rows (X)"); - endif - s = size (rr); - if (! ((max (s) == k) && (min (s) == 1))) - error ("t_test_regression: RR must be a vector of length columns (X)"); - endif - - rr = reshape (rr, 1, k); - y = reshape (y, T, 1); - [b, v] = ols (y, x); - df = T - k; - t = (rr * b - r) / sqrt (v * rr * inv (x' * x) * rr'); - cdf = tcdf (t, df); - - if (strcmp (alt, "!=") || strcmp (alt, "<>")) - pval = 2 * min (cdf, 1 - cdf); - elseif (strcmp (alt, ">")) - pval = 1 - cdf; - elseif (strcmp (alt, "<")) - pval = cdf; - else - error ("t_test_regression: the value '%s' for ALT is not possible", alt); - endif - - if (nargout == 0) - printf ("pval: %g\n", pval); - endif - -endfunction
--- a/scripts/statistics/tests/u_test.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,87 +0,0 @@ -## Copyright (C) 1995-2017 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {[@var{pval}, @var{z}] =} u_test (@var{x}, @var{y}, @var{alt}) -## For two samples @var{x} and @var{y}, perform a Mann-Whitney U-test of -## the null hypothesis -## PROB (@var{x} > @var{y}) == 1/2 == PROB (@var{x} < @var{y}). -## -## Under the null, the test statistic @var{z} approximately follows a -## standard normal distribution. Note that this test is equivalent to the -## Wilcoxon rank-sum test. -## -## With the optional argument string @var{alt}, the alternative of interest -## can be selected. If @var{alt} is @qcode{"!="} or @qcode{"<>"}, the null -## is tested against the two-sided alternative -## PROB (@var{x} > @var{y}) != 1/2. If @var{alt} is @qcode{">"}, the one-sided -## alternative PROB (@var{x} > @var{y}) > 1/2 is considered. Similarly for -## @qcode{"<"}, the one-sided alternative PROB (@var{x} > @var{y}) < 1/2 is -## considered. The default is the two-sided case. -## -## The p-value of the test is returned in @var{pval}. -## -## If no output argument is given, the p-value of the test is displayed. -## @end deftypefn - -## This implementation is still incomplete---for small sample sizes, -## the normal approximation is rather bad ... - -## Author: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: Mann-Whitney U-test - -function [pval, z] = u_test (x, y, alt) - - if (nargin < 2 || nargin > 3) - print_usage (); - endif - - if (! (isvector (x) && isvector (y))) - error ("u_test: both X and Y must be vectors"); - endif - - n_x = length (x); - n_y = length (y); - r = ranks ([(reshape (x, 1, n_x)), (reshape (y, 1, n_y))]); - z = (sum (r(1 : n_x)) - n_x * (n_x + n_y + 1) / 2) ... - / sqrt (n_x * n_y * (n_x + n_y + 1) / 12); - - cdf = stdnormal_cdf (z); - - if (nargin == 2) - alt = "!="; - endif - - if (! ischar (alt)) - error ("u_test: ALT must be a string"); - endif - if (strcmp (alt, "!=") || strcmp (alt, "<>")) - pval = 2 * min (cdf, 1 - cdf); - elseif (strcmp (alt, ">")) - pval = cdf; - elseif (strcmp (alt, "<")) - pval = 1 - cdf; - else - error ("u_test: option %s not recognized", alt); - endif - - if (nargout == 0) - printf (" pval: %g\n", pval); - endif - -endfunction
--- a/scripts/statistics/tests/var_test.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,80 +0,0 @@ -## Copyright (C) 1995-2017 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {[@var{pval}, @var{f}, @var{df_num}, @var{df_den}] =} var_test (@var{x}, @var{y}, @var{alt}) -## For two samples @var{x} and @var{y} from normal distributions with -## unknown means and unknown variances, perform an F-test of the null -## hypothesis of equal variances. -## -## Under the null, the test statistic @var{f} follows an F-distribution with -## @var{df_num} and @var{df_den} degrees of freedom. -## -## With the optional argument string @var{alt}, the alternative of interest -## can be selected. If @var{alt} is @qcode{"!="} or @qcode{"<>"}, the null -## is tested against the two-sided alternative @code{var (@var{x}) != var -## (@var{y})}. If @var{alt} is @qcode{">"}, the one-sided alternative -## @code{var (@var{x}) > var (@var{y})} is used. Similarly for "<", the -## one-sided alternative @code{var (@var{x}) > var (@var{y})} is used. The -## default is the two-sided case. -## -## The p-value of the test is returned in @var{pval}. -## -## If no output argument is given, the p-value of the test is displayed. -## @end deftypefn - -## Author: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: F test to compare two variances - -function [pval, f, df_num, df_den] = var_test (x, y, alt) - - if (nargin < 2 || nargin > 3) - print_usage (); - endif - - if (! (isvector (x) && isvector (y))) - error ("var_test: both X and Y must be vectors"); - endif - - df_num = length (x) - 1; - df_den = length (y) - 1; - f = var (x) / var (y); - cdf = fcdf (f, df_num, df_den); - - if (nargin == 2) - alt = "!="; - endif - - if (! ischar (alt)) - error ("var_test: ALT must be a string"); - endif - if (strcmp (alt, "!=") || strcmp (alt, "<>")) - pval = 2 * min (cdf, 1 - cdf); - elseif (strcmp (alt, ">")) - pval = 1 - cdf; - elseif (strcmp (alt, "<")) - pval = cdf; - else - error ("var_test: option %s not recognized", alt); - endif - - if (nargout == 0) - printf ("pval: %g\n", pval); - endif - -endfunction
--- a/scripts/statistics/tests/welch_test.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,86 +0,0 @@ -## Copyright (C) 1995-2017 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {[@var{pval}, @var{t}, @var{df}] =} welch_test (@var{x}, @var{y}, @var{alt}) -## For two samples @var{x} and @var{y} from normal distributions with -## unknown means and unknown and not necessarily equal variances, -## perform a Welch test of the null hypothesis of equal means. -## -## Under the null, the test statistic @var{t} approximately follows a -## Student distribution with @var{df} degrees of freedom. -## -## With the optional argument string @var{alt}, the alternative of interest -## can be selected. If @var{alt} is @qcode{"!="} or @qcode{"<>"}, the null -## is tested against the two-sided alternative -## @code{mean (@var{x}) != @var{m}}. If @var{alt} is @qcode{">"}, the -## one-sided alternative mean(x) > @var{m} is considered. Similarly for -## @qcode{"<"}, the one-sided alternative mean(x) < @var{m} is considered. -## The default is the two-sided case. -## -## The p-value of the test is returned in @var{pval}. -## -## If no output argument is given, the p-value of the test is displayed. -## @end deftypefn - -## Author: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: Welch two-sample t test - -function [pval, t, df] = welch_test (x, y, alt) - - if (nargin < 2 || nargin > 3) - print_usage (); - endif - - if (! (isvector (x) && isvector (y))) - error ("welch_test: both X and Y must be vectors"); - endif - - n_x = length (x); - n_y = length (y); - mu_x = sum (x) / n_x; - mu_y = sum (y) / n_y; - v_x = sumsq (x - mu_x) / (n_x * (n_x - 1)); - v_y = sumsq (y - mu_y) / (n_y * (n_y - 1)); - c = v_x / (v_x + v_y); - df = 1 / (c^2 / (n_x - 1) + (1 - c)^2 / (n_y - 1)); - t = (mu_x - mu_y) / sqrt (v_x + v_y); - cdf = tcdf (t, df); - - if (nargin == 2) - alt = "!="; - endif - - if (! ischar (alt)) - error ("welch_test: ALT must be a string"); - endif - if (strcmp (alt, "!=") || strcmp (alt, "<>")) - pval = 2 * min (cdf, 1 - cdf); - elseif (strcmp (alt, ">")) - pval = 1 - cdf; - elseif (strcmp (alt, "<")) - pval = cdf; - else - error ("welch_test: option %s not recognized", alt); - endif - - if (nargout == 0) - printf (" pval: %g\n", pval); - endif - -endfunction
--- a/scripts/statistics/tests/wilcoxon_test.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,93 +0,0 @@ -## Copyright (C) 1995-2017 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {[@var{pval}, @var{z}] =} wilcoxon_test (@var{x}, @var{y}, @var{alt}) -## For two matched-pair sample vectors @var{x} and @var{y}, perform a -## Wilcoxon signed-rank test of the null hypothesis -## PROB (@var{x} > @var{y}) == 1/2. -## -## Under the null, the test statistic @var{z} approximately follows a -## standard normal distribution when @var{n} > 25. -## -## @strong{Caution:} This function assumes a normal distribution for @var{z} -## and thus is invalid for @var{n} @leq{} 25. -## -## With the optional argument string @var{alt}, the alternative of interest -## can be selected. If @var{alt} is @qcode{"!="} or @qcode{"<>"}, the null -## is tested against the two-sided alternative -## PROB (@var{x} > @var{y}) != 1/2. If alt is @qcode{">"}, the one-sided -## alternative PROB (@var{x} > @var{y}) > 1/2 is considered. Similarly for -## @qcode{"<"}, the one-sided alternative PROB (@var{x} > @var{y}) < 1/2 is -## considered. The default is the two-sided case. -## -## The p-value of the test is returned in @var{pval}. -## -## If no output argument is given, the p-value of the test is displayed. -## @end deftypefn - -## Author: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: Wilcoxon signed-rank test - -function [pval, z] = wilcoxon_test (x, y, alt) - - if (nargin < 2 || nargin > 3) - print_usage (); - endif - - if (! (isvector (x) && isvector (y) && (length (x) == length (y)))) - error ("wilcoxon_test: X and Y must be vectors of the same length"); - endif - - n = length (x); - x = reshape (x, 1, n); - y = reshape (y, 1, n); - d = x - y; - d = d(find (d != 0)); - n = length (d); - if (n > 25) - r = ranks (abs (d)); - z = sum (r(find (d > 0))); - z = ((z - n * (n + 1) / 4) / sqrt (n * (n + 1) * (2 * n + 1) / 24)); - else - error ("wilcoxon_test: implementation requires more than 25 different pairs"); - endif - - cdf = stdnormal_cdf (z); - - if (nargin == 2) - alt = "!="; - endif - - if (! ischar (alt)) - error ("wilcoxon_test: ALT must be a string"); - elseif (strcmp (alt, "!=") || strcmp (alt, "<>")) - pval = 2 * min (cdf, 1 - cdf); - elseif (strcmp (alt, ">")) - pval = 1 - cdf; - elseif (strcmp (alt, "<")) - pval = cdf; - else - error ("wilcoxon_test: option %s not recognized", alt); - endif - - if (nargout == 0) - printf (" pval: %g\n", pval); - endif - -endfunction
--- a/scripts/statistics/tests/z_test.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,119 +0,0 @@ -## Copyright (C) 1995-2017 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {[@var{pval}, @var{z}] =} z_test (@var{x}, @var{m}, @var{v}, @var{alt}) -## Perform a Z-test of the null hypothesis @code{mean (@var{x}) == @var{m}} -## for a sample @var{x} from a normal distribution with unknown mean and known -## variance @var{v}. -## -## Under the null, the test statistic @var{z} follows a standard normal -## distribution. -## -## With the optional argument string @var{alt}, the alternative of interest -## can be selected. If @var{alt} is @qcode{"!="} or @qcode{"<>"}, the null -## is tested against the two-sided alternative -## @code{mean (@var{x}) != @var{m}}. If @var{alt} is @qcode{">"}, the -## one-sided alternative @code{mean (@var{x}) > @var{m}} is considered. -## Similarly for @qcode{"<"}, the one-sided alternative -## @code{mean (@var{x}) < @var{m}} is considered. The default is the two-sided -## case. -## -## The p-value of the test is returned in @var{pval}. -## -## If no output argument is given, the p-value of the test is displayed along -## with some information. -## @end deftypefn - -## Author: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: Test for mean of a normal sample with known variance - -function [pval, z] = z_test (x, m, v, alt) - - if (nargin < 3 || nargin > 4) - print_usage (); - endif - - if (! isvector (x)) - error ("z_test: X must be a vector"); - endif - if (! isscalar (m)) - error ("z_test: M must be a scalar"); - endif - if (! (isscalar (v) && (v > 0))) - error ("z_test: V must be a positive scalar"); - endif - - n = length (x); - z = sqrt (n/v) * (sum (x) / n - m); - cdf = stdnormal_cdf (z); - - if (nargin == 3) - alt = "!="; - endif - - if (! ischar (alt)) - error ("z_test: ALT must be a string"); - elseif (strcmp (alt, "!=") || strcmp (alt, "<>")) - pval = 2 * min (cdf, 1 - cdf); - elseif (strcmp (alt, ">")) - pval = 1 - cdf; - elseif (strcmp (alt, "<")) - pval = cdf; - else - error ("z_test: option %s not recognized", alt); - endif - - if (nargout == 0) - s = ["Z-test of mean(x) == %g against mean(x) %s %g,\n", ... - "with known var(x) == %g:\n", ... - " pval = %g\n"]; - printf (s, m, alt, m, v, pval); - endif - -endfunction - - -%!test -%! ## Two-sided (also the default option) -%! x = rand (10,1); n = length (x); -%! u0 = 0.5; v = 1/12; # true mean, var -%! pval = z_test (x, u0, v, "!="); -%! if (mean (x) >= u0) -%! zval = abs (norminv (0.5*pval)); -%! else -%! zval = -abs (norminv (0.5*pval)); -%! endif -%! unew = zval * sqrt (v/n) + u0; -%! assert (mean (x), unew, 100*eps); - -%!test -%! x = rand (10,1); n = length (x); -%! u0 = 0.5; v = 1/12; -%! pval = z_test (x, u0, v, ">"); -%! zval = norminv (1-pval); -%! unew = zval * sqrt (v/n) + u0; -%! assert (mean (x), unew, 100*eps); - -%!test -%! x = rand (10,1); n = length (x); -%! u0 = 0.5; v = 1/12; -%! pval = z_test (x, u0, v, "<"); -%! zval = norminv (pval); -%! unew = zval * sqrt (v/n) + u0; -%! assert (mean (x), unew, 100*eps);
--- a/scripts/statistics/tests/z_test_2.m Sun Jan 07 09:57:32 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,144 +0,0 @@ -## Copyright (C) 1995-2017 Kurt Hornik -## -## This file is part of Octave. -## -## Octave is free software: you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## Octave is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with Octave; see the file COPYING. If not, see -## <https://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {} {[@var{pval}, @var{z}] =} z_test_2 (@var{x}, @var{y}, @var{v_x}, @var{v_y}, @var{alt}) -## For two samples @var{x} and @var{y} from normal distributions with unknown -## means and known variances @var{v_x} and @var{v_y}, perform a Z-test of the -## hypothesis of equal means. -## -## Under the null, the test statistic @var{z} follows a standard normal -## distribution. -## -## With the optional argument string @var{alt}, the alternative of interest -## can be selected. If @var{alt} is @qcode{"!="} or @qcode{"<>"}, the null -## is tested against the two-sided alternative -## @code{mean (@var{x}) != mean (@var{y})}. If alt is @qcode{">"}, the -## one-sided alternative @code{mean (@var{x}) > mean (@var{y})} is used. -## Similarly for @qcode{"<"}, the one-sided alternative -## @code{mean (@var{x}) < mean (@var{y})} is used. The default is the -## two-sided case. -## -## The p-value of the test is returned in @var{pval}. -## -## If no output argument is given, the p-value of the test is displayed along -## with some information. -## @end deftypefn - -## Author: KH <Kurt.Hornik@wu-wien.ac.at> -## Description: Compare means of two normal samples with known variances - -function [pval, z] = z_test_2 (x, y, v_x, v_y, alt) - - if (nargin < 4 || nargin > 5) - print_usage (); - endif - - if (! (isvector (x) && isvector (y))) - error ("z_test_2: both X and Y must be vectors"); - elseif (! (isscalar (v_x) && (v_x > 0) - && isscalar (v_y) && (v_y > 0))) - error ("z_test_2: both V_X and V_Y must be positive scalars"); - endif - - n_x = length (x); - n_y = length (y); - mu_x = sum (x) / n_x; - mu_y = sum (y) / n_y; - z = (mu_x - mu_y) / sqrt (v_x / n_x + v_y / n_y); - cdf = stdnormal_cdf (z); - - if (nargin == 4) - alt = "!="; - endif - - if (! ischar (alt)) - error ("z_test_2: ALT must be a string"); - elseif (strcmp (alt, "!=") || strcmp (alt, "<>")) - pval = 2 * min (cdf, 1 - cdf); - elseif (strcmp (alt, ">")) - pval = 1 - cdf; - elseif (strcmp (alt, "<")) - pval = cdf; - else - error ("z_test_2: option %s not recognized", alt); - endif - - if (nargout == 0) - s = ["Two-sample Z-test of mean(x) == mean(y) against ", ... - "mean(x) %s mean(y),\n", ... - "with known var(x) == %g and var(y) == %g:\n", ... - " pval = %g\n"]; - printf (s, alt, v_x, v_y, pval); - endif - -endfunction - -#!test -%! ## Two-sided (also the default option) -%! x = randn (100, 1); v_x = 2; x = v_x * x; -%! [pval, z] = z_test_2 (x, x, v_x, v_x); -%! zval_exp = 0; pval_exp = 1.0; -%! assert (zval, zval_exp, eps); -%! assert (pval, pval_exp, eps); - -#!test -%! ## Two-sided (also the default option) -%! x = randn (10000, 1); v_x = 2; x = v_x * x; n_x = length (x); -%! y = randn (20000, 1); v_y = 3; y = v_y * y; n_y = length (y); -%! [pval, z] = z_test_2 (x, y, v_x, v_y); -%! if (mean (x) >= mean (y)) -%! zval = abs (norminv (0.5*pval)); -%! else -%! zval = -abs (norminv (0.5*pval)); -%! endif -%! unew = zval * sqrt (v_x/n_x + v_y/n_y); -%! delmu = mean (x) - mean (y); -%! assert (delmu, unew, 100*eps); - -#!test -%! x = randn (100, 1); v_x = 2; x = v_x * x; -%! [pval, z] = z_test_2 (x, x, v_x, v_x, ">"); -%! zval_exp = 0; pval_exp = 0.5; -%! assert (zval, zval_exp, eps); -%! assert (pval, pval_exp, eps); - -%!test -%! x = randn (10000, 1); v_x = 2; x = v_x * x; n_x = length (x); -%! y = randn (20000, 1); v_y = 3; y = v_y * y; n_y = length (y); -%! [pval, z] = z_test_2 (x, y, v_x, v_y, ">"); -%! zval = norminv (1-pval); -%! unew = zval * sqrt (v_x/n_x + v_y/n_y); -%! delmu = mean (x) - mean (y); -%! assert (delmu, unew, 100*eps); - -%!test -%! x = randn (100, 1); v_x = 2; x = v_x * x; -%! [pval, zval] = z_test_2 (x, x, v_x, v_x, "<"); -%! zval_exp = 0; pval_exp = 0.5; -%! assert (zval, zval_exp, eps); -%! assert (pval, pval_exp, eps); - -%!test -%! x = randn (10000, 1); v_x = 2; x = v_x * x; n_x = length (x); -%! y = randn (20000, 1); v_y = 3; y = v_y * y; n_y = length (y); -%! [pval, z] = z_test_2 (x, y, v_x, v_y, "<"); -%! zval = norminv (pval); -%! unew = zval * sqrt (v_x/n_x + v_y/n_y); -%! delmu = mean (x) - mean (y); -%! assert (delmu, unew, 100*eps);
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/scripts/statistics/var.m Sun Jan 07 17:13:23 2018 -0800 @@ -0,0 +1,130 @@ +## Copyright (C) 1995-2017 Kurt Hornik +## +## This file is part of Octave. +## +## Octave is free software: you can redistribute it and/or modify it +## under the terms of the GNU General Public License as published by +## the Free Software Foundation, either version 3 of the License, or +## (at your option) any later version. +## +## Octave is distributed in the hope that it will be useful, but +## WITHOUT ANY WARRANTY; without even the implied warranty of +## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +## GNU General Public License for more details. +## +## You should have received a copy of the GNU General Public License +## along with Octave; see the file COPYING. If not, see +## <https://www.gnu.org/licenses/>. + +## -*- texinfo -*- +## @deftypefn {} {} var (@var{x}) +## @deftypefnx {} {} var (@var{x}, @var{opt}) +## @deftypefnx {} {} var (@var{x}, @var{opt}, @var{dim}) +## Compute the variance of the elements of the vector @var{x}. +## +## The variance is defined as +## @tex +## $$ +## {\rm var} (x) = \sigma^2 = {\sum_{i=1}^N (x_i - \bar{x})^2 \over N - 1} +## $$ +## where $\bar{x}$ is the mean value of @var{x} and $N$ is the number of +## elements of @var{x}. +## +## @end tex +## @ifnottex +## +## @example +## @group +## var (@var{x}) = 1/(N-1) SUM_i (@var{x}(i) - mean(@var{x}))^2 +## @end group +## @end example +## +## where @math{N} is the length of the @var{x} vector. +## +## @end ifnottex +## If @var{x} is a matrix, compute the variance for each column and return +## them in a row vector. +## +## The argument @var{opt} determines the type of normalization to use. +## Valid values are +## +## @table @asis +## @item 0: +## normalize with @math{N-1}, provides the best unbiased estimator of the +## variance [default] +## +## @item 1: +## normalizes with @math{N}, this provides the second moment around the mean +## @end table +## +## If @math{N} is equal to 1 the value of @var{opt} is ignored and +## normalization by @math{N} is used. +## +## If the optional argument @var{dim} is given, operate along this dimension. +## @seealso{cov, std, skewness, kurtosis, moment} +## @end deftypefn + +## Author: KH <Kurt.Hornik@wu-wien.ac.at> +## Description: Compute variance + +function retval = var (x, opt = 0, dim) + + if (nargin < 1 || nargin > 3) + print_usage (); + endif + + if (! (isnumeric (x) || islogical (x))) + error ("var: X must be a numeric vector or matrix"); + endif + + if (isempty (opt)) + opt = 0; + elseif (opt != 0 && opt != 1) + error ("var: normalization OPT must be 0 or 1"); + endif + + nd = ndims (x); + sz = size (x); + if (nargin < 3) + ## Find the first non-singleton dimension. + (dim = find (sz > 1, 1)) || (dim = 1); + else + if (! (isscalar (dim) && dim == fix (dim) && dim > 0)) + error ("var: DIM must be an integer and a valid dimension"); + endif + endif + + n = size (x, dim); + if (n == 1) + if (isa (x, "single")) + retval = zeros (sz, "single"); + else + retval = zeros (sz); + endif + elseif (numel (x) > 0) + retval = sumsq (center (x, dim), dim) / (n - 1 + opt); + else + error ("var: X must not be empty"); + endif + +endfunction + + +%!assert (var (13), 0) +%!assert (var (single (13)), single (0)) +%!assert (var ([1,2,3]), 1) +%!assert (var ([1,2,3], 1), 2/3, eps) +%!assert (var ([1,2,3], [], 1), [0,0,0]) +%!assert (var ([1,2,3], [], 3), [0,0,0]) + +## Test input validation +%!error var () +%!error var (1,2,3,4) +%!error <X must be a numeric> var (['A'; 'B']) +%!error <OPT must be 0 or 1> var (1, -1) +%!error <FLAG must be 0 or 1> skewness (1, 2) +%!error <FLAG must be 0 or 1> skewness (1, [1 0]) +%!error <DIM must be an integer> var (1, [], ones (2,2)) +%!error <DIM must be an integer> var (1, [], 1.5) +%!error <DIM must be .* a valid dimension> var (1, [], 0) +%!error <X must not be empty> var ([], 1)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/scripts/statistics/zscore.m Sun Jan 07 17:13:23 2018 -0800 @@ -0,0 +1,108 @@ +## Copyright (C) 1995-2017 Kurt Hornik +## +## This file is part of Octave. +## +## Octave is free software: you can redistribute it and/or modify it +## under the terms of the GNU General Public License as published by +## the Free Software Foundation, either version 3 of the License, or +## (at your option) any later version. +## +## Octave is distributed in the hope that it will be useful, but +## WITHOUT ANY WARRANTY; without even the implied warranty of +## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +## GNU General Public License for more details. +## +## You should have received a copy of the GNU General Public License +## along with Octave; see the file COPYING. If not, see +## <https://www.gnu.org/licenses/>. + +## -*- texinfo -*- +## @deftypefn {} {@var{z} =} zscore (@var{x}) +## @deftypefnx {} {@var{z} =} zscore (@var{x}, @var{opt}) +## @deftypefnx {} {@var{z} =} zscore (@var{x}, @var{opt}, @var{dim}) +## @deftypefnx {} {[@var{z}, @var{mu}, @var{sigma}] =} zscore (@dots{}) +## Compute the Z score of @var{x} +## +## If @var{x} is a vector, subtract its mean and divide by its standard +## deviation. If the standard deviation is zero, divide by 1 instead. +## +## The optional parameter @var{opt} determines the normalization to use when +## computing the standard deviation and has the same definition as the +## corresponding parameter for @code{std}. +## +## If @var{x} is a matrix, calculate along the first non-singleton dimension. +## If the third optional argument @var{dim} is given, operate along this +## dimension. +## +## The optional outputs @var{mu} and @var{sigma} contain the mean and standard +## deviation. +## +## @seealso{mean, std, center} +## @end deftypefn + +## Author: KH <Kurt.Hornik@wu-wien.ac.at> +## Description: Subtract mean and divide by standard deviation + +function [z, mu, sigma] = zscore (x, opt, dim) + + if (nargin < 1 || nargin > 3 ) + print_usage (); + endif + + if (! (isnumeric (x) || islogical (x))) + error ("zscore: X must be a numeric vector or matrix"); + endif + + if (nargin < 2) + opt = 0; + else + if (opt != 0 && opt != 1 || ! isscalar (opt)) + error ("zscore: OPT must be empty, 0, or 1"); + endif + endif + + nd = ndims (x); + sz = size (x); + if (nargin < 3) + ## Find the first non-singleton dimension. + (dim = find (sz > 1, 1)) || (dim = 1); + else + if (!(isscalar (dim) && dim == fix (dim)) + || !(1 <= dim && dim <= nd)) + error ("zscore: DIM must be an integer and a valid dimension"); + endif + endif + + n = sz(dim); + if (n == 0) + z = x; + else + + if (isinteger (x)) + x = double (x); + endif + + mu = mean (x, dim); + sigma = std (x, opt, dim); + s = sigma; + s(s==0) = 1; + z = (x - mu) ./ s; + endif + +endfunction + + +%!assert (zscore ([1,2,3]), [-1,0,1]) +%!assert (zscore (single ([1,2,3])), single ([-1,0,1])) +%!assert (zscore (int8 ([1,2,3])), [-1,0,1]) +%!assert (zscore (ones (3,2,2,2)), zeros (3,2,2,2)) +%!assert (zscore ([2,0,-2;0,2,0;-2,-2,2]), [1,0,-1;0,1,0;-1,-1,1]) + +## Test input validation +%!error zscore () +%!error zscore (1, 2, 3) +%!error zscore (['A'; 'B']) +%!error zscore (1, ones (2,2)) +%!error zscore (1, 1.5) +%!error zscore (1, 1, 0) +%!error zscore (1, 3)