Mercurial > octave
view scripts/statistics/kendall.m @ 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 | scripts/statistics/base/kendall.m@194eb4bd202b |
children | 6652d3823428 |
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## 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))