Mercurial > octave-nkf
changeset 20209:d9341b422488 stable
doc: Update more docstrings to have one sentence summary as first line.
Reviewed statistics/ and @ftp/ in scripts directory.
* scripts/@ftp/ascii.m, scripts/@ftp/binary.m, scripts/@ftp/cd.m,
scripts/@ftp/dir.m, scripts/@ftp/ftp.m, scripts/@ftp/mget.m,
scripts/@ftp/mput.m, scripts/statistics/base/center.m,
scripts/statistics/base/cloglog.m, scripts/statistics/base/cov.m,
scripts/statistics/base/gls.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/lscov.m, scripts/statistics/base/mahalanobis.m,
scripts/statistics/base/mean.m, scripts/statistics/base/meansq.m,
scripts/statistics/base/median.m, scripts/statistics/base/mode.m,
scripts/statistics/base/moment.m, scripts/statistics/base/ols.m,
scripts/statistics/base/ppplot.m, scripts/statistics/base/prctile.m,
scripts/statistics/base/probit.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/table.m,
scripts/statistics/base/var.m, scripts/statistics/base/zscore.m,
scripts/statistics/distributions/betainv.m,
scripts/statistics/distributions/binoinv.m,
scripts/statistics/distributions/binopdf.m,
scripts/statistics/distributions/cauchy_cdf.m,
scripts/statistics/distributions/cauchy_inv.m,
scripts/statistics/distributions/cauchy_pdf.m,
scripts/statistics/distributions/chi2cdf.m,
scripts/statistics/distributions/chi2inv.m,
scripts/statistics/distributions/chi2pdf.m,
scripts/statistics/distributions/discrete_cdf.m,
scripts/statistics/distributions/discrete_inv.m,
scripts/statistics/distributions/discrete_pdf.m,
scripts/statistics/distributions/empirical_cdf.m,
scripts/statistics/distributions/empirical_inv.m,
scripts/statistics/distributions/empirical_pdf.m,
scripts/statistics/distributions/expcdf.m,
scripts/statistics/distributions/expinv.m,
scripts/statistics/distributions/exppdf.m,
scripts/statistics/distributions/finv.m,
scripts/statistics/distributions/fpdf.m,
scripts/statistics/distributions/gamcdf.m,
scripts/statistics/distributions/gaminv.m,
scripts/statistics/distributions/gampdf.m,
scripts/statistics/distributions/geoinv.m,
scripts/statistics/distributions/geopdf.m,
scripts/statistics/distributions/hygecdf.m,
scripts/statistics/distributions/hygeinv.m,
scripts/statistics/distributions/hygepdf.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/logistic_inv.m,
scripts/statistics/distributions/logncdf.m,
scripts/statistics/distributions/logninv.m,
scripts/statistics/distributions/lognpdf.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/poisscdf.m,
scripts/statistics/distributions/poissinv.m,
scripts/statistics/distributions/poisspdf.m,
scripts/statistics/distributions/stdnormal_cdf.m,
scripts/statistics/distributions/stdnormal_pdf.m,
scripts/statistics/distributions/tcdf.m,
scripts/statistics/distributions/tinv.m,
scripts/statistics/distributions/tpdf.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/wblcdf.m,
scripts/statistics/distributions/wblinv.m,
scripts/statistics/distributions/wblpdf.m,
scripts/statistics/distributions/wienrnd.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/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/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:
Update more docstrings to have one sentence summary as first line.
line wrap: on
line diff
--- a/scripts/@ftp/ascii.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/@ftp/ascii.m Sun May 10 16:07:41 2015 -0700 @@ -19,8 +19,9 @@ ## -*- texinfo -*- ## @deftypefn {Function File} {} ascii (@var{f}) ## Set the FTP connection @var{f} to use ASCII mode for transfers. -## ASCII mode is only appropriate for text files as it will convert -## the remote host's newline representation to the local host's newline +## +## ASCII mode is only appropriate for text files as it will convert the +## remote host's newline representation to the local host's newline ## representation. ## ## @var{f} is an FTP object returned by the @code{ftp} function.
--- a/scripts/@ftp/binary.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/@ftp/binary.m Sun May 10 16:07:41 2015 -0700 @@ -19,6 +19,7 @@ ## -*- texinfo -*- ## @deftypefn {Function File} {} binary (@var{f}) ## Set the FTP connection @var{f} to use binary mode for transfers. +## ## In binary mode there is no conversion of newlines from the remote ## representation to the local representation. ##
--- a/scripts/@ftp/cd.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/@ftp/cd.m Sun May 10 16:07:41 2015 -0700 @@ -24,8 +24,8 @@ ## @var{f} is an FTP object returned by the @code{ftp} function. ## ## If @var{path} is not specified, return the remote current working -## directory. Otherwise, set the remote directory to @var{path} and -## return the new remote working directory. +## directory. Otherwise, set the remote directory to @var{path} and return +## the new remote working directory. ## ## If the directory does not exist, an error message is printed and the ## working directory is not changed.
--- a/scripts/@ftp/dir.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/@ftp/dir.m Sun May 10 16:07:41 2015 -0700 @@ -18,8 +18,7 @@ ## -*- texinfo -*- ## @deftypefn {Function File} {@var{lst} =} dir (@var{f}) -## List the current directory in verbose form for the FTP connection -## @var{f}. +## List the current directory in verbose form for the FTP connection @var{f}. ## ## @var{f} is an FTP object returned by the @code{ftp} function. ## @end deftypefn
--- a/scripts/@ftp/ftp.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/@ftp/ftp.m Sun May 10 16:07:41 2015 -0700 @@ -20,6 +20,7 @@ ## @deftypefn {Function File} {@var{f} =} ftp (@var{host}) ## @deftypefnx {Function File} {@var{f} =} ftp (@var{host}, @var{username}, @var{password}) ## Connect to the FTP server @var{host} with @var{username} and @var{password}. +## ## If @var{username} and @var{password} are not specified, user ## @qcode{"anonymous"} with no password is used. The returned FTP object ## @var{f} represents the established FTP connection.
--- a/scripts/@ftp/mget.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/@ftp/mget.m Sun May 10 16:07:41 2015 -0700 @@ -21,8 +21,9 @@ ## @deftypefnx {Function File} {} mget (@var{f}, @var{dir}) ## @deftypefnx {Function File} {} mget (@var{f}, @var{remote_name}, @var{target}) ## Download a remote file @var{file} or directory @var{dir} to the local -## directory on the FTP connection @var{f}. @var{f} is an FTP object -## returned by the @code{ftp} function. +## directory on the FTP connection @var{f}. +## +## @var{f} is an FTP object returned by the @code{ftp} function. ## ## The arguments @var{file} and @var{dir} can include wildcards and any ## files or directories on the remote server that match will be downloaded.
--- a/scripts/@ftp/mput.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/@ftp/mput.m Sun May 10 16:07:41 2015 -0700 @@ -18,9 +18,10 @@ ## -*- texinfo -*- ## @deftypefn {Function File} {} mput (@var{f}, @var{file}) -## Upload the local file @var{file} into the current remote directory on -## the FTP connection @var{f}. @var{f} is an FTP object returned by the -## ftp function. +## Upload the local file @var{file} into the current remote directory on the +## FTP connection @var{f}. +## +## @var{f} is an FTP object returned by the ftp function. ## ## The argument @var{file} is passed through the @code{glob} function and any ## files that match the wildcards in @var{file} will be uploaded.
--- a/scripts/statistics/base/center.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/base/center.m Sun May 10 16:07:41 2015 -0700 @@ -20,9 +20,19 @@ ## -*- texinfo -*- ## @deftypefn {Function File} {} center (@var{x}) ## @deftypefnx {Function File} {} 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
--- a/scripts/statistics/base/cloglog.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/base/cloglog.m Sun May 10 16:07:41 2015 -0700 @@ -18,7 +18,9 @@ ## -*- texinfo -*- ## @deftypefn {Function File} {} cloglog (@var{x}) -## Return the complementary log-log function of @var{x}, defined as +## Return the complementary log-log function of @var{x}. +## +## The complementary log-log function is defined as ## @tex ## $$ ## {\rm cloglog}(x) = - \log (- \log (x))
--- a/scripts/statistics/base/cov.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/base/cov.m Sun May 10 16:07:41 2015 -0700 @@ -56,7 +56,7 @@ ## normalize with @math{N}, this provides the second moment around the mean ## @end table ## -## @sc{matlab} compatibility: Octave always computes the covariance matrix. +## Compatibility Note:: Octave always computes the covariance matrix. ## For two inputs, however, @sc{matlab} 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 scalar rather than
--- a/scripts/statistics/base/gls.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/base/gls.m Sun May 10 16:07:41 2015 -0700 @@ -18,7 +18,9 @@ ## -*- texinfo -*- ## @deftypefn {Function File} {[@var{beta}, @var{v}, @var{r}] =} gls (@var{y}, @var{x}, @var{o}) -## Generalized least squares estimation for the multivariate model +## Generalized least squares model. +## +## Perform a generalized least squares estimation for the multivariate model ## @tex ## $y = x b + e$ ## with $\bar{e} = 0$ and cov(vec($e$)) = $(s^2)o$,
--- a/scripts/statistics/base/histc.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/base/histc.m Sun May 10 16:07:41 2015 -0700 @@ -21,7 +21,7 @@ ## @deftypefn {Function File} {@var{n} =} histc (@var{x}, @var{edges}) ## @deftypefnx {Function File} {@var{n} =} histc (@var{x}, @var{edges}, @var{dim}) ## @deftypefnx {Function File} {[@var{n}, @var{idx}] =} histc (@dots{}) -## Produce histogram counts. +## 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 @@ -31,9 +31,9 @@ ## 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 @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}
--- a/scripts/statistics/base/iqr.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/base/iqr.m Sun May 10 16:07:41 2015 -0700 @@ -20,8 +20,10 @@ ## @deftypefn {Function File} {} iqr (@var{x}) ## @deftypefnx {Function File} {} 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}. +## 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. ##
--- a/scripts/statistics/base/kendall.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/base/kendall.m Sun May 10 16:07:41 2015 -0700 @@ -22,10 +22,10 @@ ## @cindex Kendall's Tau ## Compute Kendall's @var{tau}. ## -## For two data vectors @var{x}, @var{y} of common length @var{n}, -## Kendall's @var{tau} 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 +## For two data vectors @var{x}, @var{y} of common length @var{n}, Kendall's +## @var{tau} 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) $$
--- a/scripts/statistics/base/kurtosis.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/base/kurtosis.m Sun May 10 16:07:41 2015 -0700 @@ -21,7 +21,9 @@ ## @deftypefn {Function File} {} kurtosis (@var{x}) ## @deftypefnx {Function File} {} kurtosis (@var{x}, @var{flag}) ## @deftypefnx {Function File} {} kurtosis (@var{x}, @var{flag}, @var{dim}) -## Compute the sample kurtosis of the elements of @var{x}: +## Compute the sample kurtosis of the elements of @var{x}. +## +## The sample kurtosis is defined as ## @tex ## $$ ## \kappa_1 = {{{1\over N}\,
--- a/scripts/statistics/base/logit.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/base/logit.m Sun May 10 16:07:41 2015 -0700 @@ -18,7 +18,9 @@ ## -*- texinfo -*- ## @deftypefn {Function File} {} logit (@var{p}) -## For each component of @var{p}, return the logit of @var{p} defined as +## 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) @@ -31,7 +33,7 @@ ## @end example ## ## @end ifnottex -## @seealso{logistic_cdf} +## @seealso{probit, logistic_cdf} ## @end deftypefn ## Author: KH <Kurt.Hornik@wu-wien.ac.at>
--- a/scripts/statistics/base/lscov.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/base/lscov.m Sun May 10 16:07:41 2015 -0700 @@ -20,6 +20,7 @@ ## @deftypefnx {Function File} {[@var{x}, @var{stdx}, @var{mse}, @var{S}] =} lscov (@dots{}) ## ## Compute a generalized linear least squares fit. +## ## Estimate @var{x} under the model @var{b} = @var{A}@var{x} + @var{w}, ## where the noise @var{w} is assumed to follow a normal distribution ## with covariance matrix @math{{\sigma^2} V}. @@ -28,25 +29,24 @@ ## size of the vector/array of constant terms @var{b} must be n-by-k. ## ## The optional input argument @var{V} may be a n-by-1 vector of positive -## weights (inverse variances), or a n-by-n symmetric positive -## semidefinite matrix representing the covariance of @var{b}. If -## @var{V} is not supplied, the ordinary least squares solution is -## returned. +## weights (inverse variances), or a n-by-n symmetric positive semidefinite +## matrix representing the covariance of @var{b}. If @var{V} is not +## supplied, the ordinary least squares solution is returned. ## -## The @var{alg} input argument, a guidance on solution method to use, -## is currently ignored. +## The @var{alg} input argument, a guidance on solution method to use, is +## currently ignored. ## -## Besides the least-squares estimate matrix @var{x} (p-by-k), the -## function also returns @var{stdx} (p-by-k), the error standard -## deviation of estimated @var{x}; @var{mse} (k-by-1), the estimated -## data error covariance scale factors (@math{\sigma^2}); and @var{S} -## (p-by-p, or p-by-p-by-k if k > 1), the error covariance of @var{x}. +## Besides the least-squares estimate matrix @var{x} (p-by-k), the function +## also returns @var{stdx} (p-by-k), the error standard deviation of +## estimated @var{x}; @var{mse} (k-by-1), the estimated data error covariance +## scale factors (@math{\sigma^2}); and @var{S} (p-by-p, or p-by-p-by-k if k +## > 1), the error covariance of @var{x}. ## ## Reference: @nospell{Golub and Van Loan} (1996), -## Matrix Computations (3rd Ed.), Johns Hopkins, Section 5.6.3 +## @cite{Matrix Computations (3rd Ed.)}, Johns Hopkins, Section 5.6.3 ## +## @seealso{ols, gls, lsqnonneg} ## @end deftypefn -## @seealso{ols, gls, lsqnonneg} ## Author: Nir Krakauer
--- a/scripts/statistics/base/mahalanobis.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/base/mahalanobis.m Sun May 10 16:07:41 2015 -0700 @@ -19,9 +19,10 @@ ## -*- texinfo -*- ## @deftypefn {Function File} {} mahalanobis (@var{x}, @var{y}) ## Return the Mahalanobis' D-square distance between the multivariate -## samples @var{x} and @var{y}, which must have the same number of -## components (columns), but may have a different number of observations -## (rows). +## samples @var{x} and @var{y}. +## +## The data @var{x} and @var{y} must have the same number of components +## (columns), but may have a different number of observations (rows). ## @end deftypefn ## Author: Friedrich Leisch <leisch@ci.tuwien.ac.at>
--- a/scripts/statistics/base/mean.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/base/mean.m Sun May 10 16:07:41 2015 -0700 @@ -22,6 +22,9 @@ ## @deftypefnx {Function File} {} mean (@var{x}, @var{opt}) ## @deftypefnx {Function File} {} 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 $$ ## @end tex @@ -35,6 +38,8 @@ ## If @var{x} is a matrix, compute the mean for each column and return them ## in a row vector. ## +## If the optional argument @var{dim} is given, operate along this dimension. +## ## The optional argument @var{opt} selects the type of mean to compute. ## The following options are recognized: ## @@ -49,10 +54,8 @@ ## Compute the harmonic mean. ## @end table ## -## If the optional argument @var{dim} is given, operate along this dimension. -## -## Both @var{dim} and @var{opt} are optional. If both are supplied, -## either may appear first. +## Both @var{dim} and @var{opt} are optional. If both are supplied, either +## may appear first. ## @seealso{median, mode} ## @end deftypefn
--- a/scripts/statistics/base/meansq.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/base/meansq.m Sun May 10 16:07:41 2015 -0700 @@ -21,6 +21,8 @@ ## @deftypefn {Function File} {} meansq (@var{x}) ## @deftypefnx {Function File} {} meansq (@var{x}, @var{dim}) ## Compute the mean square of the elements of the vector @var{x}. +## +## The mean square is defined as ## @tex ## $$ ## {\rm meansq} (x) = {\sum_{i=1}^N {x_i}^2 \over N}
--- a/scripts/statistics/base/median.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/base/median.m Sun May 10 16:07:41 2015 -0700 @@ -21,8 +21,8 @@ ## @deftypefn {Function File} {} median (@var{x}) ## @deftypefnx {Function File} {} median (@var{x}, @var{dim}) ## Compute the median value of the elements of the vector @var{x}. -## If the elements of @var{x} are sorted, the median is defined -## as +## +## When the elements of @var{x} are sorted, the median is defined as ## @tex ## $$ ## {\rm median} (x) = @@ -41,9 +41,10 @@ ## @end example ## ## @end ifnottex -## 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. +## 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
--- a/scripts/statistics/base/mode.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/base/mode.m Sun May 10 16:07:41 2015 -0700 @@ -21,6 +21,7 @@ ## @deftypefnx {Function File} {} mode (@var{x}, @var{dim}) ## @deftypefnx {Function File} {[@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. @@ -28,8 +29,10 @@ ## 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 -## in the dataset. The cell array @var{c} contains all of the elements -## with the maximum frequency. +## the dataset. +## +## The cell array @var{c} contains all of the elements with the maximum +## frequency. ## @seealso{mean, median} ## @end deftypefn
--- a/scripts/statistics/base/moment.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/base/moment.m Sun May 10 16:07:41 2015 -0700 @@ -42,6 +42,8 @@ ## 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: ## @@ -104,8 +106,6 @@ ## @end ifnottex ## @end table ## -## If the optional argument @var{dim} is given, operate along this dimension. -## ## If both @var{type} and @var{dim} are given they may appear in any order. ## @seealso{var, skewness, kurtosis} ## @end deftypefn
--- a/scripts/statistics/base/ols.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/base/ols.m Sun May 10 16:07:41 2015 -0700 @@ -18,7 +18,9 @@ ## -*- texinfo -*- ## @deftypefn {Function File} {[@var{beta}, @var{sigma}, @var{r}] =} ols (@var{y}, @var{x}) -## Ordinary least squares estimation for the multivariate model +## Ordinary least squares estimation. +## +## OLS applies to the multivariate model ## @tex ## $y = x b + e$ ## with @@ -34,13 +36,12 @@ ## $b$ is a $k \times p$ matrix, and $e$ is a $t \times p$ matrix. ## @end tex ## @ifnottex -## @math{y} is a @math{t} by @math{p} matrix, @math{x} is a @math{t} by -## @math{k} matrix, @math{b} is a @math{k} by @math{p} matrix, and -## @math{e} is a @math{t} by @math{p} matrix. +## @math{y} is a @math{t} by @math{p} matrix, @math{x} is a @math{t} by @math{k} +## matrix, @math{b} is a @math{k} by @math{p} matrix, and @math{e} is a +## @math{t} by @math{p} matrix. ## @end ifnottex ## -## Each row of @var{y} and @var{x} is an observation and each column a -## variable. +## Each row of @var{y} and @var{x} is an observation and each column a variable. ## ## The return values @var{beta}, @var{sigma}, and @var{r} are defined as ## follows.
--- a/scripts/statistics/base/ppplot.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/base/ppplot.m Sun May 10 16:07:41 2015 -0700 @@ -21,26 +21,29 @@ ## 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. +## @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 +## 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. +## @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 arguments are given, the data are plotted directly. +## If no output is requested then the data are plotted immediately. ## @end deftypefn ## Author: KH <Kurt.Hornik@wu-wien.ac.at>
--- a/scripts/statistics/base/prctile.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/base/prctile.m Sun May 10 16:07:41 2015 -0700 @@ -21,17 +21,19 @@ ## @deftypefnx {Function File} {@var{q} =} prctile (@var{x}, @var{p}) ## @deftypefnx {Function File} {@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. All non-numeric -## values (NaNs) of @var{x} are ignored. +## 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{y} contains the +## 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{y} 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 -## the first non-singleton dimension. +## +## 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
--- a/scripts/statistics/base/probit.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/base/probit.m Sun May 10 16:07:41 2015 -0700 @@ -18,8 +18,9 @@ ## -*- texinfo -*- ## @deftypefn {Function File} {} probit (@var{p}) -## For each component of @var{p}, return the probit (the quantile of the -## standard normal distribution) of @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
--- a/scripts/statistics/base/range.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/base/range.m Sun May 10 16:07:41 2015 -0700 @@ -21,9 +21,11 @@ ## @deftypefn {Function File} {} range (@var{x}) ## @deftypefnx {Function File} {} 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}. +## 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. ##
--- a/scripts/statistics/base/ranks.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/base/ranks.m Sun May 10 16:07:41 2015 -0700 @@ -19,8 +19,9 @@ ## -*- texinfo -*- ## @deftypefn {Function File} {} 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. +## adjusted for ties. +## +## If the optional argument @var{dim} is given, operate along this dimension. ## @seealso{spearman, kendall} ## @end deftypefn
--- a/scripts/statistics/base/run_count.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/base/run_count.m Sun May 10 16:07:41 2015 -0700 @@ -19,12 +19,12 @@ ## -*- texinfo -*- ## @deftypefn {Function File} {} run_count (@var{x}, @var{n}) ## @deftypefnx {Function File} {} 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}. +## 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. +## 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>
--- a/scripts/statistics/base/runlength.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/base/runlength.m Sun May 10 16:07:41 2015 -0700 @@ -17,9 +17,14 @@ ## <http://www.gnu.org/licenses/>. ## -*- texinfo -*- -## @deftypefn {Function File} {[count, value] =} runlength (@var{x}) -## Find the lengths of all sequences of common values. Return the -## vector of lengths and the value that was repeated. +## @deftypefn {Function File} {count =} runlength (@var{x}) +## @deftypefnx {Function File} {[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 @@ -27,6 +32,7 @@ ## @result{} [2, 1, 3, 1, 4] ## @end group ## @end example +## @seealso{run_count} ## @end deftypefn function [count, value] = runlength (x)
--- a/scripts/statistics/base/skewness.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/base/skewness.m Sun May 10 16:07:41 2015 -0700 @@ -21,7 +21,9 @@ ## @deftypefn {Function File} {} skewness (@var{x}) ## @deftypefnx {Function File} {} skewness (@var{x}, @var{flag}) ## @deftypefnx {Function File} {} skewness (@var{x}, @var{flag}, @var{dim}) -## Compute the sample skewness of the elements of @var{x}: +## Compute the sample skewness of the elements of @var{x}. +## +## The sample skewness is defined as ## @tex ## $$ ## {\rm skewness} (@var{x}) = {{{1\over N}\,
--- a/scripts/statistics/base/spearman.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/base/spearman.m Sun May 10 16:07:41 2015 -0700 @@ -25,12 +25,12 @@ ## For two data vectors @var{x} and @var{y}, Spearman's @var{rho} is the ## correlation coefficient of the ranks of @var{x} and @var{y}. ## -## If @var{x} and @var{y} are drawn from independent distributions, -## @var{rho} has zero mean and variance @code{1 / (n - 1)}, and is -## asymptotically normally distributed. +## If @var{x} and @var{y} are drawn from independent distributions, @var{rho} +## has zero mean and variance @code{1 / (n - 1)}, and is asymptotically +## normally distributed. ## -## @code{spearman (@var{x})} is equivalent to @code{spearman (@var{x}, -## @var{x})}. +## @code{spearman (@var{x})} is equivalent to +## @code{spearman (@var{x}, @var{x})}. ## @seealso{ranks, kendall} ## @end deftypefn
--- a/scripts/statistics/base/statistics.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/base/statistics.m Sun May 10 16:07:41 2015 -0700 @@ -23,8 +23,9 @@ ## 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 @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
--- a/scripts/statistics/base/std.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/base/std.m Sun May 10 16:07:41 2015 -0700 @@ -21,6 +21,8 @@ ## @deftypefnx {Function File} {} std (@var{x}, @var{opt}) ## @deftypefnx {Function File} {} 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 ## $$ ## {\rm std} (x) = \sigma = \sqrt{{\sum_{i=1}^N (x_i - \bar{x})^2 \over N - 1}} @@ -39,8 +41,8 @@ ## where @math{N} is the number of elements. ## @end ifnottex ## -## If @var{x} is a matrix, compute the standard deviation for -## each column and return them in a row vector. +## If @var{x} is a matrix, compute the standard deviation for each column and +## return them in a row vector. ## ## The argument @var{opt} determines the type of normalization to use. ## Valid values are
--- a/scripts/statistics/base/table.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/base/table.m Sun May 10 16:07:41 2015 -0700 @@ -19,8 +19,9 @@ ## -*- texinfo -*- ## @deftypefn {Function File} {[@var{t}, @var{l_x}] =} table (@var{x}) ## @deftypefnx {Function File} {[@var{t}, @var{l_x}, @var{l_y}] =} table (@var{x}, @var{y}) -## Create a contingency table @var{t} from data vectors. The @var{l_x} and -## @var{l_y} vectors are the corresponding levels. +## Create a contingency table @var{t} from data vectors. +## +## The @var{l_x} and @var{l_y} vectors are the corresponding levels. ## ## Currently, only 1- and 2-dimensional tables are supported. ## @end deftypefn
--- a/scripts/statistics/base/var.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/base/var.m Sun May 10 16:07:41 2015 -0700 @@ -21,6 +21,8 @@ ## @deftypefnx {Function File} {} var (@var{x}, @var{opt}) ## @deftypefnx {Function File} {} var (@var{x}, @var{opt}, @var{dim}) ## Compute the variance of the elements of the vector @var{x}. +## +## The variance is defined as ## @tex ## $$ ## {\rm var} (x) = \sigma^2 = {\sum_{i=1}^N (x_i - \bar{x})^2 \over N - 1} @@ -36,8 +38,8 @@ ## @end example ## ## @end ifnottex -## If @var{x} is a matrix, compute the variance for each column -## and return them in a row vector. +## 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 @@ -51,8 +53,8 @@ ## normalizes with @math{N}, this provides the second moment around the mean ## @end table ## -## If @math{N==1} the value of @var{opt} is ignored and normalization -## by @math{N} is used. +## If @math{N==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}
--- a/scripts/statistics/base/zscore.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/base/zscore.m Sun May 10 16:07:41 2015 -0700 @@ -17,21 +17,25 @@ ## <http://www.gnu.org/licenses/>. ## -*- texinfo -*- -## @deftypefn {Function File} {[@var{z}, @var{mu}, @var{sigma}] =} zscore (@var{x}) -## @deftypefnx {Function File} {[@var{z}, @var{mu}, @var{sigma}] =} zscore (@var{x}, @var{opt}) -## @deftypefnx {Function File} {[@var{z}, @var{mu}, @var{sigma}] =} zscore (@var{x}, @var{opt}, @var{dim}) +## @deftypefn {Function File} {@var{z} =} zscore (@var{x}) +## @deftypefnx {Function File} {@var{z} =} zscore (@var{x}, @var{opt}) +## @deftypefnx {Function File} {@var{z} =} zscore (@var{x}, @var{opt}, @var{dim}) +## @deftypefnx {Function File} {[@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 is the same as the +## +## 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, do the above along the first non-singleton -## dimension. If the third optional argument @var{dim} is given, operate -## along this dimension. +## 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 mean and standard deviation along @var{dim} are given in @var{mu} -## and @var{sigma} respectively. +## The optional outputs @var{mu} and @var{sigma} contain the mean and standard +## deviation. ## ## @seealso{mean, std, center} ## @end deftypefn
--- a/scripts/statistics/distributions/betainv.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/distributions/betainv.m Sun May 10 16:07:41 2015 -0700 @@ -19,9 +19,8 @@ ## -*- texinfo -*- ## @deftypefn {Function File} {} 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}. +## 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>
--- a/scripts/statistics/distributions/binoinv.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/distributions/binoinv.m Sun May 10 16:07:41 2015 -0700 @@ -19,8 +19,8 @@ ## -*- texinfo -*- ## @deftypefn {Function File} {} 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 +## 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
--- a/scripts/statistics/distributions/binopdf.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/distributions/binopdf.m Sun May 10 16:07:41 2015 -0700 @@ -19,10 +19,10 @@ ## -*- texinfo -*- ## @deftypefn {Function File} {} 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. +## 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>
--- a/scripts/statistics/distributions/cauchy_cdf.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/distributions/cauchy_cdf.m Sun May 10 16:07:41 2015 -0700 @@ -20,10 +20,11 @@ ## -*- texinfo -*- ## @deftypefn {Function File} {} cauchy_cdf (@var{x}) ## @deftypefnx {Function File} {} 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. +## 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>
--- a/scripts/statistics/distributions/cauchy_inv.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/distributions/cauchy_inv.m Sun May 10 16:07:41 2015 -0700 @@ -20,10 +20,11 @@ ## -*- texinfo -*- ## @deftypefn {Function File} {} cauchy_inv (@var{x}) ## @deftypefnx {Function File} {} 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. +## 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>
--- a/scripts/statistics/distributions/cauchy_pdf.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/distributions/cauchy_pdf.m Sun May 10 16:07:41 2015 -0700 @@ -20,10 +20,11 @@ ## -*- texinfo -*- ## @deftypefn {Function File} {} cauchy_pdf (@var{x}) ## @deftypefnx {Function File} {} 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. +## 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>
--- a/scripts/statistics/distributions/chi2cdf.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/distributions/chi2cdf.m Sun May 10 16:07:41 2015 -0700 @@ -19,9 +19,9 @@ ## -*- texinfo -*- ## @deftypefn {Function File} {} 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. +## 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>
--- a/scripts/statistics/distributions/chi2inv.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/distributions/chi2inv.m Sun May 10 16:07:41 2015 -0700 @@ -19,9 +19,8 @@ ## -*- texinfo -*- ## @deftypefn {Function File} {} 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. +## 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>
--- a/scripts/statistics/distributions/chi2pdf.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/distributions/chi2pdf.m Sun May 10 16:07:41 2015 -0700 @@ -19,9 +19,8 @@ ## -*- texinfo -*- ## @deftypefn {Function File} {} 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. +## 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>
--- a/scripts/statistics/distributions/discrete_cdf.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/distributions/discrete_cdf.m Sun May 10 16:07:41 2015 -0700 @@ -19,9 +19,9 @@ ## -*- texinfo -*- ## @deftypefn {Function File} {} 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}. +## 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)
--- a/scripts/statistics/distributions/discrete_inv.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/distributions/discrete_inv.m Sun May 10 16:07:41 2015 -0700 @@ -19,9 +19,9 @@ ## -*- texinfo -*- ## @deftypefn {Function File} {} 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}. +## 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>
--- a/scripts/statistics/distributions/discrete_pdf.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/distributions/discrete_pdf.m Sun May 10 16:07:41 2015 -0700 @@ -19,9 +19,9 @@ ## -*- texinfo -*- ## @deftypefn {Function File} {} 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}. +## 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>
--- a/scripts/statistics/distributions/empirical_cdf.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/distributions/empirical_cdf.m Sun May 10 16:07:41 2015 -0700 @@ -19,8 +19,8 @@ ## -*- texinfo -*- ## @deftypefn {Function File} {} 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 +## 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
--- a/scripts/statistics/distributions/empirical_inv.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/distributions/empirical_inv.m Sun May 10 16:07:41 2015 -0700 @@ -19,8 +19,8 @@ ## -*- texinfo -*- ## @deftypefn {Function File} {} 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 +## 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
--- a/scripts/statistics/distributions/empirical_pdf.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/distributions/empirical_pdf.m Sun May 10 16:07:41 2015 -0700 @@ -19,8 +19,8 @@ ## -*- texinfo -*- ## @deftypefn {Function File} {} 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 +## 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
--- a/scripts/statistics/distributions/expcdf.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/distributions/expcdf.m Sun May 10 16:07:41 2015 -0700 @@ -19,9 +19,8 @@ ## -*- texinfo -*- ## @deftypefn {Function File} {} 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}. +## 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
--- a/scripts/statistics/distributions/expinv.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/distributions/expinv.m Sun May 10 16:07:41 2015 -0700 @@ -19,8 +19,8 @@ ## -*- texinfo -*- ## @deftypefn {Function File} {} 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}. +## 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>
--- a/scripts/statistics/distributions/exppdf.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/distributions/exppdf.m Sun May 10 16:07:41 2015 -0700 @@ -19,8 +19,8 @@ ## -*- texinfo -*- ## @deftypefn {Function File} {} 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}. +## 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>
--- a/scripts/statistics/distributions/finv.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/distributions/finv.m Sun May 10 16:07:41 2015 -0700 @@ -19,9 +19,8 @@ ## -*- texinfo -*- ## @deftypefn {Function File} {} 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. +## 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>
--- a/scripts/statistics/distributions/fpdf.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/distributions/fpdf.m Sun May 10 16:07:41 2015 -0700 @@ -19,9 +19,8 @@ ## -*- texinfo -*- ## @deftypefn {Function File} {} 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. +## 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>
--- a/scripts/statistics/distributions/gamcdf.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/distributions/gamcdf.m Sun May 10 16:07:41 2015 -0700 @@ -19,9 +19,9 @@ ## -*- texinfo -*- ## @deftypefn {Function File} {} 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}. +## 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>
--- a/scripts/statistics/distributions/gaminv.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/distributions/gaminv.m Sun May 10 16:07:41 2015 -0700 @@ -19,9 +19,9 @@ ## -*- texinfo -*- ## @deftypefn {Function File} {} 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}. +## 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>
--- a/scripts/statistics/distributions/gampdf.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/distributions/gampdf.m Sun May 10 16:07:41 2015 -0700 @@ -20,8 +20,8 @@ ## -*- texinfo -*- ## @deftypefn {Function File} {} 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}. +## (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>
--- a/scripts/statistics/distributions/geoinv.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/distributions/geoinv.m Sun May 10 16:07:41 2015 -0700 @@ -19,8 +19,8 @@ ## -*- texinfo -*- ## @deftypefn {Function File} {} 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}. +## 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}).
--- a/scripts/statistics/distributions/geopdf.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/distributions/geopdf.m Sun May 10 16:07:41 2015 -0700 @@ -19,8 +19,8 @@ ## -*- texinfo -*- ## @deftypefn {Function File} {} 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}. +## 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}).
--- a/scripts/statistics/distributions/hygecdf.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/distributions/hygecdf.m Sun May 10 16:07:41 2015 -0700 @@ -20,11 +20,11 @@ ## -*- texinfo -*- ## @deftypefn {Function File} {} 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. +## 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}.
--- a/scripts/statistics/distributions/hygeinv.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/distributions/hygeinv.m Sun May 10 16:07:41 2015 -0700 @@ -19,12 +19,13 @@ ## -*- texinfo -*- ## @deftypefn {Function File} {} 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. +## 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}.
--- a/scripts/statistics/distributions/hygepdf.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/distributions/hygepdf.m Sun May 10 16:07:41 2015 -0700 @@ -20,10 +20,11 @@ ## -*- texinfo -*- ## @deftypefn {Function File} {} 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. +## 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}.
--- a/scripts/statistics/distributions/kolmogorov_smirnov_cdf.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/distributions/kolmogorov_smirnov_cdf.m Sun May 10 16:07:41 2015 -0700 @@ -20,7 +20,9 @@ ## -*- texinfo -*- ## @deftypefn {Function File} {} kolmogorov_smirnov_cdf (@var{x}, @var{tol}) ## Return the cumulative distribution function (CDF) at @var{x} of the -## Kolmogorov-Smirnov distribution, +## Kolmogorov-Smirnov distribution. +## +## This is defined as ## @tex ## $$ Q(x) = \sum_{k=-\infty}^\infty (-1)^k \exp (-2 k^2 x^2) $$ ## @end tex
--- a/scripts/statistics/distributions/laplace_cdf.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/distributions/laplace_cdf.m Sun May 10 16:07:41 2015 -0700 @@ -19,8 +19,8 @@ ## -*- texinfo -*- ## @deftypefn {Function File} {} laplace_cdf (@var{x}) -## For each element of @var{x}, compute the cumulative distribution -## function (CDF) at @var{x} of the Laplace distribution. +## 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>
--- a/scripts/statistics/distributions/laplace_inv.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/distributions/laplace_inv.m Sun May 10 16:07:41 2015 -0700 @@ -19,8 +19,8 @@ ## -*- texinfo -*- ## @deftypefn {Function File} {} 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. +## 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>
--- a/scripts/statistics/distributions/laplace_pdf.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/distributions/laplace_pdf.m Sun May 10 16:07:41 2015 -0700 @@ -19,8 +19,8 @@ ## -*- texinfo -*- ## @deftypefn {Function File} {} laplace_pdf (@var{x}) -## For each element of @var{x}, compute the probability density function -## (PDF) at @var{x} of the Laplace distribution. +## 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>
--- a/scripts/statistics/distributions/logistic_inv.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/distributions/logistic_inv.m Sun May 10 16:07:41 2015 -0700 @@ -19,8 +19,8 @@ ## -*- texinfo -*- ## @deftypefn {Function File} {} 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. +## 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>
--- a/scripts/statistics/distributions/logncdf.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/distributions/logncdf.m Sun May 10 16:07:41 2015 -0700 @@ -22,9 +22,10 @@ ## @deftypefnx {Function File} {} 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}. +## @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
--- a/scripts/statistics/distributions/logninv.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/distributions/logninv.m Sun May 10 16:07:41 2015 -0700 @@ -20,11 +20,12 @@ ## -*- texinfo -*- ## @deftypefn {Function File} {} logninv (@var{x}) ## @deftypefnx {Function File} {} 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}. +## 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
--- a/scripts/statistics/distributions/lognpdf.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/distributions/lognpdf.m Sun May 10 16:07:41 2015 -0700 @@ -20,11 +20,12 @@ ## -*- texinfo -*- ## @deftypefn {Function File} {} lognpdf (@var{x}) ## @deftypefnx {Function File} {} 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}. +## 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
--- a/scripts/statistics/distributions/nbincdf.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/distributions/nbincdf.m Sun May 10 16:07:41 2015 -0700 @@ -20,15 +20,14 @@ ## -*- texinfo -*- ## @deftypefn {Function File} {} 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}. +## (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. +## 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. +## 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>
--- a/scripts/statistics/distributions/nbininv.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/distributions/nbininv.m Sun May 10 16:07:41 2015 -0700 @@ -19,16 +19,15 @@ ## -*- texinfo -*- ## @deftypefn {Function File} {} 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}. +## 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. +## 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. +## 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>
--- a/scripts/statistics/distributions/nbinpdf.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/distributions/nbinpdf.m Sun May 10 16:07:41 2015 -0700 @@ -19,16 +19,15 @@ ## -*- texinfo -*- ## @deftypefn {Function File} {} 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}. +## 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. +## 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. +## 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>
--- a/scripts/statistics/distributions/nbinrnd.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/distributions/nbinrnd.m Sun May 10 16:07:41 2015 -0700 @@ -22,8 +22,8 @@ ## @deftypefnx {Function File} {} nbinrnd (@var{n}, @var{p}, @var{r}) ## @deftypefnx {Function File} {} nbinrnd (@var{n}, @var{p}, @var{r}, @var{c}, @dots{}) ## @deftypefnx {Function File} {} 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}. +## 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
--- a/scripts/statistics/distributions/normcdf.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/distributions/normcdf.m Sun May 10 16:07:41 2015 -0700 @@ -20,9 +20,9 @@ ## -*- texinfo -*- ## @deftypefn {Function File} {} normcdf (@var{x}) ## @deftypefnx {Function File} {} 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}. +## 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
--- a/scripts/statistics/distributions/norminv.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/distributions/norminv.m Sun May 10 16:07:41 2015 -0700 @@ -20,8 +20,8 @@ ## -*- texinfo -*- ## @deftypefn {Function File} {} norminv (@var{x}) ## @deftypefnx {Function File} {} 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 +## 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.
--- a/scripts/statistics/distributions/normpdf.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/distributions/normpdf.m Sun May 10 16:07:41 2015 -0700 @@ -20,8 +20,8 @@ ## -*- texinfo -*- ## @deftypefn {Function File} {} normpdf (@var{x}) ## @deftypefnx {Function File} {} 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 +## 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.
--- a/scripts/statistics/distributions/poisscdf.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/distributions/poisscdf.m Sun May 10 16:07:41 2015 -0700 @@ -19,9 +19,8 @@ ## -*- texinfo -*- ## @deftypefn {Function File} {} 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 -## 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>
--- a/scripts/statistics/distributions/poissinv.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/distributions/poissinv.m Sun May 10 16:07:41 2015 -0700 @@ -19,9 +19,8 @@ ## -*- texinfo -*- ## @deftypefn {Function File} {} 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}. +## 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: KH <Kurt.Hornik@wu-wien.ac.at>
--- a/scripts/statistics/distributions/poisspdf.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/distributions/poisspdf.m Sun May 10 16:07:41 2015 -0700 @@ -19,8 +19,8 @@ ## -*- texinfo -*- ## @deftypefn {Function File} {} 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}. +## 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>
--- a/scripts/statistics/distributions/stdnormal_cdf.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/distributions/stdnormal_cdf.m Sun May 10 16:07:41 2015 -0700 @@ -19,8 +19,8 @@ ## -*- texinfo -*- ## @deftypefn {Function File} {} stdnormal_cdf (@var{x}) -## For each element of @var{x}, compute the cumulative distribution -## function (CDF) at @var{x} of the standard normal distribution +## 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
--- a/scripts/statistics/distributions/stdnormal_pdf.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/distributions/stdnormal_pdf.m Sun May 10 16:07:41 2015 -0700 @@ -19,9 +19,9 @@ ## -*- texinfo -*- ## @deftypefn {Function File} {} 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). +## 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>
--- a/scripts/statistics/distributions/tcdf.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/distributions/tcdf.m Sun May 10 16:07:41 2015 -0700 @@ -20,9 +20,9 @@ ## -*- texinfo -*- ## @deftypefn {Function File} {} 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, i.e., PROB (t(@var{n}) @leq{} @var{x}). +## 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>
--- a/scripts/statistics/distributions/tinv.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/distributions/tinv.m Sun May 10 16:07:41 2015 -0700 @@ -19,10 +19,12 @@ ## -*- texinfo -*- ## @deftypefn {Function File} {} 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. +## 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,
--- a/scripts/statistics/distributions/tpdf.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/distributions/tpdf.m Sun May 10 16:07:41 2015 -0700 @@ -19,9 +19,9 @@ ## -*- texinfo -*- ## @deftypefn {Function File} {} 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. +## 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>
--- a/scripts/statistics/distributions/unidcdf.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/distributions/unidcdf.m Sun May 10 16:07:41 2015 -0700 @@ -19,8 +19,8 @@ ## -*- texinfo -*- ## @deftypefn {Function File} {} 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 +## 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
--- a/scripts/statistics/distributions/unidinv.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/distributions/unidinv.m Sun May 10 16:07:41 2015 -0700 @@ -19,8 +19,8 @@ ## -*- texinfo -*- ## @deftypefn {Function File} {} 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 +## 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
--- a/scripts/statistics/distributions/unidpdf.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/distributions/unidpdf.m Sun May 10 16:07:41 2015 -0700 @@ -19,13 +19,13 @@ ## -*- texinfo -*- ## @deftypefn {Function File} {} 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 +## 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} @leq{} @code{bitmax} -## (@w{@math{2^{53} - 1}} on IEEE-754 compatible systems). +## Warning: The underlying implementation uses the double class and will only +## be accurate for @var{n} @leq{} @code{bitmax} (@w{@math{2^{53} - 1}} on +## IEEE-754 compatible systems). ## @end deftypefn function pdf = unidpdf (x, n)
--- a/scripts/statistics/distributions/unidrnd.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/distributions/unidrnd.m Sun May 10 16:07:41 2015 -0700 @@ -24,6 +24,7 @@ ## @deftypefnx {Function File} {} 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
--- a/scripts/statistics/distributions/unifcdf.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/distributions/unifcdf.m Sun May 10 16:07:41 2015 -0700 @@ -20,8 +20,8 @@ ## -*- texinfo -*- ## @deftypefn {Function File} {} unifcdf (@var{x}) ## @deftypefnx {Function File} {} 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 +## 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.
--- a/scripts/statistics/distributions/unifinv.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/distributions/unifinv.m Sun May 10 16:07:41 2015 -0700 @@ -20,9 +20,8 @@ ## -*- texinfo -*- ## @deftypefn {Function File} {} unifinv (@var{x}) ## @deftypefnx {Function File} {} 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}]. +## 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
--- a/scripts/statistics/distributions/wblcdf.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/distributions/wblcdf.m Sun May 10 16:07:41 2015 -0700 @@ -23,7 +23,9 @@ ## @deftypefnx {Function File} {} 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}, which is +## parameter @var{shape}. +## +## This is defined as ## @tex ## $$ 1 - e^{-({x \over scale})^{shape}} $$ ## for $x \geq 0$.
--- a/scripts/statistics/distributions/wblinv.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/distributions/wblinv.m Sun May 10 16:07:41 2015 -0700 @@ -22,8 +22,8 @@ ## @deftypefnx {Function File} {} wblinv (@var{x}, @var{scale}) ## @deftypefnx {Function File} {} 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}. +## Weibull distribution with scale parameter @var{scale} and +## shape parameter @var{shape}. ## ## Default values are @var{scale} = 1, @var{shape} = 1. ## @end deftypefn
--- a/scripts/statistics/distributions/wblpdf.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/distributions/wblpdf.m Sun May 10 16:07:41 2015 -0700 @@ -22,8 +22,10 @@ ## @deftypefnx {Function File} {} wblpdf (@var{x}, @var{scale}) ## @deftypefnx {Function File} {} 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} which is given by +## 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
--- a/scripts/statistics/distributions/wienrnd.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/distributions/wienrnd.m Sun May 10 16:07:41 2015 -0700 @@ -19,11 +19,13 @@ ## -*- texinfo -*- ## @deftypefn {Function File} {} 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. +## on the interval [0, @var{t}]. ## -## The optional parameter @var{n} gives the number of summands used for +## 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
--- a/scripts/statistics/models/private/logistic_regression_derivatives.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/models/private/logistic_regression_derivatives.m Sun May 10 16:07:41 2015 -0700 @@ -20,6 +20,7 @@ ## @deftypefn {Function File} {[@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
--- a/scripts/statistics/models/private/logistic_regression_likelihood.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/models/private/logistic_regression_likelihood.m Sun May 10 16:07:41 2015 -0700 @@ -19,6 +19,7 @@ ## -*- texinfo -*- ## @deftypefn {Function File} {[@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
--- a/scripts/statistics/tests/anova.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/tests/anova.m Sun May 10 16:07:41 2015 -0700 @@ -18,27 +18,28 @@ ## -*- texinfo -*- ## @deftypefn {Function File} {[@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. +## 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. +## 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. +## 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}. +## 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. +## 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>
--- a/scripts/statistics/tests/chisquare_test_homogeneity.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/tests/chisquare_test_homogeneity.m Sun May 10 16:07:41 2015 -0700 @@ -24,8 +24,8 @@ ## (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. +## 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}.
--- a/scripts/statistics/tests/chisquare_test_independence.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/tests/chisquare_test_independence.m Sun May 10 16:07:41 2015 -0700 @@ -18,13 +18,14 @@ ## -*- texinfo -*- ## @deftypefn {Function File} {[@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. +## Perform a chi-square test for independence based on the contingency table +## @var{x}. ## -## The p-value (1 minus the CDF of this distribution at chisq) of the -## test is returned in @var{pval}. +## 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
--- a/scripts/statistics/tests/cor_test.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/tests/cor_test.m Sun May 10 16:07:41 2015 -0700 @@ -22,19 +22,19 @@ ## 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. +## 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 optional argument string @var{method} specifies which correlation +## coefficient to use for testing. If @var{method} is @qcode{"pearson"} +## (default), the (usual) Pearson's produt 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: ##
--- a/scripts/statistics/tests/f_test_regression.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/tests/f_test_regression.m Sun May 10 16:07:41 2015 -0700 @@ -21,11 +21,11 @@ ## 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. +## 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}. +## 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. ##
--- a/scripts/statistics/tests/hotelling_test.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/tests/hotelling_test.m Sun May 10 16:07:41 2015 -0700 @@ -19,8 +19,8 @@ ## -*- texinfo -*- ## @deftypefn {Function File} {[@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}}. +## 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
--- a/scripts/statistics/tests/kolmogorov_smirnov_test.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/tests/kolmogorov_smirnov_test.m Sun May 10 16:07:41 2015 -0700 @@ -19,7 +19,8 @@ ## -*- texinfo -*- ## @deftypefn {Function File} {[@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 dist. I.e., +## 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. ## @@ -32,18 +33,18 @@ ## @end example ## ## @noindent -## @var{dist} can be any string for which a function @var{dist_cdf} +## @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. +## 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}. ##
--- a/scripts/statistics/tests/kolmogorov_smirnov_test_2.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/tests/kolmogorov_smirnov_test_2.m Sun May 10 16:07:41 2015 -0700 @@ -18,21 +18,21 @@ ## -*- texinfo -*- ## @deftypefn {Function File} {[@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. I.e., if F and G are the CDFs corresponding to the -## @var{x} and @var{y} samples, respectively, then the null is that F == -## G. +## 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. +## 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}. ##
--- a/scripts/statistics/tests/kruskal_wallis_test.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/tests/kruskal_wallis_test.m Sun May 10 16:07:41 2015 -0700 @@ -20,29 +20,27 @@ ## @deftypefn {Function File} {[@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. +## 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. +## 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}, +## 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). +## 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}. +## 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
--- a/scripts/statistics/tests/manova.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/tests/manova.m Sun May 10 16:07:41 2015 -0700 @@ -18,18 +18,20 @@ ## -*- texinfo -*- ## @deftypefn {Function File} {} 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. +## Perform a one-way multivariate analysis of variance (MANOVA). ## -## 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 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.
--- a/scripts/statistics/tests/mcnemar_test.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/tests/mcnemar_test.m Sun May 10 16:07:41 2015 -0700 @@ -18,12 +18,12 @@ ## -*- texinfo -*- ## @deftypefn {Function File} {[@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. +## 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. +## 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}.
--- a/scripts/statistics/tests/prop_test_2.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/tests/prop_test_2.m Sun May 10 16:07:41 2015 -0700 @@ -18,19 +18,20 @@ ## -*- texinfo -*- ## @deftypefn {Function File} {[@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. +## 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. ## -## 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. +## 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}. ##
--- a/scripts/statistics/tests/run_test.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/tests/run_test.m Sun May 10 16:07:41 2015 -0700 @@ -18,9 +18,11 @@ ## -*- texinfo -*- ## @deftypefn {Function File} {[@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}. Can be used to test whether -## @var{x} contains independent data. +## 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}. ##
--- a/scripts/statistics/tests/sign_test.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/tests/sign_test.m Sun May 10 16:07:41 2015 -0700 @@ -19,20 +19,21 @@ ## -*- texinfo -*- ## @deftypefn {Function File} {[@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. +## 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. +## 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}. ##
--- a/scripts/statistics/tests/t_test.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/tests/t_test.m Sun May 10 16:07:41 2015 -0700 @@ -19,19 +19,19 @@ ## -*- texinfo -*- ## @deftypefn {Function File} {[@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. +## 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. +## 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}. ##
--- a/scripts/statistics/tests/t_test_2.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/tests/t_test_2.m Sun May 10 16:07:41 2015 -0700 @@ -18,20 +18,20 @@ ## -*- texinfo -*- ## @deftypefn {Function File} {[@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. +## 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. +## 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}. ##
--- a/scripts/statistics/tests/t_test_regression.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/tests/t_test_regression.m Sun May 10 16:07:41 2015 -0700 @@ -20,21 +20,20 @@ ## @deftypefn {Function File} {[@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. +## 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. +## 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}. ##
--- a/scripts/statistics/tests/u_test.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/tests/u_test.m Sun May 10 16:07:41 2015 -0700 @@ -19,18 +19,20 @@ ## -*- texinfo -*- ## @deftypefn {Function File} {[@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. +## 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. +## 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}. ##
--- a/scripts/statistics/tests/var_test.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/tests/var_test.m Sun May 10 16:07:41 2015 -0700 @@ -20,18 +20,18 @@ ## @deftypefn {Function File} {[@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. +## 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. +## 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}. ##
--- a/scripts/statistics/tests/welch_test.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/tests/welch_test.m Sun May 10 16:07:41 2015 -0700 @@ -21,16 +21,17 @@ ## 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 +## 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. +## @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}. ##
--- a/scripts/statistics/tests/wilcoxon_test.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/tests/wilcoxon_test.m Sun May 10 16:07:41 2015 -0700 @@ -19,20 +19,22 @@ ## -*- texinfo -*- ## @deftypefn {Function File} {[@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. +## 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 +## 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. +## 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}. ##
--- a/scripts/statistics/tests/z_test.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/tests/z_test.m Sun May 10 16:07:41 2015 -0700 @@ -18,24 +18,26 @@ ## -*- texinfo -*- ## @deftypefn {Function File} {[@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. +## 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}. ## -## 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 +## 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 +## 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. +## 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>
--- a/scripts/statistics/tests/z_test_2.m Sat May 09 22:50:09 2015 -0700 +++ b/scripts/statistics/tests/z_test_2.m Sun May 10 16:07:41 2015 -0700 @@ -18,24 +18,26 @@ ## -*- texinfo -*- ## @deftypefn {Function File} {[@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. +## 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. ## -## 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 +## 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. +## 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. +## 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>