Mercurial > octave
view scripts/statistics/base/kurtosis.m @ 20174: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.
author | Rik <rik@octave.org> |
---|---|
date | Sun, 10 May 2015 16:07:41 -0700 |
parents | 9fc020886ae9 |
children | 76f67400649e |
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## Copyright (C) 2013-2015 Julien Bect ## Copyright (C) 1996-2015 John W. Eaton ## ## This file is part of Octave. ## ## Octave is free software; you can redistribute it and/or modify it ## under the terms of the GNU General Public License as published by ## the Free Software Foundation; either version 3 of the License, or (at ## your option) any later version. ## ## Octave is distributed in the hope that it will be useful, but ## WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with Octave; see the file COPYING. If not, see ## <http://www.gnu.org/licenses/>. ## -*- texinfo -*- ## @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}. ## ## The sample kurtosis is defined as ## @tex ## $$ ## \kappa_1 = {{{1\over N}\, ## \sum_{i=1}^N (@var{x}_i - \bar{@var{x}})^4} \over \sigma^4}, ## $$ ## where $N$ is the length of @var{x}, $\bar{@var{x}}$ its mean, and $\sigma$ ## its (uncorrected) standard deviation. ## @end tex ## @ifnottex ## ## @example ## @group ## mean ((@var{x} - mean (@var{x})).^4) ## k1 = ------------------------ ## std (@var{x}).^4 ## @end group ## @end example ## ## @end ifnottex ## ## @noindent ## The optional argument @var{flag} controls which normalization is used. ## If @var{flag} is equal to 1 (default value, used when @var{flag} is omitted ## or empty), return the sample kurtosis as defined above. If @var{flag} is ## equal to 0, return the @w{"bias-corrected"} kurtosis coefficient instead: ## @tex ## $$ ## \kappa_0 = 3 + {\scriptstyle N - 1 \over \scriptstyle (N - 2)(N - 3)} \, ## \left( (N + 1)\, \kappa_1 - 3 (N - 1) \right) ## $$ ## @end tex ## @ifnottex ## ## @example ## @group ## N - 1 ## k0 = 3 + -------------- * ((N + 1) * k1 - 3 * (N - 1)) ## (N - 2)(N - 3) ## @end group ## @end example ## ## @end ifnottex ## The bias-corrected kurtosis coefficient is obtained by replacing the sample ## second and fourth central moments by their unbiased versions. It is an ## unbiased estimate of the population kurtosis for normal populations. ## ## If @var{x} is a matrix, or more generally a multi-dimensional array, return ## the kurtosis along the first non-singleton dimension. If the optional ## @var{dim} argument is given, operate along this dimension. ## ## @seealso{var, skewness, moment} ## @end deftypefn ## Author: KH <Kurt.Hornik@wu-wien.ac.at> ## Created: 29 July 1994 ## Adapted-By: jwe function y = kurtosis (x, flag, dim) if (nargin < 1) || (nargin > 3) print_usage (); endif if (! (isnumeric (x) || islogical (x))) error ("kurtosis: X must be a numeric vector or matrix"); endif if (nargin < 2 || isempty (flag)) flag = 1; # default: do not use the "bias corrected" version else if (! isscalar (flag) || (flag != 0 && flag != 1)) error ("kurtosis: FLAG must be 0 or 1"); endif endif nd = ndims (x); sz = size (x); if (nargin < 3) ## Find the first non-singleton dimension. (dim = find (sz > 1, 1)) || (dim = 1); else if (! (isscalar (dim) && dim == fix (dim)) || ! (1 <= dim && dim <= nd)) error ("kurtosis: DIM must be an integer and a valid dimension"); endif endif n = sz(dim); sz(dim) = 1; x = center (x, dim); # center also promotes integer, logical to double v = var (x, 1, dim); # normalize with 1/N y = sum (x .^ 4, dim); idx = (v != 0); y(idx) = y(idx) ./ (n * v(idx) .^ 2); y(! idx) = NaN; ## Apply bias correction to the second and fourth central sample moment if (flag == 0) if (n > 3) C = (n - 1) / ((n - 2) * (n - 3)); y = 3 + C * ((n + 1) * y - 3 * (n - 1)); else y(:) = NaN; endif endif endfunction %!test %! x = [-1; 0; 0; 0; 1]; %! y = [x, 2*x]; %! assert (kurtosis (y), [2.5, 2.5], sqrt (eps)); %!assert (kurtosis ([-3, 0, 1]) == kurtosis ([-1, 0, 3])) %!assert (kurtosis (ones (3, 5)), NaN (1, 5)) %!assert (kurtosis ([1:5 10; 1:5 10], 0, 2), 5.4377317925288901 * [1; 1], 8 * eps) %!assert (kurtosis ([1:5 10; 1:5 10], 1, 2), 2.9786509002956195 * [1; 1], 8 * eps) %!assert (kurtosis ([1:5 10; 1:5 10], [], 2), 2.9786509002956195 * [1; 1], 8 * eps) ## Test behaviour on single input %!assert (kurtosis (single ([1:5 10])), single (2.9786513), eps ("single")) %!assert (kurtosis (single ([1 2]), 0), single (NaN)) ## Verify no "divide-by-zero" warnings %!test %! wstate = warning ("query", "Octave:divide-by-zero"); %! warning ("on", "Octave:divide-by-zero"); %! unwind_protect %! lastwarn (""); # clear last warning %! kurtosis (1); %! assert (lastwarn (), ""); %! unwind_protect_cleanup %! warning (wstate, "Octave:divide-by-zero"); %! end_unwind_protect ## Test input validation %!error kurtosis () %!error kurtosis (1, 2, 3) %!error <X must be a numeric vector or matrix> kurtosis (['A'; 'B']) %!error <FLAG must be 0 or 1> kurtosis (1, 2) %!error <FLAG must be 0 or 1> kurtosis (1, [1 0]) %!error <DIM must be an integer> kurtosis (1, [], ones (2,2)) %!error <DIM must be an integer> kurtosis (1, [], 1.5) %!error <DIM must be .* a valid dimension> kurtosis (1, [], 0) %!error <DIM must be .* a valid dimension> kurtosis (1, [], 3)