Mercurial > octave
view scripts/statistics/skewness.m @ 27985:9f9ac219896d
maint: Remove remaining "Author:" instances from code base.
* __ftp__.cc, load-save.cc, urlwrite.cc, xnorm.cc, xnorm.h, cconv2.f,
cdotc3.f, cmatm3.f, csconv2.f, dconv2.f, ddot3.f, dmatm3.f, sconv2.f, sdot3.f,
smatm3.f, zconv2.f, zdconv2.f, zdotc3.f, zmatm3.f, crsf2csf.f, zrsf2csf.f,
oct-norm.cc, oct-norm.h, lin2mu.m, mu2lin.m, bincoeff.m, blkdiag.m, deal.m,
gradient.m, interpft.m, nextpow2.m, postpad.m, prepad.m, repmat.m, shift.m,
xor.m, griddata.m, rotx.m, roty.m, rotz.m, voronoin.m, getappdata.m,
isappdata.m, rmappdata.m, setappdata.m, colormap.m, gray.m, gray2ind.m,
im2double.m, image.m, imagesc.m, imread.m, imshow.m, ind2gray.m, ind2rgb.m,
ocean.m, __imread__.m, rgb2ind.m, javachk.m, ClassHelper.java, usejava.m,
findstr.m, commutation_matrix.m, cross.m, gls.m, housh.m, isdefinite.m,
ishermitian.m, issymmetric.m, logm.m, null.m, ols.m, orth.m, qzhess.m, rref.m,
dos.m, nargoutchk.m, orderfields.m, parseparams.m, __w2mpth__.m, unix.m,
untar.m, unzip.m, expand_rel_paths.m, make_rel_paths.m, daspect.m, orient.m,
pbaspect.m, rticks.m, thetaticks.m, xticklabels.m, xticks.m, yticklabels.m,
yticks.m, zticklabels.m, zticks.m, comet.m, contourf.m, plot3.m, cla.m,
copyobj.m, findfigs.m, hdl2struct.m, linkaxes.m, __ghostscript__.m,
__gnuplot_get_var__.m, __gnuplot_has_feature__.m, __gnuplot_has_terminal__.m,
__gnuplot_open_stream__.m, __gnuplot_print__.m, struct2hdl.m, subplot.m,
compan.m, conv.m, deconv.m, mpoles.m, poly.m, polyder.m, polyfit.m, polyint.m,
polyout.m, polyreduce.m, polyval.m, polyvalm.m, residue.m, roots.m, ismember.m,
__parse_movargs__.m, detrend.m, fftconv.m, fftfilt.m, fftshift.m, filter2.m,
movfun.m, movslice.m, ichol.m, pcg.m, beta.m, ellipke.m, lcm.m, nchoosek.m,
pow2.m, primes.m, pascal.m, rosser.m, wilkinson.m, corr.m, kurtosis.m,
skewness.m, base2dec.m, bin2dec.m, blanks.m, deblank.m, dec2base.m, dec2bin.m,
dec2hex.m, hex2dec.m, index.m, rindex.m, strjoin.m, substr.m, untabify.m,
calendar.m, datestr.m, eomday.m, now.m, weekday.m:
Remove remaining "Author:" instances from code base.
author | Rik <rik@octave.org> |
---|---|
date | Tue, 21 Jan 2020 14:35:03 -0800 |
parents | 7f1cec12c240 |
children | 28de41192f3c 0a5b15007766 |
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######################################################################## ## ## Copyright (C) 1996-2020 The Octave Project Developers ## ## See the file COPYRIGHT.md in the top-level directory of this ## distribution or <https://octave.org/copyright/>. ## ## This file is part of Octave. ## ## Octave is free software: you can redistribute it and/or modify it ## under the terms of the GNU General Public License as published by ## the Free Software Foundation, either version 3 of the License, or ## (at your option) any later version. ## ## Octave is distributed in the hope that it will be useful, but ## WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with Octave; see the file COPYING. If not, see ## <https://www.gnu.org/licenses/>. ## ######################################################################## ## -*- texinfo -*- ## @deftypefn {} {} skewness (@var{x}) ## @deftypefnx {} {} skewness (@var{x}, @var{flag}) ## @deftypefnx {} {} skewness (@var{x}, @var{flag}, @var{dim}) ## Compute the sample skewness of the elements of @var{x}. ## ## The sample skewness is defined as ## @tex ## $$ ## {\rm skewness} (@var{x}) = {{{1\over N}\, ## \sum_{i=1}^N (x_i - \bar{x})^3} \over \sigma^3}, ## $$ ## where $N$ is the length of @var{x}, $\bar{x}$ its mean and $\sigma$ ## its (uncorrected) standard deviation. ## @end tex ## @ifnottex ## ## @example ## @group ## mean ((@var{x} - mean (@var{x})).^3) ## skewness (@var{X}) = ------------------------. ## std (@var{x}).^3 ## @end group ## @end example ## ## @end ifnottex ## ## @noindent ## The optional argument @var{flag} controls which normalization is used. ## If @var{flag} is equal to 1 (default value, used when @var{flag} is omitted ## or empty), return the sample skewness as defined above. If @var{flag} is ## equal to 0, return the adjusted skewness coefficient instead: ## @tex ## $$ ## {\rm skewness} (@var{x}) = {\sqrt{N (N - 1)} \over N - 2} \times \, ## {{{1 \over N} \sum_{i=1}^N (x_i - \bar{x})^3} \over \sigma^3} ## $$ ## @end tex ## @ifnottex ## ## @example ## @group ## sqrt (N*(N-1)) mean ((@var{x} - mean (@var{x})).^3) ## skewness (@var{X}, 0) = -------------- * ------------------------. ## (N - 2) std (@var{x}).^3 ## @end group ## @end example ## ## @noindent ## where @math{N} is the length of the @var{x} vector. ## ## @end ifnottex ## The adjusted skewness coefficient is obtained by replacing the sample second ## and third central moments by their bias-corrected versions. ## ## If @var{x} is a matrix, or more generally a multi-dimensional array, return ## the skewness along the first non-singleton dimension. If the optional ## @var{dim} argument is given, operate along this dimension. ## ## @seealso{var, kurtosis, moment} ## @end deftypefn function y = skewness (x, flag, dim) if (nargin < 1) || (nargin > 3) print_usage (); endif if (! (isnumeric (x) || islogical (x))) error ("skewness: X must be a numeric vector or matrix"); endif if (nargin < 2 || isempty (flag)) flag = 1; # default: do not use the "bias corrected" version elseif (! isscalar (flag) || (flag != 0 && flag != 1)) error ("skewness: FLAG must be 0 or 1"); endif nd = ndims (x); sz = size (x); if (nargin < 3) ## Find the first non-singleton dimension. (dim = find (sz > 1, 1)) || (dim = 1); else if (! (isscalar (dim) && dim == fix (dim) && dim > 0)) error ("skewness: DIM must be an integer and a valid dimension"); endif endif n = size (x, dim); sz(dim) = 1; x = center (x, dim); # center also promotes integer, logical to double s = std (x, 1, dim); # Normalize with 1/N y = sum (x .^ 3, dim); idx = (s != 0); y(idx) ./= (n * s(idx) .^ 3); y(! idx) = NaN; ## Apply bias correction to the second and third central sample moment if (flag == 0) if (n > 2) y *= sqrt (n * (n - 1)) / (n - 2); else y(:) = NaN; endif endif endfunction %!assert (skewness ([-1, 0, 1]), 0) %!assert (skewness ([-2, 0, 1]) < 0) %!assert (skewness ([-1, 0, 2]) > 0) %!assert (skewness ([-3, 0, 1]) == -1 * skewness ([-1, 0, 3])) %!assert (skewness (ones (3, 5)), NaN (1, 5)) %!assert (skewness (1, [], 3), NaN) %!test %! x = [0; 0; 0; 1]; %! y = [x, 2*x]; %! assert (skewness (y), 1.154700538379251 * [1 1], 5*eps); %!assert (skewness ([1:5 10; 1:5 10], 0, 2), 1.439590274527954 * [1; 1], eps) %!assert (skewness ([1:5 10; 1:5 10], 1, 2), 1.051328089232020 * [1; 1], 2*eps) %!assert (skewness ([1:5 10; 1:5 10], [], 2), 1.051328089232020 * [1; 1], 2*eps) ## Test behavior on single input %!assert (skewness (single ([1:5 10])), single (1.0513283), eps ("single")) %!assert (skewness (single ([1 2]), 0), single (NaN)) ## Verify no warnings %!test %! lastwarn (""); # clear last warning %! skewness (1); %! assert (lastwarn (), ""); ## Test input validation %!error skewness () %!error skewness (1, 2, 3) %!error <X must be a numeric vector or matrix> skewness (['A'; 'B']) %!error <FLAG must be 0 or 1> skewness (1, 2) %!error <FLAG must be 0 or 1> skewness (1, [1 0]) %!error <DIM must be an integer> skewness (1, [], ones (2,2)) %!error <DIM must be an integer> skewness (1, [], 1.5) %!error <DIM must be .* a valid dimension> skewness (1, [], 0)