X-Git-Url: https://git.creatis.insa-lyon.fr/pubgit/?p=CreaPhase.git;a=blobdiff_plain;f=octave_packages%2Fm%2Fstatistics%2Fbase%2Fskewness.m;fp=octave_packages%2Fm%2Fstatistics%2Fbase%2Fskewness.m;h=d2905d294d876eb87041a40d9775c4191e545137;hp=0000000000000000000000000000000000000000;hb=1c0469ada9531828709108a4882a751d2816994a;hpb=63de9f36673d49121015e3695f2c336ea92bc278 diff --git a/octave_packages/m/statistics/base/skewness.m b/octave_packages/m/statistics/base/skewness.m new file mode 100644 index 0000000..d2905d2 --- /dev/null +++ b/octave_packages/m/statistics/base/skewness.m @@ -0,0 +1,100 @@ +## Copyright (C) 1996-2012 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 +## . + +## -*- texinfo -*- +## @deftypefn {Function File} {} skewness (@var{x}) +## @deftypefnx {Function File} {} skewness (@var{x}, @var{dim}) +## Compute the skewness of the elements of the vector @var{x}. +## @tex +## $$ +## {\rm skewness} (x) = {1\over N \sigma^3} \sum_{i=1}^N (x_i-\bar{x})^3 +## $$ +## where $\bar{x}$ is the mean value of $x$. +## @end tex +## @ifnottex +## +## @example +## skewness (x) = 1/N std(x)^(-3) sum ((x - mean(x)).^3) +## @end example +## +## @end ifnottex +## +## @noindent +## If @var{x} is a matrix, return the skewness along the +## first non-singleton dimension of the matrix. If the optional +## @var{dim} argument is given, operate along this dimension. +## @seealso{var, kurtosis, moment} +## @end deftypefn + +## Author: KH +## Created: 29 July 1994 +## Adapted-By: jwe + +function retval = skewness (x, dim) + + if (nargin != 1 && nargin != 2) + print_usage (); + endif + + if (! (isnumeric (x) || islogical (x))) + error ("skewness: X must be a numeric vector or matrix"); + endif + + nd = ndims (x); + sz = size (x); + if (nargin != 2) + ## Find the first non-singleton dimension. + (dim = find (sz > 1, 1)) || (dim = 1); + else + if (!(isscalar (dim) && dim == fix (dim)) + || !(1 <= dim && dim <= nd)) + error ("skewness: 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 to double for next line + retval = zeros (sz, class (x)); + s = std (x, [], dim); + idx = find (s > 0); + x = sum (x .^ 3, dim); + retval(idx) = x(idx) ./ (n * s(idx) .^ 3); + +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])); +%!test +%! x = [0; 0; 0; 1]; +%! y = [x, 2*x]; +%! assert(all (abs (skewness (y) - [0.75, 0.75]) < sqrt (eps))); + +%!assert (skewness (single(1)), single(0)); + +%% Test input validation +%!error skewness () +%!error skewness (1, 2, 3) +%!error skewness (['A'; 'B']) +%!error skewness (1, ones(2,2)) +%!error skewness (1, 1.5) +%!error skewness (1, 0) +%!error skewness (1, 3)