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view scripts/statistics/base/skewness.m @ 8920:eb63fbe60fab
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author | John W. Eaton <jwe@octave.org> |
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date | Sat, 07 Mar 2009 10:41:27 -0500 |
parents | 81d6ab3ac93c |
children | 1bf0ce0930be |
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## Copyright (C) 1996, 1997, 1998, 1999, 2000, 2002, 2004, 2005, 2006, ## 2007, 2008, 2009 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} {} skewness (@var{x}, @var{dim}) ## If @var{x} is a vector of length @math{n}, return the skewness ## @iftex ## @tex ## $$ ## {\rm skewness} (x) = {1\over N \sigma(x)^3} \sum_{i=1}^N (x_i-\bar{x})^3 ## $$ ## where $\bar{x}$ is the mean value of $x$. ## @end tex ## @end iftex ## @ifnottex ## ## @example ## skewness (x) = N^(-1) std(x)^(-3) sum ((x - mean(x)).^3) ## @end example ## @end ifnottex ## ## @noindent ## of @var{x}. 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. ## @end deftypefn ## Author: KH <Kurt.Hornik@wu-wien.ac.at> ## Created: 29 July 1994 ## Adapted-By: jwe function retval = skewness (x, dim) if (nargin != 1 && nargin != 2) print_usage (); endif nd = ndims (x); sz = size (x); if (nargin != 2) ## Find the first non-singleton dimension. dim = 1; while (dim < nd + 1 && sz(dim) == 1) dim = dim + 1; endwhile if (dim > nd) dim = 1; endif else if (! (isscalar (dim) && dim == round (dim)) && dim > 0 && dim < (nd + 1)) error ("skewness: dim must be an integer and valid dimension"); endif endif if (! ismatrix (x)) error ("skewness: x has to be a matrix or a vector"); endif c = sz(dim); idx = ones (1, nd); idx (dim) = c; x = x - repmat (mean (x, dim), idx); sz(dim) = 1; retval = zeros (sz); s = std (x, [], dim); ind = find (s > 0); x = sum (x .^ 3, dim); retval(ind) = x(ind) ./ (c * s(ind) .^ 3); endfunction %!error skewness (); %!error skewness (1, 2, 3);