Mercurial > octave-antonio
view scripts/statistics/base/skewness.m @ 11436:e151e23f73bc
Overhaul base statistics functions and documentation of same.
Add or improve input validation.
Add input validation tests.
Add functional tests.
Improve or re-write documentation strings.
author | Rik <octave@nomad.inbox5.com> |
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date | Mon, 03 Jan 2011 21:23:08 -0800 |
parents | 4c335d398c8d |
children | fd0a3ac60b0e |
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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}) ## @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) = N^(-1) 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 <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 if (!isnumeric(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); if (isempty (dim)) dim = 1; endif else if (!(isscalar (dim) && dim == round (dim)) || !(1 <= dim && dim <= nd)) error ("skewness: DIM must be an integer and a valid dimension"); endif endif c = sz(dim); idx = ones (1, nd); idx(dim) = c; x = x - repmat (mean (x, dim), idx); sz(dim) = 1; retval = zeros (sz, class (x)); s = std (x, [], dim); ind = find (s > 0); x = sum (x .^ 3, dim); retval(ind) = x(ind) ./ (c * s(ind) .^ 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))); %% Test input validation %!error skewness () %!error skewness (1, 2, 3) %!error skewness ([true true]) %!error skewness (1, ones(2,2)) %!error skewness (1, 1.5) %!error skewness (1, 0) %!error skewness (1, 3)