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## Copyright (C) 1996 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 2, 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, write to the Free
## Software Foundation, 59 Temple Place - Suite 330, Boston, MA
## 02111-1307, USA.
## usage: skewness (x)
##
## If x is a vector of length N, return the skewness
##
## skewness (x) = N^(-1) std(x)^(-3) SUM_i (x(i)-mean(x))^3
##
## of x.
##
## If x is a matrix, return a row vector containing the skewness for each
## column.
## Author: KH <Kurt.Hornik@ci.tuwien.ac.at>
## Created: 29 July 1994
## Adapted-By: jwe
function retval = skewness (x)
if (nargin != 1)
usage ("skewness (x)");
endif
if (is_vector (x))
x = x - mean (x);
if (! any (x))
retval = 0;
else
retval = sum (x .^ 3) / (length (x) * std (x) ^ 3);
endif
elseif (is_matrix (x))
[nr, nc] = size (x);
x = x - ones (nr, 1) * mean (x);
retval = zeros (1, nc);
s = std (x);
ind = find (s > 0);
retval (ind) = sum (x (:, ind) .^ 3) ./ (nr * s (ind) .^ 3);
else
error ("skewness: x has to be a matrix or a vector.");
endif
endfunction
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