### 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.

function retval = skewness (x)

  ## Written by KH (Kurt.Hornik@ci.tuwien.ac.at) on Jul 29, 1994.

  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