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skewness.m

function R = skewness(i,DIM)
% SKEWNESS estimates the skewness 
%
% y = skewness(x,DIM)
%   calculates skewness of x in dimension DIM
%
% DIM dimension
%     1: STATS of columns
%     2: STATS of rows
%     default or []: first DIMENSION, with more than 1 element
%
% features:
% - can deal with NaN's (missing values)
% - dimension argument 
% - compatible to Matlab and Octave
%
% see also: SUMSKIPNAN, STATISTIC
%
% REFERENCE(S):
% http://mathworld.wolfram.com/


%    This program 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 of the License, or
%    (at your option) any later version.
%
%    This program 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 this program; If not, see <http://www.gnu.org/licenses/>.

%     Copyright (C) 2000-2003 by Alois Schloegl <a.schloegl@ieee.org>   
%     $Revision: 4585 $
%     $Id: skewness.m 4585 2008-02-04 13:47:45Z adb014 $


% check input arguments 

if nargin==1,
        DIM=min(find(size(i)>1));
        if isempty(DIM), DIM=1; end;
end;

[R.SUM,R.N,R.SSQ] = sumskipnan(i,DIM);    % sum

R.MEAN      = R.SUM./R.N;                 % mean 
R.SSQ0      = R.SSQ - real(R.SUM).*real(R.MEAN) - imag(R.SUM).*imag(R.MEAN); % sum square with mean removed

%if flag_implicit_unbiased_estim;    %% ------- unbiased estimates ----------- 
    n1      = max(R.N-1,0);               % in case of n=0 and n=1, the (biased) variance, STD and SEM are INF
%else
%    n1     = R.N;
%end;

R.VAR = R.SSQ0./n1;                 % variance (unbiased) 
R.STD = sqrt(R.VAR);                % standard deviation

i       = i - repmat(R.MEAN,size(i)./size(R.MEAN));
R.CM3       = sumskipnan(i.^3,DIM)./n1;
%R.CM4      = sumskipnan(i.^4,DIM)./n1;

R = R.CM3./(R.STD.^3);
%R = R.CM4./(R.VAR.^2)-3;

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