Add a useful package (from Source forge) for octave

[CreaPhase.git] / octave_packages / nan-2.5.5 / skewness.m

diff --git a/octave_packages/nan-2.5.5/skewness.m b/octave_packages/nan-2.5.5/skewness.m
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+++ b/octave_packages/nan-2.5.5/skewness.m
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+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/
+
+%    $Id: skewness.m 8223 2011-04-20 09:16:06Z schloegl $
+%    Copyright (C) 2000-2003,2010 by Alois Schloegl <alois.schloegl@gmail.com>
+%    This function is part of the NaN-toolbox
+%       http://pub.ist.ac.at/~schloegl/matlab/NaN/
+
+%    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 3 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/>.
+
+
+
+% check input arguments 
+
+if nargin==1,
+        DIM = find(size(i)>1,1);
+        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;