function [R]=y2res(Y)% Y2RES evaluates basic statistics of a data series% % R = y2res(y)%	several statistics are estimated from each column of y% % OUTPUT:%   R.N     number of samples, NaNs are not counted %   R.SUM   sum of samples%   R.MEAN  mean%   R.STD   standard deviation %   R.VAR   variance%   R.Max   Maximum%   R.Min   Minimum %   ...   and many more including:  %	MEDIAN, Quartiles, Variance, standard error of the mean (SEM), %	Coefficient of Variation, Quantization (QUANT), TRIMEAN, SKEWNESS, %	KURTOSIS, Root-Mean-Square (RMS), ENTROPY % %	$Id: y2res.m,v 1.15 2005/12/17 20:59:17 schloegl Exp $%	Copyright (C) 1996-2005 by Alois Schloegl <a.schloegl@ieee.org>%    	This is part of the TSA-toolbox %       http://octave.sourceforge.net/%	http://www.dpmi.tugraz.at/~schloegl/matlab/tsa/% 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, write to the Free Software% Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.[R.SUM, R.N, R.SSQ] = sumskipnan(Y,1);%R.S3P = sumskipnan(Y.^3,1);R.S4P = sumskipnan(Y.^4,1);%R.S5P = sumskipnan(Y.^5,1);R.MEAN	= R.SUM./R.N;R.MSQ   = R.SSQ./R.N;R.RMS	= sqrt(R.MSQ);R.SSQ0  = R.SSQ-R.SUM.*R.MEAN;		% sum square of mean removedif 1,%flag_implicit_unbiased_estim,    n1 	= max(R.N-1,0);			% in case of n=0 and n=1, the (biased) variance, STD and STE are INFelse    n1	= R.N;end;R.VAR  	= R.SSQ0./n1;	     		% variance (unbiased) R.STD  	= sqrt(R.VAR);		     	% standard deviationR.SEM  	= sqrt(R.SSQ0./(R.N.*n1)); 	% standard error of the meanR.SEV	= sqrt(n1.*(n1.*R.S4P./R.N+(R.N.^2-2*R.N+3).*(R.SSQ./R.N).^2)./(R.N.^3)); % standard error of the varianceR.Coefficient_of_variation = R.STD./R.MEAN;R.CM2	= R.SSQ0./n1;R.Max   = max(Y,[],1);R.Min   = min(Y,[],1);%R.NormEntropy = log2(sqrt(2*pi*exp(1)))+log2(R.STD);Q0500=repmat(nan,1,size(Y,2));Q0250=Q0500;Q0750=Q0500;%MODE=Q0500;for k = 1:size(Y,2),        tmp = sort(Y(:,k));        Q0250(k) = flix(tmp,R.N(k)/4   + 0.75);        Q0500(k) = flix(tmp,R.N(k)/2   + 0.50);        Q0750(k) = flix(tmp,R.N(k)*3/4 + 0.25);        tmp = diff(tmp);	pdf   = diff([0; find(tmp>0); R.N(k)])/R.N(k); % empirical probability distribution 	R.ENTROPY(k) = -sumskipnan(pdf.*log(pdf));        tmp = tmp(find(tmp));        q   = min(tmp);	qerror = 0;         if isempty(q),                q = NaN;        else                tmp = tmp/q; 		qerror = max(abs(tmp-round(tmp)));        end;        R.QUANT(k) = q; 	R.Qerror(k) = qerror; end;if any(R.Qerror*1e6>R.QUANT)	warning('(Y2RES) Quantization might not be equidistant')end;	R.MEDIAN 	= Q0500;R.Quartiles   	= [Q0250; Q0750];% R.IQR = H_spread   	= [Q0750 - Q0250];R.TRIMEAN	= [Q0250 + 2*Q0500 + Q0750]/4;Y       = Y - repmat(R.MEAN,size(Y)./size(R.MEAN));R.CM3 	= sumskipnan(Y.^3,1)./n1;R.CM4 	= sumskipnan(Y.^4,1)./n1;%R.CM5 	= sumskipnan(Y.^5,1)./n1;R.SKEWNESS = R.CM3./(R.STD.^3);R.KURTOSIS = R.CM4./(R.VAR.^2)-3;%R.Skewness.Fisher = (R.CM3)./(R.STD.^3);	%%% same as R.SKEWNESS%R.Skewness.Pearson_Mode   = (R.MEAN-R.MODE)./R.STD;%R.Skewness.Pearson_coeff1 = (3*R.MEAN-R.MODE)./R.STD;R.Skewness.Pearson_coeff2 = (3*R.MEAN-R.MEDIAN)./R.STD;R.Skewness.Bowley = (Q0750+Q0250 - 2*Q0500)./(Q0750-Q0250); % quartile skewness coefficientR.datatype = 'STAT Level 4';