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author | schloegl |
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date | Thu, 02 Apr 2015 10:00:34 +0000 |
parents | 430712382527 |
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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 % % $Id$ % Copyright (C) 1996-2005,2008 by Alois Schloegl <alois.schloegl@gmail.com> % This is part of the TSA-toolbox % http://octave.sourceforge.net/ % http://pub.ist.ac.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 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/>. [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 removed if 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 INF else n1 = R.N; end; R.VAR = R.SSQ0./n1; % variance (unbiased) R.STD = sqrt(R.VAR); % standard deviation R.SEM = sqrt(R.SSQ0./(R.N.*n1)); % standard error of the mean R.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 variance R.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 coefficient R.datatype = 'STAT Level 4';