# ITE / code / H_I_D / utilities / Edgeworth_t1_t2_t3.m

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48``` ```function [t1,t2,t3] = Edgeworth_t1_t2_t3(Y) %Computes the three kappa_ijk := E[x_i x_j x_k] based terms (t1,t2,t3) in the Edgeworth expansion based entropy estimator, see 'HShannon_Edgeworth_estimation.m'. % %INPUT: % Y: Y(:,t) is the t^th sample % %Copyright (C) 2012 Zoltan Szabo ("http://nipg.inf.elte.hu/szzoli", "szzoli (at) cs (dot) elte (dot) hu") % %This file is part of the ITE (Information Theoretical Estimators) Matlab/Octave toolbox. % %ITE 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 software 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 ITE. If not, see . d = size(Y,1);%dimension %t1: t1 = 0; for i = 1 : d %d terms kappa_iii = mean(Y(i,:).^3); t1 = t1 + kappa_iii^2; end %t2: t2 = 0; for i = 1:d for j = [1:i-1,i+1:d] %j\ne i; 2*nchoosek(d,2) terms kappa_iij = mean(Y(i,:).^2 .* Y(j,:)); t2 = t2 + kappa_iij^2; end end t2 = 3 * t2; %t3: t3 = 0; for i = [1:d-2]%i
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