Gaussian Copula and Correlation, I am trying to find gaussian copula for multiple variable, Please help me, is the u which i underline is correct or not
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N = 1000;
norm_mean = 0;
norm_var = 1;
r1= norm_mean+sqrt(norm_var)*randn(1,N);
%calculating PDF
y1 = pdf('Normal',r1,norm_mean,sqrt(norm_var));
%Random variable 2
r2= norm_mean+sqrt(norm_var)*randn(1,N);
y2 = pdf('Normal',r2,norm_mean,sqrt(norm_var));
%Random Variable 3
r3= norm_mean+sqrt(norm_var)*randn(1,N);
y3 = pdf('Normal',r3,norm_mean,sqrt(norm_var));
%Calculate correlation between columns Y1 and Y2
[rho,pval] = corr(y1(:),y2(:),'type','Spearman')
[rho1,pval1] = corr(y2(:),y3(:),'type','Spearman')
[rho2,pval2] = corr(y3(:),y1(:),'type','Spearman')
%Calculating correlation between Y1 and Y2 using corrcoef
[r,p] = corrcoef(y1(:),y2(:))
r2 = copulastat('Gaussian',rho) %check
%calculating Gaussian/Normal copula
u = copularnd('Gaussian',rho,N) +copularnd('Gaussian',rho1,N)+copularnd('Gaussian',rho2,N)
%short the numbers
[s1,i1] = sort(u(:,1));
[s2,i2] = sort(u(:,2));
% two vectors of zeros, x1 and x2, that are the same size as the sorted copula vectors
x1 = zeros(size(s1));
x2 = zeros(size(s2));
x1(i1) = sort(y1);
x2(i2) = sort(y2);
b = [betainv(u(:,1),1,2), betainv(u(:,2),1.5,2)];
figure
scatterhist(b(:,1),b(:,2))
tau_sample = corr(b,'type','Spearman')
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