How to sample Multinomial Distribution

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Mike Nguyen on 16 Dec 2017
Suppose I have the X data with dimension(VxN), and probability rho(vkj) with k is latent variable How could I sample Matrix (Av1j,...,AvKj)follows Multinomial (Xvj,rho(vkj))

Kaushik Lakshminarasimhan on 17 Dec 2017
It is difficult to read your question. Please use underscore to separate your variable names from subscripts. Here's a solution with nested loops. Perhaps you can find a way to vectorise it if the size of X is prohibitively large.
V = 50; N = 10; K = 5;
X = 100*ones(V,N); % assuming 100 trials (sample size)
rho = rand(V,N,K);
rho = rho./repmat(sum(rho,3),1,1,K);
for v = 1:V
for j = 1:N
A(v,:,j) = mnrnd(X(v,j),squeeze(rho(v,j,:))); % your A_vkj
end
end
Mike Nguyen on 17 Dec 2017
Thanks for your reply Could you tell me why we use squeeze(rho(v,j,:)) here?
Kaushik Lakshminarasimhan on 17 Dec 2017
Because mnrnd expects the second argument to be a 1xK or Kx1 vector whereas rho(v,j,:) is 1x1xK. squeeze converts the 1x1xK vector to Kx1 by removing the singleton dimension.