Generating correlated random variables

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Trambak 2012-3-13

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https://ww2.mathworks.cn/matlabcentral/answers/32148-generating-correlated-random-variables

I have two compund distributions S1 = Sum{i=1:N1} Xi, where N1 is Poisson(lambda1) and X is say LogNormal(1,2) and S2 =Sum{i=1:N2} Yi, where N2 is Poisson(lambda2) and Y is say LogNormal(2,3).I wish to generate correlated random numbers from this distribution such that the linear correlation is say rho. Any thoughts?

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Oleg Komarov 2012-3-13

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https://ww2.mathworks.cn/matlabcentral/answers/32148-generating-correlated-random-variables#answer_40642

Answer to similar question: http://www.mathworks.com/matlabcentral/answers/23173#answer_30456

EDIT

Thread with links on how to generate random numbers from given distributions other than mulitvariate normal: http://www.mathworks.com/matlabcentral/newsreader/view_thread/115379

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Oleg Komarov 2012-3-13

See my edit.

Trambak 2012-3-13

Yeah, I saw the paper. Even there, the claim is that the method works best when the marginals are symmetric (or lets say marginals are from elliptical distributions). I have not seen anything which allows to simulate correlated random numbers from fat tailed compound distributions. Copulas are an answer but then with copulas, one cannot jump from the rank correlations to the linear correlations easily without making very strong assumptions. May be I should just stick with the rank correlations only.

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