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I think the title might capture the entire question but for clarity's sake let me expand here. I have several Poisson distributed random variables, and want to model the product of pairs of these variables. I have reason to believe that many of these variables will be correlated with each other, so it seems like a Poisson model would not be a reasonable approximation of all of the resulting distributions. Is there a distribution that might be appropriate that doesn't assume independence of the variables I'm taking the product of?

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  • $\begingroup$ Do you know if the correlations are positive or negative? $\endgroup$ – gung - Reinstate Monica Dec 4 '14 at 3:19
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This paper seems to discuss multivariate poisson distribution with covariance structures. Check it out. Happy reading!

http://link.springer.com/article/10.1007%2Fs11222-005-4069-4

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