# Reference Material for Multvariate Analysis with Different Probability Distributions

I'm interested in multivariate probability distributions with different sub-distributions. Say I've collected two metrics in a population, and we then had a two dimensional probability distribution:

X1 ~ Normal(U, V) and X2 ~ Poi(Lambda)

Notice how these two variables come from different probability distributions. I've been having trouble finding reference material for multivariate analysis where the dimensions come from different distributions.

For example: the Wischart distribution works well when the variables all come from chi-square distributions. Does anyone have any reference material for probability distributions where the sub-distributions are not the same?

• What is "sub-distribution"? Did you mean marginals? – Aksakal Mar 14 '16 at 15:23
• Hmm I suppose so – user46925 Mar 14 '16 at 15:33
• So, will your joint distribution be something like $(x_1,x_2)\sim f(u,v,\lambda)?$ – Aksakal Mar 14 '16 at 15:47
• Yeah, that would be it! – user46925 Mar 14 '16 at 15:52
• Is that still a Copula? They may or may not be related variables. (I don't know yet - but I do know that one follows a Poisson and another follows a Gaussian) – user46925 Mar 14 '16 at 15:52