Product Distribution with Copula

Question

I am trying to create a joint probability function that is of the form:

f(a,b,c)=f1(a).f2(b).f3(c).copula

where

copula=CopulaDistribution[{"MultivariateT",R,2},{f1, f2, f3}]

and

f1, f2, f3 are marginal distributions.

I do this by using the code

ProductDistribution[copula,f1,f2,f3]

Clearly, I should be able to simulate from this product distribution (and I am). However, my problem is that Mathematica thinks there are 6 variables (3 from copula, and 3 from the marginals). This obviously should not be the case as there should only be 3 variables corresponding to the marginals

What can I do to rectify this issue?

Answer 1

If I understand you correctly, you are trying to combine the four distributions copula,f1,f2,f3 by means of ProductDistribution. However, ProductDistribution is meant to "represent the joint distribution with independent component distributions", according to its documentation. Consequently, the variables of each of your four distributions must be independent, for a total of six.

Perhaps, you should use TransformedDistribution instead of ProductDistribution, as described in 69347, although it is difficult to know without a more complete understanding of what you are trying to accomplish.