Can I have different degrees of freedom for each dimension in a Multivariate t Distribution? The functions that I use in Matlab (mvtpdf) and Mathematica (MultivariateTDistribution) accept only one parameter of degrees of freedom. What I want is to have different degrees of freedom for each dimension. I think this will represent my data more efficiently. Is this possible?
I interpret your question as being, can I construct a multivariate distribution that has student-T distributions with different degrees of freedom as its marginals.
You can do it with copulas. You could use