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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?

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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 CopulaDistribution [see ref-page] in Mathematica 8 to construct a multivariate distribution with arbitrary set of marginals. The choice of copula kernel depends on details of what you are trying to achieve.

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