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In this paper, we propose a new kind of multivariate  t  distribution by allowing different degrees of freedom for each univariate component. Compared with the classical multivariate  t  distribution, it is more flexible in the model specification that can be used to deal with the variant amounts of tail weights on marginals in multivariate data modeling. In particular, it could include components following the multivariate normal distribution, and it contains the product of independent  t -distributions as a special case. Subsequently, it is extended to the regression model as the joint distribution of the error terms. Important distributional properties are explored and useful statistical methods are developed. The flexibility of the specified structure in better capturing the characteristic of data is exemplified by both simulation studies and real data analyses.

A new multivariate t distribution with variant tail weights and its application in robust regression analysis