A new class of multivariate distributions: Scale mixture of Kotz-type distributions

This paper proposes a new family of multivariate distributions as the scale mixture of the multivariate Kotz-type distribution and the inverse generalized gamma distribution. Definition and some of the main properties are given. It is shown that the new family belongs to the elliptically contoured distributions family, and as a result of the mixing approach it includes the longer tailed distributions than the Kotz-type distribution. Thus, the new family may be regarded as a useful extension of the Kotz-type distribution for robustness purposes. It is also shown that the multivariate t -distribution and the generalized versions of the multivariate t -distribution introduced by Arellano-Valle and Bolfarine [1995. On some characterizations of the t distribution. Statist Probab. Lett. 25, 79–85.] and Arslan [2004. Family of multivariate generalized t distributions. J. Multivar. Anal. 89, 329–337.] belong to the new family. Therefore, to unify all the standard and generalized versions of the t -distribution we call this new class of the distributions as the “family of t -type distributions”.