Family of multivariate generalized t distributions

In this paper, we introduce a new family of multivariate distributions as the scale mixture of the multivariate power exponential distribution introduced by Gómez et al. (Comm. Statist. Theory Methods 27(3) (1998) 589) and the inverse generalized gamma distribution. Since the resulting family includes the multivariate t distribution and the multivariate generalization of the univariate GT distribution introduced by McDonald and Newey (Econometric Theory 18 (11) (1988) 4039) we call this family as the "multivariate generalized t-distributions family", or MGT for short. We show that this family of distributions belongs to the elliptically contoured distributions family, and investigate the properties. We give the stochastic representation of a random variable distributed as a multivariate generalized t distribution. We give the marginal distribution, the conditional distribution and the distribution of the quadratic forms. We also investigate the other properties, such as, asymmetry, kurtosis and the characteristic function. © 2003 Elsevier Inc. All rights reserved.St. Cloud State UniversityThe author would like to thank two anonymous referees and the handling editor for their very valuable comments, corrections and remarks, which improved this work. The author acknowledges Cukurova University, Turkey and St. Cloud State University, MN, US for the financial supports. Also, the author gratefully acknowledges Brazilian financial support from CNPq Project 478712/01-2