A class of weighted multivariate distributions related to doubly truncated multivariate t-distribution

This article introduces a class of weighted multivariate t-distributions, which includes the multivariate generalized Student t and multivariate skew t as its special members. This class is defined as the marginal distribution of a doubly truncated multivariate generalized Student t-distribution and studied from several aspects such as weighting of probability density functions, inequality constrained multivariate Student t-distributions, scale mixtures of multivariate normal and probabilistic representations. The relationships among these aspects are given, and various properties of the class are also discussed. Necessary theories and two applications are provided.