Generalized Matrix t Distribution Based on New Matrix Gamma Distribution

Abstract

In this paper a generalized matrix variate gamma distribution, which includes a trace function in the kernel of the density, is introduced. Some important statistical properties including Laplace transform, distributions of functions, expected value of the determinant and expected value of zonal polynomial of the generalized gamma matrix are derived. Further, by using the distribution of the inverse of this newly defined generalized gamma matrix as the prior for the characteristic matrix of a matrix variate normal distribution, a new generalized matrix t type family of distributions is generated. Some important statistical characteristics of this family are also exhibited.

Keywords

• Bayes estimator
• Generalized matrix gamma distribution
• Generalized matrix t distribution
• Zonal polynomial