ABSTRACT
This chapter discusses the matrix variate t-distribution. Because of its applications in Bayesian inference, many researchers have studied this distribution. The chapter describes various properties of the random matrix T using its p.d.f. and the synthetic representation. It derives expected values of the random matrix T and some of its functions. The chapter defines the inverted matrix variate t-distribution, and introduces the type of distributions that were derived by Olkin and Rubin. Tan studied their properties and called them disguised matrix variate t-distributions because of their similarities with matrix variate t-distribution and relationship with matrix variate beta distribution. The chapter also derives the lower and upper disguised matrix variate t-densities. Tan defined a restricted form of the matrix variate t-distribution which occurs in the derivation of the posterior distribution of a parameter of a generalized multivariate normal process. The chapter explores this restricted matrix variate t-distribution.
