ABSTRACT
This chapter defines the matrix variate Dirichlet type I and II distributions. The matrix variate Dirichlet distributions are special cases of the matrix variate Liouville distributions. The chapter also defines and derives the inverse Dirichlet distribution. The inverse Dirichlet distribution can be obtained from the matrix variate Dirichlet Type I distribution by means of an inverse transformation. The chapter studies certain properties of matrix variate Dirichlet type I and II distributions. It also derives factorizations of the matrix variate Dirichlet density. Using suitable inverse transformations, one can derive the matrix variate Dirichlet distribution from the independent beta matrices. Tiao and Guttman derived certain asymptotic distribution for the univariate Dirichlet type I distribution. The chapter gives the matrix variate generalization of their result due to Javier and Gupta. It discusses distributions that are closely related to the matrix variate Dirichlet type I and type II distributions.
