Multivariate Distributions

Abstract

A matrix-exponential distribution is characterized by having a rational moment-generating function, so it is natural to define the class of multivariate matrix-exponential distributions as the class containing all distributions with a joint transform that is a rational function. Before we analyze these multivariate matrix-exponential distributions in their full generality, we will discuss an important subclass based on linear rewards of the sojourn times in the states of the Markov jump process underlying a phase-type distribution. We start with a less general case, because little is currently known about the general class of multivariate matrix-exponential distributions.