A new class of multivariate phase type distributions

A new class of multivariate phase type distributions (denoted by MPH*) is defined, based upon the total accumulated reward until absorption in a finite state, continuous time Markov chain. This new class is shown to be a strict superset of the class of multivariate phase type distributions MPH introduced by Assaf, Langberg, Savits and Shaked. A conjectured property (viz. closure under finite convolutions) of the class MPH is proved using the class MPH* defined here. Computational techniques for the distributions in MPH* are discussed. Closure properties of MPH* are stated and an open problem is discussed.