PH-Invariant Polytopes and Coxian Representations of Phase Type Distributions

In this paper, we study the relationship between phase type (PH) distributions, PH-invariant polytopes, and Coxian representations of PH-distributions. Explicit links are established between vectors in PH-invariant polytopes, PH-representations, and probability measures. A method is developed for the construction of PH-invariant polytopes associated with ordered Coxian representations. The relationship between PH-invariant polytopes and spectral polynomial algorithms is explored as well. Furthermore, a generic algorithm for computing bi-diagonal PH-representations of PH-distributions is developed. Numerical examples are provided to gain insight into the problems of interest.