Matching More Than Three Moments with Acyclic Phase Type Distributions

Abstract

This paper presents a matching procedure for generating an acyclic phase type distribution of order N given the first 2N − 1 moments, if they are feasible. The matching procedure uses an iterative approach and, theoretically, it can be applied to match an arbitrary number of moments. The first step of the iterative procedure contains the solution of an equation of order N and the order is decreased by one in each consecutive step. Apart from these equations, the procedure makes use of explicit expressions. The practical applicability of the proposed procedure is limited by the numerical accuracy of the solution of these equations and the complexity of the involved expressions. We present examples for matching more than 10 moments with acyclic phase type distributions.

Keywords:

• Acyclic phase type distribution
• Moment matching

AMS Subject Classification:

• Primary 60J20
• Secondary 60E99

ACKNOWLEDGMENT

We would like to thank the encouragement of the associate editor, which led us to the proof of Theorems 3.2.1 and 3.2.2. András Horváth was supported in part by Miur project Firb-Perf and EEC project Crutial.

Notes

¹A survey of fitting algorithms can be found in Reference ^[6] .