Matching Three Moments with Minimal Acyclic Phase Type Distributions

Abstract

Abstract A number of approximate analysis techniques are based on matching moments of continuous time phase type (PH) distributions. This paper presents an explicit method to compose minimal order continuous time acyclic phase type (APH) distributions with a given first three moments. To this end we also evaluate the bounds for the first three moments of order n APH distributions (APH(n)). The investigations of these properties are based on a basic transformation, which extends the APH(n − 1) class with an additional phase in order to describe the APH(n) class. Key Words: Acyclic phase type distributionsMoment boundsMoment fittingMathematics Subject Classification: Primary 60J99Secondary 60J10 ACKNOWLEDGMENT This work is supported by the Italian-Hungarian R&D program, by OKTA under grant T-34972 and by MIUR under the project FIRB–Perf.