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Bounds on the mean and squared coefficient of variation of phase-type distributions

Part of: Distribution theory - Probability Markov processes

Published online by Cambridge University Press:  22 November 2021

Qi-Ming He
Qi-Ming He*
Affiliation:
University of Waterloo
*
*Postal address: Department of Management Sciences, University of Waterloo, 200 University Avenue West, Waterloo, Canada N2L 3G1. q7he@uwaterloo.ca
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Abstract

We consider a class of phase-type distributions (PH-distributions), to be called the MMPP class of PH-distributions, and find bounds of their mean and squared coefficient of variation (SCV). As an application, we have shown that the SCV of the event-stationary inter-event time for Markov modulated Poisson processes (MMPPs) is greater than or equal to unity, which answers an open problem for MMPPs. The results are useful for selecting proper PH-distributions and counting processes in stochastic modeling.

Keywords

Phase-type distributionmeansquared coefficient of variationMarkov modulated Poisson processdoubly stochastic matrixM-matrix

MSC classification

Primary: 60J27: Continuous-time Markov processes on discrete state spaces
Secondary: 60E15: Inequalities; stochastic orderings
Type
Original Article
Information
Journal of Applied Probability , Volume 58 , Issue 4 , December 2021 , pp. 880 - 889
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Copyright
© The Author(s), 2021. Published by Cambridge University Press on behalf of Applied Probability Trust

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