Encyclopedia of Operations Research and Management Science

2001 Edition
| Editors: Saul I. Gass, Carl M. Harris

Phase-type probability distributions

Reference work entry
DOI: https://doi.org/10.1007/1-4020-0611-X_755

The probability distributions of phase-type, or PH-distributions, form a useful general class for the representation of nonnegative random variables. A comprehensive discussion of their basic properties is given in Neuts (1981). There are parallel definitions and properties of discrete and continuous PH-distributions. This discussion emphasizes the continuous case.

A probability distribution F(⋅) on [0, ∞)is ofphasetype if it can arise as the absorption time distribution of an (m + 1)-state Markov chain with m transient states 1,..., m and an absorbing state 0. The generator Qv of such a Markov chain is written as
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© Kluwer Academic Publishers 2001

Authors and Affiliations

  1. 1.The University of ArizonaTucsonUSA