Computing the Phase-Type Renewal and Related Functions


Kao, Edward P.C.   (1988, ASQC and the American Statistical Association)   University of Houston, Houston, TX

Technometrics    Vol. 30    No. 1
QICID: 9340    February 1988    pp. 87-93
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Article Abstract

This article presents a procedure for computing the renewal function, the renewal density, the integral of the renewal function, and the variance function of phase-type renewal processes. The procedure hinges on the computation of the state probability vector of a continuous-time Markov chain. This is accomplished by using a randomization approach that is simple, efficient, and numerically stable and does not require numerical integration. I discuss approximating arbitrary interrenewal distributions by phase-type distributions so that the procedure can be used to approximate renewal and related functions.


Markov chains,Renewal process,Statistics

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