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On probability generating functions for waiting time distributions of compound patterns in a sequence of multistate trials

Part of: Distribution theory - Probability Markov processes

Published online by Cambridge University Press:  14 July 2016

James C. Fu  and
Y. M. Chang
James C. Fu*
Affiliation:
University of Manitoba
Y. M. Chang*
Affiliation:
University of Manitoba
*
∗ Postal address: Department of Statistics, University of Manitoba, Winnipeg, Manitoba, Canada.
∗ Postal address: Department of Statistics, University of Manitoba, Winnipeg, Manitoba, Canada.
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Abstract

Probability generation functions of waiting time distributions of runs and patterns have been used successfully in various areas of statistics and applied probability. In this paper, we provide a simple way to obtain the probability generating functions for waiting time distributions of compound patterns by using the finite Markov chain imbedding method. We also study the characters of waiting time distributions for compound patterns. A computer algorithm based on Markov chain imbedding technique has been developed for automatically computing the distribution, probability generating function, and mean of waiting time for a compound pattern.

Keywords

Probability generating functioncompound patternMarkov chain imbeddingtransition probability matrix

MSC classification

Primary: 60E05: Distributions
Secondary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)
Type
Research Papers
Information
Journal of Applied Probability , Volume 39 , Issue 1 , March 2002 , pp. 70 - 80
Copyright
Copyright © Applied Probability Trust 2002 

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Footnotes

This work was supported in part by Nature Science and Engineering Research Council of Canada, under Grant A-9216.

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