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Waiting times for patterns in a sequence of multistate trials

Part of: Distribution theory - Probability Markov processes

Published online by Cambridge University Press:  14 July 2016

Demetrios L. Antzoulakos
Demetrios L. Antzoulakos*
Affiliation:
University of Piraeus
*
∗ Postal address: Department of Statistics and Insurance Science, University of Piraeus, 18534 Piraeus, Greece. Email address: [email protected]
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Abstract

Let Xn, n ≥ 1 be a sequence of trials taking values in a given set A, let ∊ be a pattern (simple or compound), and let Xr,∊ be a random variable denoting the waiting time for the rth occurrence of ∊. In the present article a finite Markov chain imbedding method is developed for the study of Xr,∊ in the case of the non-overlapping and overlapping way of counting runs and patterns. Several extensions and generalizations are also discussed.

Keywords

Markov chainmultistate trialspatternwaiting time distributionsooner and later waiting time problemsreliability

MSC classification

Primary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)
Secondary: 60E05: Distributions
Type
Research Papers
Information
Journal of Applied Probability , Volume 38 , Issue 2 , June 2001 , pp. 508 - 518
Copyright
Copyright © Applied Probability Trust 2001 

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