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Sooner waiting time problems in a sequence of trinary trials

Part of:Distribution theory - ProbabilityMarkov processes

Published online by Cambridge University Press:  14 July 2016

M. V. Koutras and
V. A. Alexandrou
M. V. Koutras*
Affiliation:
University of Athens
V. A. Alexandrou*
Affiliation:
University of Athens
*
∗ Postal address: Department of Mathematics, University of Athens, Panepistemiopolis, 15784, Greece.
∗ Postal address: Department of Mathematics, University of Athens, Panepistemiopolis, 15784, Greece.
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Abstract

Let X 1 , X 2 ,· ·· be a (linear or circular) sequence of trials with three possible outcomes (say S, S∗ or F) in each trial. In this paper, the waiting time for the first appearance of an S-run of length k or an S∗-run of length r is systematically investigated. Exact formulae and Chen-Stein approximations are derived for the distribution of the waiting times in both linear and circular problems and their asymptotic behaviour is illustrated. Probability generating functions are also obtained when the trials are identical. Finally, practical applications of these results are discussed in some detail.

Keywords

SUCCESS RUNSSOONER WAITING TIMESMULTISTATE TRIALSMARKOV CHAINSCHEN-STEIN APPROXIMATIONS

MSC classification

Primary:60E05: Distributions
Secondary:60J10: Markov chains (discrete-time Markov processes on discrete state spaces)

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 34 , Issue 3 , September 1997, pp. 593 - 609
Copyright
Copyright © Applied Probability Trust 1997 

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