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Success runs in a two-state Markov chain

Published online by Cambridge University Press:  14 July 2016

M. B. Rajarshi
M. B. Rajarshi*
Affiliation:
University of Poona, India
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Abstract

Success runs of a fixed length in a two-state Markov chain are discussed. The results are analogous to those in the case of independent Bernoulli trials. The generating function of the waiting time for the first occurrence of a success run is obtained from the theory of recurrent events. Under certain conditions, the distribution of the number of long runs in a large number of trials is shown to be Poisson.

Keywords

SUCCESS RUNS IN A TWO-STATE MARKOV CHAINRECURRENT EVENTGENERATING FUNCTIONSPOISSON DISTRIBUTION OF LONG RUNS
Type
Short Communications
Information
Journal of Applied Probability , Volume 11 , Issue 1 , March 1974 , pp. 190 - 192
Copyright
Copyright © Applied Probability Trust 1974 

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References

Feller, W. (1965) An Introduction to Probability Theory and its Applications. Vol. I. 2nd ed. John Wiley, New York.Google Scholar