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A limiting distribution for Bernoulli trials with second-order Markov dependence

Published online by Cambridge University Press:  14 July 2016

Barron Brainerd
Barron Brainerd*
Affiliation:
University of Toronto
*
∗ Postal address: Department of Mathematics, University of Toronto, Toronto, M5S 1A1, Canada.
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Abstract

Let ℰ be an event governed by a homogeneous second-order two-state Markov chain. Assume the steady state has been achieved. Consider Nm the number of times that ℰ occurs in m successive trials. The limiting distribution of P(Nm = k) is obtained under the condition that mP(ℰ)=λ.

Keywords

SECOND-ORDER MARKOV CHAINSLIMITING DISTRIBUTIONPÓLYA-AEPPLI DISTRIBUTIONLAGUERRE FUNCTIONS

Information

Type
Short Communications
Information
Journal of Applied Probability , Volume 20 , Issue 2 , June 1983 , pp. 419 - 422
Copyright
Copyright © Applied Probability Trust 1983 

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References

[1] Brainerd, B. and Chang, S. M. (1983) The distribution of the number of ocurrences of an event governed by two state Markov chains of first and second order. Canad. J. Statist. 10, 225–231.CrossRefGoogle Scholar
[2] Patil, G. P. and Joshi, S. W. (1968) A Dictionary and Bibliography of Discrete Distributions. Hafner, New York.Google Scholar
[3] Rainville, E. D. (1960) Special Functions. Macmillan, New York.Google Scholar
[4] Wang, Y. H. (1981) On the limit of the Markov binomial distribution. J. Appl. Prob. 18, 937–942.CrossRefGoogle Scholar