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On the limit of the Markov binomial distribution

Published online by Cambridge University Press:  14 July 2016

Y. H. Wang
Y. H. Wang*
Affiliation:
Concordia University
*
∗ Postal address: Department of Mathematics, Concordia University, 1455 de Maisonneuve Blvd. W, Montreal H3G 1M8, Canada.
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Abstract

Let X 1X 2, · ·· be a Markov Bernoulli sequence with initial probabilities p of success and q = 1 – p of failure, and probabilities 1 – (1 – π) p, (1 – π) p in the first row and (1 – π) (1 – p), (1 – π) p + πin the second row of the transition matrix. If we define Sn = Σi=1 n Xi , then the limit distribution P{Sn = k} is obtained when n →∞, np →λ.

Keywords

MARKOV CHAINBERNOULLI SEQUENCEBINOMIALLIMITING DISTRIBUTIONCOMPOUND POISSONNEGATIVE BINOMIAL

Information

Type
Short Communications
Information
Journal of Applied Probability , Volume 18 , Issue 4 , December 1981 , pp. 937 - 942
Copyright
Copyright © Applied Probability Trust 1981 

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