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September, 1973 The Joint Probability Generating Function for Run-Lengths in Regenerative Binary Markov Chains, with Applications
I. J. Good
Ann. Statist. 1(5): 933-939 (September, 1973). DOI: 10.1214/aos/1176342513

Abstract

Gontcharov obtained the joint probability generating function for the numbers of runs of all lengths, both of successes and failures, in a Bernoulli sequence. This is here generalized to a class of regenerative binary Markov processes. For an allied class of Markov processes, the probability generating function is obtained for a "total score" defined in terms of runs of successes only, and asymptotic formulas are derived for the expectation and variance of the score.

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I. J. Good. "The Joint Probability Generating Function for Run-Lengths in Regenerative Binary Markov Chains, with Applications." Ann. Statist. 1 (5) 933 - 939, September, 1973. https://doi.org/10.1214/aos/1176342513

Information

Published: September, 1973
First available in Project Euclid: 12 April 2007

zbMATH: 0269.60005
MathSciNet: MR341612
Digital Object Identifier: 10.1214/aos/1176342513

Keywords: binary Markov chains , Regenerative Markov chains , runs in Markov chains

Rights: Copyright © 1973 Institute of Mathematical Statistics

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Vol.1 • No. 5 • September, 1973
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