The Annals of Statistics

The Joint Probability Generating Function for Run-Lengths in Regenerative Binary Markov Chains, with Applications

I. J. Good

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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.

Article information

Source
Ann. Statist., Volume 1, Number 5 (1973), 933-939.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176342513

Digital Object Identifier
doi:10.1214/aos/1176342513

Mathematical Reviews number (MathSciNet)
MR341612

Zentralblatt MATH identifier
0269.60005

JSTOR
links.jstor.org

Keywords
Regenerative Markov chains binary Markov chains runs in Markov chains

Citation

Good, I. J. The Joint Probability Generating Function for Run-Lengths in Regenerative Binary Markov Chains, with Applications. Ann. Statist. 1 (1973), no. 5, 933--939. doi:10.1214/aos/1176342513. https://projecteuclid.org/euclid.aos/1176342513


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