The Annals of Statistics
- Ann. Statist.
- Volume 1, Number 5 (1973), 933-939.
The Joint Probability Generating Function for Run-Lengths in Regenerative Binary Markov Chains, with Applications
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.
Ann. Statist., Volume 1, Number 5 (1973), 933-939.
First available in Project Euclid: 12 April 2007
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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