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.
Citation
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
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