Abstract
The geometric type and inverse Polýa-Eggenberger type distributions of waiting time for success runs of lengthk in two-state Markov dependent trials are derived by using the probability generating function method and the combinatorial method. The second is related to the minimal sufficient partition of the sample space. The first two moments of the geometric type distribution are obtained. Generalizations to ballot type probabilities of which negative binomial probabilities are special cases are considered. Since the probabilities do not form a proper distribution, a modification is introduced and new distributions of orderk for Markov dependent trials are developed.
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Mohanty, S.G. Success runs of lengthk in Markov dependent trials. Ann Inst Stat Math 46, 777–796 (1994). https://doi.org/10.1007/BF00773482
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DOI: https://doi.org/10.1007/BF00773482