Abstract
The exact probability distribution functions (pdf's) of the sooner andlater waiting time random variables (rv's) for the succession quota problemare derived presently in the case of Markov dependent trials. This is doneby means of combinatorial arguments. The probability generating functions(pgf's) of these rv's are then obtained by means of enumerating generatingfunctions (enumerators). Obvious modifications of the proofs provideanalogous results for the occurrence of frequency quotas and such a resultis established regarding the pdf of a frequency and succession quotas rv.Longest success and failure runs are also considered and their jointcumulative distribution function (cdf) is obtained.
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Antzoulakos, D.L., Philippou, A.N. Probability Distribution Functions of Succession Quotas in the Case of Markov Dependent Trials. Annals of the Institute of Statistical Mathematics 49, 531–539 (1997). https://doi.org/10.1023/A:1003123013300
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DOI: https://doi.org/10.1023/A:1003123013300