GENERALIZED BINOMIAL AND NEGATIVE BINOMIAL DISTRIBUTIONS OF ORDER k BY THE/-OVERLAPPING ENUMERATION SCHEME
نویسنده
چکیده
A b s t r a c t . In this paper, we investigate the exact distribution of the waiting time for the r-th t-overlapping occurrence of success-runs of a specified length in a sequence of two state Markov dependent trials. The probability generating functions are derived explicitly, and as asymptotic results, relationships of a negative binomial distribution of order k and an extended Poisson distribution of order k are discussed. We provide further insights into the run-related problems from the viewpoint of the t-overlapping enumeration scheme. We also study the exact distribution of the number of t-overlapping occurrences of success-runs in a fixed number of trials and derive the probability generating functions. The present work extends several properties of distributions of order k and leads us a new type of geneses of the discrete distributions.
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