On hypergeometric and related distributions of order k

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Let Nn,k,g,d be the hypergeometric random variable of order k≥1, equal to the number of success runs of length k contained in an ordered without replacement sample of size n drawn from a dichotomous urn. with g good items and d defectives. We give an alternative formula for P(Nn,k,g,d=x) that is computationally simpler than the one in Panaretos and Xekalaki (1986). Distributions of the longest success run and of waiting times for r≥1 runs of length k are also derived. We call the latter the waiting time hypergeometric r.v. of order k. © 1990, Taylor & Francis Group, LLC. All rights reserved.

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Communications in Statistics - Theory and Methods