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• W2090073576 abstract "The Polya-Eggenberger sampling scheme is considered, i.e., a ball is drawn at random from an urn containing w white (success) balls and b black (failure) balls, its color is observed, and then it is returned to the urn along with s additional balls of the same color of the ball drawn. This scheme is repeated n times, and N n, k, l, s denotes the number of l-overlapping success runs of length k. If the balls drawn are arranged on a circle, the number of l-overlapping success runs of length k is denoted by . Finally, W r, k, l, s denotes the number of drawings according to the Polya-Eggenberger sampling scheme until the rth occurrence of the l-overlapping success run of length k. Polya, inverse Polya, and circular Polya distributions of order k for l-overlapping success runs of length k are introduced as the distributions, respectively, of N n, k,l, s , W r, k, l, s , and . These distributions include as special cases known and new distributions of order k. Exact formulae are derived for their probability distribution functions and means, which generalize several results on well-known distributions of order k. Asymptotic results of the new distributions are also given, relating them, respectively, to the binomial, negative binomial, and circular binomial distributions of order k for l-overlapping success runs of length k." @default.
• W2090073576 created "2016-06-24" @default.
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• W2090073576 date "2007-03-09" @default.
• W2090073576 modified "2023-09-27" @default.
• W2090073576 title "Polya, Inverse Polya, and Circular Polya Distributions of Order<i>k</i>for<i>l</i>-Overlapping Success Runs" @default.
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• W2090073576 doi "https://doi.org/10.1080/03610920601033942" @default.
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