Vector Extensions of the Dirichlet HC and HD Functions, with Applications to the Sharing Problem

Aaron Childs ()
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Aaron Childs: McMaster University

Methodology and Computing in Applied Probability, 2010, vol. 12, issue 1, 91-109

Abstract: Abstract In this paper we apply the Dirichlet HC and HD functions to a generalization of the sharing problem in which the population is finite, and sampling is without replacement. In doing so we extend the Dirichlet HC and HD functions, and associated waiting time results, from Sobel and Frankowski (Congressus Numerantium 106:171–191, 1995) to handle vector arguments. We also provide Maple procedures for their computation. Our results for the sharing problem generalize the results for with replacement sampling given in Sobel and Frankowski (Am Math Mon 101:833–847, 1994a).

Keywords: Dirichlet I; J; C; D functions; Dirichlet HI; HJ; HC; HD functions; Sharing problem; Hypergeometric; Waiting time; Primary 60C05; Secondary 60-08 (search for similar items in EconPapers)
Date: 2010
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s11009-008-9094-2

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