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

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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).

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  1. Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, Canada, L8S 4K1

    Aaron Childs

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  1. Aaron Childs
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Correspondence to Aaron Childs.

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Childs, A. Vector Extensions of the Dirichlet HC and HD Functions, with Applications to the Sharing Problem. Methodol Comput Appl Probab 12, 91–109 (2010). https://doi.org/10.1007/s11009-008-9094-2

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  • DOI: https://doi.org/10.1007/s11009-008-9094-2

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