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

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  • Aaron Childs

    (McMaster University)

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).

Suggested Citation

  • Aaron Childs, 2010. "Vector Extensions of the Dirichlet HC and HD Functions, with Applications to the Sharing Problem," Methodology and Computing in Applied Probability, Springer, vol. 12(1), pages 91-109, March.
    • Handle: RePEc:spr:metcap:v:12:y:2010:i:1:d:10.1007_s11009-008-9094-2
    DOI: 10.1007/s11009-008-9094-2
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    References listed on IDEAS

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    1. Milton Sobel & M. Ebneshahrashoob & J. Y. Lin, 1989. "Application of dirichlet integrals for curtailment problems in sampling inspection," Naval Research Logistics (NRL), John Wiley & Sons, vol. 36(2), pages 215-238, April.
    2. Sobel, Milton & Wells, Martin, 1990. "Dirichlet integrals and moments of gamma distribution order statistics," Statistics & Probability Letters, Elsevier, vol. 9(5), pages 431-437, May.
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