EXACT AND APPROXIMATED RELATIONS BETWEEN NEGATIVE HYPERGEOMETRIC AND NEGATIVE BINOMIAL PROBABILITIES

Abstract

We derive orthogonal expansions in terms of the Meixner polynomials of the first kind for hypergeometric probabilities. We show how these expansions can be used to obtain negative binomial approximations to negative hypergeometric probabilities. Some limit properties of these approximations are studied and also the extension of these results to cumulative probabilities.

Keywords:

• Meixner polynomials of the first kind
• Orthogonal expansions
• Approximations of distributions

ACKNOWLEDGMENTS

This work was supported in part by Ministerio de Educaci ón y Cultura through Grants PB96-1416-C02-02 and HA-1977-0123. The authors also wish to express their gratitude to the reviewers and the Editor for their helpful comments.