Asymptotic factorial powers expansions for binomial and negative binomial reciprocals

Author:
Grzegorz A. Rempala

Journal:
Proc. Amer. Math. Soc. **132** (2004), 261-272

MSC (2000):
Primary 60E05, 62E20; Secondary 11B15, 05A16

DOI:
https://doi.org/10.1090/S0002-9939-03-07254-X

Published electronically:
August 13, 2003

MathSciNet review:
2021270

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: By considering the variance formula for a shifted reciprocal of a binomial proportion, the asymptotic expansions of any order for first negative moments of binomial and negative binomial distributions truncated at zero are obtained. The expansions are given in terms of the factorial powers of the number of trials . The obtained formulae are more accurate than those of Marciniak and Wesoowski (1999) and simpler, as they do not involve the Eulerian polynomials.

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Additional Information

**Grzegorz A. Rempala**

Affiliation:
Department of Mathematics, University of Louisville, Louisville, Kentucky 40292

Email:
grzes@louisville.edu

DOI:
https://doi.org/10.1090/S0002-9939-03-07254-X

Keywords:
Factorial power,
asymptotic expansions,
indirect estimator,
inverse moments,
elementary symmetric polynomial,
positive binomial distribution,
truncated negative binomial distribution

Received by editor(s):
March 1, 2001

Received by editor(s) in revised form:
August 1, 2002

Published electronically:
August 13, 2003

Dedicated:
To my parents

Communicated by:
Richard A. Davis

Article copyright:
© Copyright 2003
American Mathematical Society