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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
Published electronically: August 13, 2003
MathSciNet review: 2021270
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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 $n$. The obtained formulae are more accurate than those of Marciniak and Weso\lowski (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: http://dx.doi.org/10.1090/S0002-9939-03-07254-X
PII: S 0002-9939(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