Asymptotic factorial powers expansions for binomial and negative binomial reciprocals
Author:
Grzegorz A. Rempala
Journal:
Proc. Amer. Math. Soc. 132 (2004), 261272
MSC (2000):
Primary 60E05, 62E20; Secondary 11B15, 05A16
Published electronically:
August 13, 2003
MathSciNet review:
2021270
Fulltext PDF Free Access
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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 . 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:
http://dx.doi.org/10.1090/S000299390307254X
PII:
S 00029939(03)07254X
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
