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April, 1987 Asymptotic Expansions in the Poisson Limit Theorem
A. D. Barbour
Ann. Probab. 15(2): 748-766 (April, 1987). DOI: 10.1214/aop/1176992169


Asymptotic expansions for the distributions of sums of independent nonnegative integer random variables in the neighbourhood of the Poisson distribution are derived, together with explicit estimates of the truncation error. Expansions are also derived for the expectations of at most polynomially growing functions of such sums. Applications to the Poisson binomial and Poisson negative binomial approximations are considered. The method used is an adaptation of the Stein-Chen approach.


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A. D. Barbour. "Asymptotic Expansions in the Poisson Limit Theorem." Ann. Probab. 15 (2) 748 - 766, April, 1987.


Published: April, 1987
First available in Project Euclid: 19 April 2007

zbMATH: 0622.60049
MathSciNet: MR885141
Digital Object Identifier: 10.1214/aop/1176992169

Primary: 60G50
Secondary: 60F05

Keywords: asymptotic expansions , nonnegative summands , Poisson approximation

Rights: Copyright © 1987 Institute of Mathematical Statistics

Vol.15 • No. 2 • April, 1987
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