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August, 1975 A General Poisson Approximation Theorem
R. J. Serfling
Ann. Probab. 3(4): 726-731 (August, 1975). DOI: 10.1214/aop/1176996313


A sum of nonnegative integer-valued random variables may be treated as a Poisson variable if the summands have sufficiently high probabilities of taking 0 value and sufficiently weak mutual dependence. This paper presents simple exact upper bounds for the error of such an approximation. An application is made to obtain a new extension for dependent events of the divergent part of the Borel-Cantelli lemma. The bounds are illustrated for the case of Markov-dependent Bernoulli trials. The method of the paper is to reduce the general problem to the special case of independent 0-1 summands and then make use of known bounds for this special case.


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R. J. Serfling. "A General Poisson Approximation Theorem." Ann. Probab. 3 (4) 726 - 731, August, 1975.


Published: August, 1975
First available in Project Euclid: 19 April 2007

zbMATH: 0321.60018
MathSciNet: MR380946
Digital Object Identifier: 10.1214/aop/1176996313

Primary: 60F05

Keywords: Borel-Cantelli lemma , dependent summands , Markov-dependent Bernoulli trials , Poisson approximation

Rights: Copyright © 1975 Institute of Mathematical Statistics


Vol.3 • No. 4 • August, 1975
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