The Annals of Probability

A General Poisson Approximation Theorem

R. J. Serfling

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Abstract

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.

Article information

Source
Ann. Probab., Volume 3, Number 4 (1975), 726-731.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176996313

Digital Object Identifier
doi:10.1214/aop/1176996313

Mathematical Reviews number (MathSciNet)
MR380946

Zentralblatt MATH identifier
0321.60018

JSTOR
links.jstor.org

Subjects
Primary: 60F05: Central limit and other weak theorems

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

Citation

Serfling, R. J. A General Poisson Approximation Theorem. Ann. Probab. 3 (1975), no. 4, 726--731. doi:10.1214/aop/1176996313. https://projecteuclid.org/euclid.aop/1176996313


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