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October, 1977 Two Applications of a Poisson Approximation for Dependent Events
Norman Kaplan
Ann. Probab. 5(5): 787-794 (October, 1977). DOI: 10.1214/aop/1176995720

Abstract

Recent results have estimated the error when sums of dependent nonnegative integer-valued random variables are approximated in distribution by a Poisson variable. Two problems are considered where these results can be used to provide simple solutions. The first problem studies the asymptotic behavior, as $\alpha \rightarrow 0$, of the number of independent random arcs of length $\alpha$ needed to cover a circle of unit circumference at least $m$ times $(m \geqq 1)$. The second problem deals with urn schemes.

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Norman Kaplan. "Two Applications of a Poisson Approximation for Dependent Events." Ann. Probab. 5 (5) 787 - 794, October, 1977. https://doi.org/10.1214/aop/1176995720

Information

Published: October, 1977
First available in Project Euclid: 19 April 2007

zbMATH: 0379.60030
MathSciNet: MR445581
Digital Object Identifier: 10.1214/aop/1176995720

Subjects:
Primary: 60K99

Keywords: Poisson approximation , random covering , urn scheme

Rights: Copyright © 1977 Institute of Mathematical Statistics

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Vol.5 • No. 5 • October, 1977
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