The Annals of Probability

Two Applications of a Poisson Approximation for Dependent Events

Norman Kaplan

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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.

Article information

Source
Ann. Probab., Volume 5, Number 5 (1977), 787-794.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176995720

Digital Object Identifier
doi:10.1214/aop/1176995720

Mathematical Reviews number (MathSciNet)
MR445581

Zentralblatt MATH identifier
0379.60030

JSTOR
links.jstor.org

Subjects
Primary: 60K99: None of the above, but in this section

Keywords
Poisson approximation random covering urn scheme

Citation

Kaplan, Norman. Two Applications of a Poisson Approximation for Dependent Events. Ann. Probab. 5 (1977), no. 5, 787--794. doi:10.1214/aop/1176995720. https://projecteuclid.org/euclid.aop/1176995720


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