## The Annals of Probability

### Two Applications of a Poisson Approximation for Dependent Events

Norman Kaplan

#### 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

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