## The Annals of Probability

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

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

#### 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