## The Annals of Probability

### Compound Poisson Approximation for Nonnegative Random Variables Via Stein's Method

#### Abstract

The aim of this paper is to extend Stein's method to a compound Poisson distribution setting. The compound Poisson distributions of concern here are those of the form POIS$(\nu)$, where $\nu$ is a finite positive measure on $(0, \infty)$. A number of results related to these distributions are established. These in turn are used in a number of examples to give bounds for the error in the compound Poisson approximation to the distribution of a sum of random variables.

#### Article information

Source
Ann. Probab., Volume 20, Number 4 (1992), 1843-1866.

Dates
First available in Project Euclid: 19 April 2007

https://projecteuclid.org/euclid.aop/1176989531

Digital Object Identifier
doi:10.1214/aop/1176989531

Mathematical Reviews number (MathSciNet)
MR1188044

Zentralblatt MATH identifier
0765.60015

JSTOR