The Annals of Probability

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

A. D. Barbour, Louis H. Y. Chen, and Wei-Liem Loh

Full-text: Open access

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

Permanent link to this document
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
links.jstor.org

Subjects
Primary: 60E15: Inequalities; stochastic orderings
Secondary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)

Keywords
Stein's method compound Poisson distribution total variation distance rate of convergence

Citation

Barbour, A. D.; Chen, Louis H. Y.; Loh, Wei-Liem. Compound Poisson Approximation for Nonnegative Random Variables Via Stein's Method. Ann. Probab. 20 (1992), no. 4, 1843--1866. doi:10.1214/aop/1176989531. https://projecteuclid.org/euclid.aop/1176989531


Export citation