# Compound Poisson approximation for nonnegative random variables via Stein's method

Barbour, A D; Chen, L; Loh, W-L (1992). Compound Poisson approximation for nonnegative random variables via Stein's method. The Annals of Probability, 20(4):1843-1866.

## 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.

## 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.

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Item Type: Journal Article, refereed, original work 07 Faculty of Science > Institute of Mathematics 510 Mathematics Stein's method, compound Poisson distribution, total variation distance, rate of convergence English 1992 13 Apr 2010 11:34 29 Jul 2020 19:51 Institute of Mathematical Statistics 0091-1798 Hybrid https://doi.org/10.1214/aop/1176989531

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