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.
Publié le : 1992-10-14
Classification:
Stein's method,
compound Poisson distribution,
total variation distance,
rate of convergence,
60E15,
60J10
@article{1176989531,
author = {Barbour, A. D. and Chen, Louis H. Y. and Loh, Wei-Liem},
title = {Compound Poisson Approximation for Nonnegative Random Variables Via Stein's Method},
journal = {Ann. Probab.},
volume = {20},
number = {4},
year = {1992},
pages = { 1843-1866},
language = {en},
url = {http://dml.mathdoc.fr/item/1176989531}
}
Barbour, A. D.; Chen, Louis H. Y.; Loh, Wei-Liem. Compound Poisson Approximation for Nonnegative Random Variables Via Stein's Method. Ann. Probab., Tome 20 (1992) no. 4, pp. 1843-1866. http://gdmltest.u-ga.fr/item/1176989531/