The Annals of Probability

Kerstan's method for compound Poisson approximation

Bero Roos

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Abstract

We consider the approximation of the distribution of the sum of independent but not necessarily identically distributed random variables by a compound Poisson distribution and also by a finite signed measure of higher accuracy. Using Kerstan's method, some new bounds for the total variation distance are presented. Recently, several authors had difficulties applying Stein's method to the problem given. For instance, Barbour, Chen and Loh used this method in the case of random variables on the nonnegative integers. Under additional assumptions, they obtained some bounds for the total variation distance containing an undesirable log term. In the present paper, we shall show that Kerstan's approach works without such restrictions and yields bounds without log terms.

Article information

Source
Ann. Probab., Volume 31, Number 4 (2003), 1754-1771.

Dates
First available in Project Euclid: 12 November 2003

Permanent link to this document
https://projecteuclid.org/euclid.aop/1068646365

Digital Object Identifier
doi:10.1214/aop/1068646365

Mathematical Reviews number (MathSciNet)
MR2016599

Zentralblatt MATH identifier
1041.62011

Subjects
Primary: 62E17: Approximations to distributions (nonasymptotic)
Secondary: 60F05: Central limit and other weak theorems 60G50: Sums of independent random variables; random walks

Keywords
Compound Poisson approximation discrete self-decomposable distributions discrete unimodal distributions finite signed measure Kerstan's method sums of independent random variables total variation distance

Citation

Roos, Bero. Kerstan's method for compound Poisson approximation. Ann. Probab. 31 (2003), no. 4, 1754--1771. doi:10.1214/aop/1068646365. https://projecteuclid.org/euclid.aop/1068646365


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