Open Access
October 2003 Kerstan's method for compound Poisson approximation
Bero Roos
Ann. Probab. 31(4): 1754-1771 (October 2003). DOI: 10.1214/aop/1068646365


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.


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Bero Roos. "Kerstan's method for compound Poisson approximation." Ann. Probab. 31 (4) 1754 - 1771, October 2003.


Published: October 2003
First available in Project Euclid: 12 November 2003

zbMATH: 1041.62011
MathSciNet: MR2016599
Digital Object Identifier: 10.1214/aop/1068646365

Primary: 62E17
Secondary: 60F05 , 60G50

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

Rights: Copyright © 2003 Institute of Mathematical Statistics

Vol.31 • No. 4 • October 2003
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