The Annals of Probability
- Ann. Probab.
- Volume 31, Number 4 (2003), 1754-1771.
Kerstan's method for compound Poisson approximation
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.
Ann. Probab., Volume 31, Number 4 (2003), 1754-1771.
First available in Project Euclid: 12 November 2003
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Compound Poisson approximation discrete self-decomposable distributions discrete unimodal distributions finite signed measure Kerstan's method sums of independent random variables total variation distance
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