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.
Publié le : 2003-10-14
Classification:
Compound Poisson approximation,
discrete self-decomposable distributions,
discrete unimodal distributions,
finite signed measure,
Kerstan's method,
sums of independent random variables,
total variation distance,
62E17,
60F05,
60G50
@article{1068646365,
author = {Roos, Bero},
title = {Kerstan's method for compound Poisson approximation},
journal = {Ann. Probab.},
volume = {31},
number = {1},
year = {2003},
pages = { 1754-1771},
language = {en},
url = {http://dml.mathdoc.fr/item/1068646365}
}
Roos, Bero. Kerstan's method for compound Poisson approximation. Ann. Probab., Tome 31 (2003) no. 1, pp. 1754-1771. http://gdmltest.u-ga.fr/item/1068646365/