Let $X_1, X_2,\dots, X_n$ be a sequence of integer-valued random
variables that are either associated or negatively associated.We present a
simple upper bound for the distance between the distribution of the sumof $X_i$
and a sum of $n$ independent randomvariables with the same marginals as
$X_i$. An upper bound useful for establishing a compound Poisson approximation
for $\Sigma_{i=1}^nX_i$ is also provided. The new bounds are of the same order
as the much acclaimed Stein–Chen bound.
Publié le : 2000-11-14
Classification:
Association,
negative association,
positive-negative dependence,
probability metrics,
compound Poisson approximation,
rate of convergence,
60E15,
62E17,
60G50
@article{1019487610,
author = {Boutsikas, Michael V. and Koutras, Markos V.},
title = {A bound for the distribution of the sum of discrete associated or
negatively associated random variables},
journal = {Ann. Appl. Probab.},
volume = {10},
number = {2},
year = {2000},
pages = { 1137-1150},
language = {en},
url = {http://dml.mathdoc.fr/item/1019487610}
}
Boutsikas, Michael V.; Koutras, Markos V. A bound for the distribution of the sum of discrete associated or
negatively associated random variables. Ann. Appl. Probab., Tome 10 (2000) no. 2, pp. 1137-1150. http://gdmltest.u-ga.fr/item/1019487610/