A bound for the distribution of the sum of discrete associated or negatively associated random variables

Abstract

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.