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

Let X1,X2,.,Xn 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 Xi and a sum of n independent randomvariables with the same marginals as Xi. An upper bound useful for establishing a compound Poisson approximation for .ni=1Xi is also provided. The new bounds are of the same order as the much acclaimed Stein.Chen bound.