A pointwise Poisson approximation for independent binomial random variables

Abstract

This paper uses the Stein-Chen method and the binomial w-functions to derive a non-uniform bound for the point metric between the distribution of a sum of independent binomial random variables, each with parameters mi and pi, and a Poisson distribution with mean P n=1 mipi. In view of this bound, the Poisson distribution can be used as an approximation of the distribution of the summands when all pi are small.