A bound on Poisson approximation for independent binomial random variables

摘要

This paper uses the Stein-Chen method and the binomial w-functions toderive a non-uniform bound for approximating the cumulative distribu-tion function of a sum of independent binomial random variables, eachwith parameters mi and pi, by a cumulative Poisson distribution func-tion with meanPni=1mipi. With this bound, the cumulative Poissondistribution function can be used as an approximation of the cumulativedistribution function of the summands when all pi are small.