A bound on the Poisson-binomial relative error

Abstract

This paper adapts the Stein–Chen method to determine a bound of the relative error of Poisson approximation to the binomial distribution with parameters n and p in the form of a distribution function. Furthermore, we also give a bound of the ratio among the binomial and Poisson distribution functions. For these bounds, it is pointed out that, for small p or small λ , n p , each result of the Stein–Chen method yields a good Poisson approximation. Finally, we give some numerical examples for each result.