A bound on the Poisson-binomial relative error

This paper adapts the Stein–Chen method to determine a bound of the relative error of Poisson approximation to the binomial distribution with parameters nn and pp 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 pp or small λλ, npnp, each result of the Stein–Chen method yields a good Poisson approximation. Finally, we give some numerical examples for each result.