Asymptotics and sharp bounds in the Poisson approximation to the Poisson-binomial distribution

Abstract

The Poisson-binomial distribution is approximated by a Poisson law with respect to a new multi-metric (difference metric) unifying a broad class of probability metrics between discrete distributions. The accompanying non-metric situation is also considered leading to moderate- and large-deviation results. Using the Charlier B expansion and Fourier arguments, sharp bounds and asymptotic relations are given.