On moderate deviations in Poisson approximation

Abstract

The tail behaviour of Poisson distribution is very different from that of normal distribution and the right tail probabilities of counts of rare events are generally better approximated by the moderate deviations in Poisson distribution. We demonstrate that the moderate deviations in Poisson approximation generally require an adjustment and, with suitable adjustment, we establish better error estimates of the moderate deviations in Poisson approximation than those in [Chen, Fang & Shao (2013a)]. Our estimates contain no unspecified constants and are easy to apply. We illustrate the use of the theorems in three applications: Poisson binomial distribution, matching problem and 2-runs. The paper complements the works of [Chen & Choi (1992), Barbour, Chen & Choi (1995), Chen, Fang & Shao (2013a].