An expansion of the probability mass function that may be used to improve Poisson approximations (Q1855630)

Two different expansion methods for improving Poisson approximations are presented and compared. The first expansion (of Edgeworth-type) is based on approximation of the moment generating function and leads to accurate results near the mean of the distribution. The second (so-called pfm-based) expansion focuses on approximating the probability mass function directly. Properties of pmf-based expansions are investigated. It occurs that these expansions give accurate results in the tails of the distributions but have problems for points near the mean. Thus these two expansions have their strength in totally different parts of distributions, but pfm-based expansions may often be effective when Poisson approximations seem unreasonable.