Poisson Approximation and the Chen-Stein ethod

TLDR: The Chen-Stein method of Poisson approximation is a powerful tool for computing an error bound when approximating probabilities using the Poisson distribution as mentioned in this paper, in many cases, this bound may be given in terms of first and second moments alone.

Abstract: The Chen-Stein method of Poisson approximation is a powerful tool for computing an error bound when approximating probabilities using the Poisson distribution. In many cases, this bound may be given in terms of first and second moments alone. We present a background of the method and state some fundamental Poisson approximation theorems. The body of this paper is an illustration, through varied examples, of the wide applica- bility and utility of the Chen-Stein method. These examples include birth- day coincidences, head runs in coin tosses, random graphs, maxima of normal variates and random permutations and mappings. We conclude with an application to molecular biology. The variety of examples presented here does not exhaust the range of possible applications of the Chen-Stein method.