A new approach to Poisson approximation is proposed. The basic idea is very simple and based on properties of the Charlier polynomials and the Parseval identity. Such an approach quickly leads to new effective bounds for several Poisson approximation problems. A selected survey on diverse Poisson approximation results is also given. MSC 2000 Subject Classifications: Primary 62E17; secondary 60C...

The main purpose of this article is to introduce a new approach to Poisson approximation. Some bounds in Poisson approximation for probability distributions of a wide class of various arrays of row-wise independent discrete random variables are established via a probability distance. Some analogous results related to random sums in Poisson approximation are also considered.