Computing (Bivariate) Poisson Moments Using Stein–Chen Identities

Abstract

–The (bivariate) Poisson distribution is the most common distribution for (bivariate) count random variables. The univariate Poisson distribution is characterized by the famous Stein–Chen identity. We demonstrate that this identity allows to derive even sophisticated moment expressions in such a simple way that the corresponding computations can be presented in an introductory statistics class. Then, we newly derive different types of Stein–Chen identity for the bivariate Poisson distribution. These are shown to be very useful for computing joint moments, again in a surprisingly simple way. We also explain how to extend our results to the general multivariate case.