Poisson approximation in χ2 distance by the Stein-Chen approach

Abstract

The main purpose of the paper is to investigate the possibility of applying the Stein-Chen approach to estimate the ${\mathit{\chi }}^2$ distance between Poisson distribution and Poisson binomial distribution. Earlier results concerning ${\mathit{\chi }}^2$ distance between the above mentioned distributions either used analytical approach heavily based on the analysis of the generating functions or on rather lengthy and complicated elementary calculations. Applying the Stein-Chen approach we succeed in providing a very quick proof of upper bounds for ${\mathit{\chi }}^2$ distance that are of comparable strength to the earlier estimates obtained by other approaches.