Non-Uniform Bounds in the Poisson Approximation with Applications to Informational Distances. II

Abstract

We explore asymptotically optimal bounds for deviations of distributions of independent Bernoulli random variables from the Poisson limit in terms of the Shannon relative entropy and R\'enyi/Tsallis relative distances (including Pearson's $\chi^2$). This part generalizes the results obtained in Part I and removes any constraints on the parameters of the Bernoulli distributions.