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

## TL;DR

This paper extends previous work on bounds for how closely sums of independent Bernoulli variables approximate a Poisson distribution, using various informational distances, without parameter restrictions.

## Contribution

It generalizes earlier results by removing parameter constraints, providing asymptotically optimal bounds for distribution deviations in informational distances.

## Key findings

- Derived bounds for Bernoulli sums in terms of Shannon and Rényi distances
- Extended previous results to all Bernoulli parameters without restrictions
- Provided asymptotically optimal bounds for distribution deviations

## 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.