# Non-uniform Bounds in the Poisson Approximation with Applications to Informational Distances. I

## TL;DR

This paper derives asymptotically optimal bounds for how much Bernoulli convolutions deviate from the Poisson distribution, using informational distances like Shannon entropy and chi-squared, based on non-uniform density estimates.

## Contribution

It introduces new non-uniform bounds for deviations of Bernoulli convolutions from the Poisson limit in terms of informational distances.

## Key findings

- Established asymptotically optimal bounds for deviations
- Applied bounds to non-homogeneous Bernoulli models
- Enhanced understanding of informational distances in Poisson approximation

## Abstract

We explore asymptotically optimal bounds for deviations of Bernoulli convolutions from the Poisson limit in terms of the Shannon relative entropy and the Pearson $\chi^2$-distance. The results are based on proper non-uniform estimates for densities. They deal with models of non-homogeneous, non-degenerate Bernoulli distributions.