Improved Lower Bounds on the Total Variation Distance for the Poisson Approximation

TL;DR

This paper introduces improved lower bounds on the total variation distance for Poisson approximation of sums of Bernoulli variables, enhancing the Chen-Stein method with a novel analytical modification.

Contribution

It presents a significant improvement in lower bounds using a modified Chen-Stein analysis, advancing the theoretical understanding of Poisson approximation accuracy.

Findings

New lower bounds are tighter than previous ones.

The modified analysis yields a surprising improvement.

Applications of the bounds are discussed.

Abstract

New lower bounds on the total variation distance between the distribution of a sum of independent Bernoulli random variables and the Poisson random variable (with the same mean) are derived via the Chen-Stein method. The new bounds rely on a non-trivial modification of the analysis by Barbour and Hall (1984) which surprisingly gives a significant improvement. A use of the new lower bounds is addressed.