On the Poisson approximation of random diagonal sums of Bernoulli matrices

TL;DR

This paper develops new explicit bounds for approximating the distribution of random diagonal sums of Bernoulli matrices with a Poisson distribution, improving upon previous results using the Stein-Chen method.

Contribution

It introduces novel explicit inequalities for various distances between the sum's distribution and Poisson, including bounds that surpass earlier known results.

Findings

Improved bounds for total variation, Wasserstein, and local distances.

Explicit inequalities derived using the Stein-Chen method.

Enhanced approximation accuracy for Bernoulli matrix diagonal sums.

Abstract

We use the Stein-Chen method to prove new explicit inequalities for the total variation, Wasserstein and local distances between the distribution of a random diagonal sum of a Bernoulli matrix and a Poisson distribution. Approximation results using a finite signed measure of higher order are given as well. Some of our bounds improve on those in Theorem 4.A of A.D. Barbour, L. Holst and S. Janson (Poisson approximation. Clarendon Press, Oxford, 1992).