Relative Error of Scaled Poisson Approximation via Stein's Method

TL;DR

This paper investigates the accuracy of scaled Poisson approximations for weighted sums of independent Poisson variables, especially in tail distributions, by deriving bounds using a modified Stein-Chen method.

Contribution

It introduces a bound on the relative error of scaled Poisson approximation for tail probabilities using a novel Stein-Chen approach.

Findings

Established a bound on the relative approximation error.

Focused on tail distribution accuracy.

Applied a modified Stein-Chen method.

Abstract

We study the accuracy of a scaled Poisson approximation to the weighted sum of independent Poisson random variables, focusing on in particular the relative error of the tail distribution. A bound on the relative approximation error is established using a modified Stein-Chen method.