Approximation Results for Sums of Independent Random Variables

TL;DR

This paper uses Stein's method to improve approximation bounds for sums of independent random variables by Poisson and geometric distributions, with applications to waiting time problems.

Contribution

It provides new, tighter error bounds for Poisson and geometric approximations of sums of independent variables using Stein's method.

Findings

Error bounds are comparable or better than existing results.

Application to waiting time distribution of 2-runs.

Improved approximation accuracy in total variation distance.

Abstract

In this article, we consider Poisson and Poisson convoluted geometric approximation to the sums of $n$ independent random variables under moment conditions. We use Stein's method to derive the approximation results in total variation distance. The error bounds obtained are either comparable to or improvement over the existing bounds available in the literature. Also, we give an application to the waiting time distribution of 2-runs.