Non-uniform approximations for sums of discrete m-dependent random variables

TL;DR

This paper develops non-uniform approximation bounds for various discrete distributions to sums of m-dependent integer-valued random variables, with applications to Poisson binomial, 2-runs, and m-dependent events.

Contribution

It provides new non-uniform estimates for several classical distributions in the context of m-dependent sums, extending previous approximation techniques.

Findings

Derived bounds for Wasserstein metric from the main estimates.

Applied results to Poisson binomial, 2-runs, and m-dependent (k1,k2)-events.

Enhanced understanding of approximation accuracy for dependent discrete sums.

Abstract

Non-uniform estimates are obtained for Poisson, compound Poisson, translated Poisson, negative binomial and binomial approximations to sums of of m-dependent integer-valued random variables. Estimates for Wasserstein metric also follow easily from our results. The results are then exemplified by the approximation of Poisson binomial distribution, 2-runs and $m$-dependent $(k_1,k_2)$-events.