# Improving approximation error bounds via truncation

## TL;DR

This paper improves Poisson approximation error bounds by using truncated negative binomial distributions to match supports, leading to more accurate approximations in cases with finite support.

## Contribution

It introduces a novel approach of truncating negative binomial distributions to enhance Poisson approximation accuracy and error bounds.

## Key findings

- Truncation improves approximation error bounds.
- Matching supports reduces approximation errors.
- Method applicable to finite support scenarios.

## Abstract

One aspect of Poisson approximation is that the support of the random variable of interest is often finite while the support of the Poisson distribution is not. In this paper we will remedy this by examining truncated negative binomial (of which Poisson is a special limiting case) approximation, so as to match the two supports of both distributions, and show that this will lead to improvements in the error bounds of the approximation.