Approximation of the difference of two Poisson-like counts with Skellam

TL;DR

This paper investigates how well the Skellam distribution approximates the difference of two Poisson-like counts, especially under weak dependence, with implications for network analysis and image processing.

Contribution

It generalizes existing results by characterizing the accuracy of Skellam approximation for Poisson-like counts under weak dependence, with more concise derivations.

Findings

Skellam distribution effectively approximates differences under weak dependence.

Theoretical bounds on approximation accuracy are established.

Applications demonstrated in network analysis and image processing.

Abstract

Poisson-like behavior for event count data is ubiquitous in nature. At the same time, differencing of such counts arises in the course of data processing in a variety of areas of application. As a result, the Skellam distribution -- defined as the distribution of the difference of two independent Poisson random variables -- is a natural candidate for approximating the difference of Poisson-like event counts. However, in many contexts strict independence, whether between counts or among events within counts, is not a tenable assumption. Here we characterize the accuracy in approximating the difference of Poisson-like counts by a Skellam random variable. Our results fully generalize existing, more limited results in this direction and, at the same time, our derivations are significantly more concise and elegant. We illustrate the potential impact of these results in the context of problems from network analysis and image processing, where various forms of weak dependence can be expected.