Approximation of the difference of two Poisson-like counts by Skellam. (26th July 2018)

• Record Type: Journal Article
• Authors: Gan, H. L.; Kolaczyk, Eric D.
• Is Part Of: Journal of applied probability. Volume 55:Number 2(2018)
• Page Start: 416
• Page End: 430
• Publication Date: 2018-07-26
• Subjects: Skellam approximation, -- Stein's method, -- Poisson approximation; Primary 62E17, -- Secondary 60F05, -- 60J27; 519.2
• DOI: 10.1017/jpr.2018.27
• Languages: English
• ISSNs: 0021-9002

Abstract

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.