  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.
