Abstract
The Bernoulli and Poisson are two popular discrete count processes; however, both rely on strict assumptions that motivate their use. We instead propose a generalized count process (the Conway-Maxwell-Poisson process) that not only includes the Bernoulli and Poisson processes as special cases, but also serves as a flexible mechanism to describe count processes that approximate data with over- and under-dispersion. We introduce the process and its associated generalized waiting time distribution with several real-data applications to illustrate its flexibility for a variety of data structures.
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