On construction and simulation of count data models

The mean–variance range and the shape flexibility are important measures of the applicability of a count data model. This paper develops a method for constructing nonnegative integer-valued random variables with any interval domain, any theoretically possible mean–variance pair, and different shapes. The basic tool is a simple mean-preserving discretization procedure for random variables. Two corresponding variate generation algorithms are derived, and shown to be comparable to the alias method. As an application, our method enables production of count data models with full under- and over-dispersion flexibility and desired shape.