Author(s)

Per-Erik Hagmark

Department of Mechanics and Design, Tampere University of Technology, Tampere, Finland.

A new two-parameter count distribution is derived starting with probabilistic arguments around the gamma function and the digamma function. This model is a generalization of the Poisson model with a noteworthy assortment of qualities. For example, the mean is the main model parameter; any possible non-trivial variance or zero probability can be attained by changing the other model parameter; and all distributions are visually natural-shaped. Thus, exact modeling to any degree of over/under-dispersion or zero-inflation/deflation is possible.

Count Data; Gamma Function; Poisson Generalization; Discretization; Modeling; Over/Under-Dispersion; Zero-Inflation/Deflation

P. Hagmark, "An Exceptional Generalization of the Poisson Distribution," Open Journal of Statistics, Vol. 2 No. 3, 2012, pp. 313-318. doi: 10.4236/ojs.2012.23039.