TITLE:
An Exceptional Generalization of the Poisson Distribution
AUTHORS:
Per-Erik Hagmark
KEYWORDS:
Count Data; Gamma Function; Poisson Generalization; Discretization; Modeling; Over/Under-Dispersion; Zero-Inflation/Deflation
JOURNAL NAME:
Open Journal of Statistics,
Vol.2 No.3,
July
6,
2012
ABSTRACT: 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.