%0 Journal Article
%T An Exceptional Generalization of the Poisson Distribution
%A Per-Erik Hagmark
%J Open Journal of Statistics
%P 313-318
%@ 2161-7198
%D 2012
%I Scientific Research Publishing
%R 10.4236/ojs.2012.23039
%X 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.
%K Count Data
%K Gamma Function
%K Poisson Generalization
%K Discretization
%K Modeling
%K Over/Under-Dispersion
%K Zero-Inflation/Deflation
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=20668