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An Exceptional Generalization of the Poisson Distribution
Department of Mechanics and Design, Tampere University of Technology, Tampere, Finland
- 1 Department of Mechanics and Design, Tampere University of Technology, Tampere, Finland
Open Journal of Statistics·Volume 02 (2012)·Pages 313–318·Published 27 June 2012·DOI10.4236/ojs.2012.23039
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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.
KeywordsCount DataGamma FunctionPoisson GeneralizationDiscretizationModelingOver/Under-DispersionZero-Inflation/Deflation
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