Extended Truncated Tweedie-Poisson Model

Abstract

It has been argued that by truncating the sample space of the negative binomial and of the inverse Gaussian-Poisson mixture models at zero, one is allowed to extend the parameter space of the model. Here that is proved to be the case for the more general three parameter Tweedie-Poisson mixture model. It is also proved that the distributions in the extended part of the parameter space are not the zero truncation of mixed Poisson distributions and that, other than under the negative binomial, they are not mixtures of zero truncated Poisson distributions either. By extending the parameter space one can improve the fit when the frequency of one is larger and the right tail is heavier than is allowed by the unextended model. Extending the model also allows one to use the maximum likelihood based inference tools when the m.l.e. does not exist under the unextended model. The extended model is proved useful in the analysis of frequency count data.