The Poisson distribution is the most commonly used distribution in the context of mortality modeling and insurance claims. This is however a choice of convenience and tradition, which often cannot be justified empirically. The inadequacy of the Poisson distribution is rooted in the restricting equality of its mean and variance.

However, alternative distributions can be generated within the class of Natural Exponential Families (NEF’s) whose variance functions allow nonlinear dependence between the variance V(m) and the mean m of the underlying distributions.

The aim of this talk is expose the audience to:

– NEF’s

– Exponential Dispersion Models

– Variance Functions of an NEF’s

– Mean value parameterization of NEF’s

– Polynomial Variance Functions of NEF’s supported on N0 (natural numbers)

If time permits, applications to mortality projections will be provided.