Effects of Variations From Gamma-Poisson Assumptions

Two types of variations from negative binomial frequency are considered: mixtures of Poisson other than Gamma, and Poisson parameters that change over time. Any severity distribution can be used instead of the Gamma as a mixing distribution, and Bayesian estimators are easy to calculate from the mixed probabilities. In the case of changing frequencies over time, the Gerber-Jones model is illustrated for calculating credibilities. The Bailey-Simon method is found to be useful for testing model assumptions.