Various accident frequency models have appeared in the literature which predict the distribution of future accidents based on the number of past accidents. This article presents a method for deriving such distributions using several predictive criteria. It is assumed that an individual's accident experience is a Poisson process with the parameter a linear function of criterion variables. An iterative weighted least-squares procedure is used to solve the system of maximum likelihood equations required for estimating this parameter and a large sample test procedure is illustrated. The tenability of the model is viewed in the light of actual data.