Abstract: We considered the Bayesian estimation problem for a generalized geometric distribution with doubleparameters structure, and gave the accurate expression of Bayesian estimator of the parameters from the distribution. The distribution was applied to the shortterm aggregation risk model. A new type of aggregation risk model was proposed, and the related properties of the distribution function and an approximate model of aggregate claim amount were given. The numerical simulation results verify the asymptotic unbiasedness and consistency of Bayesian estimation. Finally, the results are applied to the automobile insurance claim data, and the fitting results of the number of insurance policies under different claim times are obtained.

Key words: zeroinflated, Bayesian estimation, shortterm aggregation risk model, numerical simulation, auto insurance claim