双参数广义几何分布的 Bayes 估计及其应用

考虑具有双参数结构广义几何分布的Bayes估计问题, 给出分布中参数Bayes估计的精确表达式, 并将该分布应用于短期聚合风险模型中, 提出一类新的聚合风险模型, 给出分布函数的相关性质及聚合理赔量的近似模型. 数值模拟结果验证了Bayes估计具有渐近无偏性与相合性. 最后将该结果应用于汽车保险索赔数据中, 得到了不同索赔次数下的保单数量拟合结果.

Bayesian Estimation for Generalized Geometric Distributionwith Double-Parameters and Its Application

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.