过度离散型数据的统计模拟与分析

Simulation Study and Analysis of Overdispersion Data

针对车险索赔次数数据经常出现的过度离散问题,采用数值模拟的方法,分别使用泊松模型(Poisson)、负二项回归模型(NB)以及广义泊松模型(GP)对不同程度的过度离散车险索赔次数数据进行拟合,并用均方误差、偏差以及AIC和BIC准则对Poisson、NB、GP三种模型的优良性进行比较分析,得到了不同条件下三种模型的优良性,并针对不同的条件给出了模型选择的建议.

Aiming at the overdispersion problem of vehicle insurance claims data, based on numerical simulation method, this paper used Poisson model（Poisson）, Negative Binomial model （NB）, Generalized Poisson model（GP） to fit the vehicle insurance claims data with different degrees of overdispersion. Moreover, we compared the superiority of the three models with mean square error（MSE）, average bias, AIC criterion, and BIC criterion. Finally, we got the superiority of three models and gave suggestions for selecting model in different conditions.