基于指数威布尔分布的组合统计模型

Composite Statistical Model Based on Exponential Weibull Distribution

保险损失数据具有尖峰厚尾的特点，使用单一分布对这类数据的拟合效果一般都不理想。文章构建一类组合统计模型，在模型中使用指数威布尔分布拟合小额损失而用转换的贝塔分布族拟合高额损失。利用组合模型密度的连续性条件，可以获得权重系数的解析表达式及阈值的数值解。使用R语言对丹麦火险数据进行分布拟合，给出六种组合模型的参数估计及拟合优度的比较。并根据似然比检验，对指数威布尔组合模型和相应的威布尔组合模型做对比分析。

Insurance loss data is characterized by sharp peak and heavy tail, and the fitting effect of this type of data by using single distribution usually does not give ideal performance. This paper constructs a new composite model, in which the exponential Weibull distribution is used to fit the smaller losses and a family of transformed beta distribution to fit larger losses. The continuity of the composite model density is used to obtain the analytical expression of weight coefficient and the numerical solution of threshold. The paper uses the R language to fit the Danish fire insurance loss data, and offers the parameter estimates of six com- posite models and the comparison of goodness-of-fit. Finally the paper conducts a contrastive analysis on the Exponential Weibull composite model and corresponding Weibull composite model by use of likelihood ratio test.