广义指数-帕累托(Ⅳ)混合模型

On the mixtures of Exponentiated Exponential-Pareto(Ⅳ)model

有限多个分布的混合模型在经济学、可靠性分析等方面应用广泛.基于实践中的许多观测数据可能取自于两个或更多的分布总体,构建了广义指数-帕累托(Ⅳ)混合模型,并研究混合模型的相关统计性质.讨论了模型中各参数对密度函数的影响,给出了模型的风险函数的具体计算公式及参数对风险函数的影响.给出了混合模型前四阶矩的解析表达式,进而得出峰度和偏度等相关统计量的计算公式.给出了平均偏差的解析表达式,并且使用EM算法给出混合模型的参数估计.实证方面,使用丹麦火险数据做拟合分析,比较了7个模型的拟合效果.结果显示,广义指数-帕累托(Ⅳ)混合模型拟合效果最优.

The application of finite mixture models are widely used in economics and reliability analysis.Based on the fact that many observational data in practice may derive from a mixture population of two or more distributions,we construct the Exponentiated Exponential-Pareto(Ⅳ)mixture model and study the related statistical properties.We discuss the influence of the parameters in the mixture model on the density function and consider the hazard function,the influence of the parameters on the hazard function is also depicted.We give the analytic expressions of the first fourth order moments,and the exact formulas for kurtosis and skewness are obtained.The mean deviation is calculated and the parameters of the mixture model are estimated via EM algorithm.On the empirical aspects,we illustrate an application to the Danish fire loss data and compare the fitting effect of seven different models.The result exhibits the fact that the Exponentiated Exponential-Pareto(Ⅳ)mixture model might be a better fitting