复合泊松分布参数估计的EM算法  

The EM Algorithm for Estimation of Parameters of Compound Poission Distribution

作　　者：王翠莲[1] 刘晓[1] 

机构地区：[1]安徽师范大学数学计算机科学学院,安徽芜湖241000

出　　处：《安徽师范大学学报（自然科学版）》2011年第2期103-106,共4页Journal of Anhui Normal University(Natural Science)

基　　金：安徽师范大学青年基金项目(2009xqn57);安徽师范大学青年基金项目(2009xqnzc15)

摘　　要：复合泊松分布是非寿险精算中的重要理赔模型,利用正规的统计方法(如极大似然估计)估计模型的参数往往比较困难,而矩估计的精度在大样本下才能有令人满意的结果.本文应用EM算法研究了复合泊松分布的参数估计问题,给出了参数满足的方程,并给出了参数的矩估结果,对两种参数估计结果,通过计算机模拟,表明EM算法对参数的估计更为有效,且EM算法在小样本下就能得到较好的估计效果.Compound poission distribution is an important claim model in non-life insurance.It is difficult to estimate the paramenters of the model by normal methods（for example the maximum-likelihood estimation）.And the precision of moments estimation has a satisfactory result under large samples.This paper studies parameters estimation for compound poission distribution by the EM algorithm,and obtains equations the parameters satisfy.We get the reasonable results that the EM algorithm is more effective than moments estimation through computer of simulations,and the EM algorithm has a preferable result under small samples.

关 键 词：复合泊松分布 EM算法 矩估计 指数分布 

分 类 号：O212.2[理学—概率论与数理统计]