一个新的复合极值分布  

A New Compound Extreme Value Distribution

作　　者：刘维钊[1] 

机构地区：[1]武汉大学经济与管理学院,湖北武汉430072

出　　处：《长江大学学报（自科版）（上旬）》2013年第2期10-13,共4页JOURNAL OF YANGTZE UNIVERSITY (NATURAL SCIENCE EDITION) SCI ＆ ENG

基　　金：国家自然科学基金项目(10771163)

摘　　要：提出了一个新的具有单调降危险率的厚尾分布,该分布通过"混合"Pareto分布和Poisson分布而成,是一种复合极值分布。导出了新分布的概率统计特性,研究了各种可应用于风险分析和可靠性工程的特征量(包括矩、熵、危险率函数、平均剩余寿命等),获得了未知参数极大似然估计的存在唯一性。数值模拟表明该极大似然估计具有良好的有限样本性质。A new heavy-tailed distribution with decreasing hazard rate is proposed.This new distribution is derived by mixing Pareto and Poisson distributions,which is one kind of compound extreme value distributions.Statistical properties of the new distribution are derived.Various characteristic quantities used for risk analysis and reliability engineering including its moments,entropy,hazard rate and mean residual life are studied.The existence and uniqueness of maximum likelihood estimate of the unknown parameter in the introduced distribution are obtained and simulation studies are performed.

关 键 词：PARETO分布 POISSON分布 极值分布 极大似然估计 

分 类 号：O212[理学—概率论与数理统计]