重尾分布尾指数估计研究进展  

Advanced in Heavy-tailed Distribution Tail Index Estimation

作　　者：刘维奇[1] 邢红卫[1] 

机构地区：[1]山西大学管理学院,山西太原030006

出　　处：《山西大学学报（自然科学版）》2012年第2期163-173,共11页Journal of Shanxi University(Natural Science Edition)

基　　金：山西省高校人文社科重点研究基地项目(2011305)

摘　　要：气象、水文、环境、电信、保险、金融等许多领域的数据不满足正态分布假设,而是具有尖峰、重尾特征.过去三十多年间,针对重尾分布及尾指数估计的研究得到了长足发展.文章回顾了冲击正态性假设的重尾分布的发现过程,描述了重尾分布的定义,极值理论及正则变换条件,并从研究内容的阶段特征、研究方法的不同类型总结、归纳、评述了各类尾指数估计方法及重尾阈值选取方法,最后就这些估计方法的不足和应用局限性以及如何改进和深化重尾指数的估计问题作了展望.Many studies show that the data in application fields,such as meteorology,hydrology,environment,telecommunications,insurance and finance,does not meet the normal distribution assumption,but illustrates spikes and heavy tail characteristics.In the last three decades,the research on heavy-tailed distributions and tail index estimation has been developed rapidly.We review the discovery process of heavy-tailed distributions challenging the normal distribution assumption,and introduce several different definitions of the heavy-tailed distribution,extreme value theory and regular variation conditions;moreover,summarize different types of tail index estimators and methods of selecting the heavy tail threshold by development periods and method types,and discuss the characteristics and shortages of these methods,finally,in term of the deficiencies and limitations of current estimators,how to deepen and improve the problem are reviewed.

关 键 词：极值理论 重尾指数估计 重尾阈值 降偏差估计 

分 类 号：O212[理学—概率论与数理统计]