Gumbel分布的简单贝叶斯估计  

A Simple Bayesian Estimation of the Gumbel Distribution

作　　者：鲁万波[1] 焦鹏[1] 

机构地区：[1]西南财经大学统计学院,四川成都610074

出　　处：《数理统计与管理》2011年第2期234-239,共6页Journal of Applied Statistics and Management

基　　金：四川省统计科学研究计划项目(2008sc093);西南财经大学"211工程"三期青年教师成长项目(211QN09020);西南财经大学"211工程三期"统计学重点学科建设项目资助

摘　　要：在实际应用中,两参数Gumbel分布的贝叶斯估计往往需要预先知道Gumbel参数的二维联合先验分布。由于获取先验分布的主观性和统计推断的复杂性,目前有关Gumbel分布贝叶斯估计理论及其性质的讨论还比较少,更不要说获得较为简单的Gumbel分布的贝叶斯估计。本文基于Kaminskiy和Vasiliy提出的简单贝叶斯估计过程,利用可靠度函数估计的区间形式表示先验信息,从而得到两个参数Gumbel分布的简单贝叶斯估计。基于此先验信息,该估计过程构造了Gumbel参数的连续联合先验分布,给出了在给定任意时点的可靠度(或累积密度)及其标准差的后验估计,为可靠性与风险评估中简单快速的使用贝叶斯估计刻画极端事件提供了可能.In practice,it is necessary to know a two- dimensional joint prior distribution of the Gumbel parameters in advance for making Bayesian estimation of two-parameter Gumbel distribution.It is relatively few results to discuss the theory and nature of Bayesian estimation of two-parameter Gumbel distribution,not to mention gaining the simply Bayesian estimation.This paper obtains Bayesian estimation of two-parameter Gumbel distribution by using a simple Bayesian estimation procedure proposed by Kaminskiy and Vasiliy.Based on this prior information,which can be presented in the form of the interval assessment of the reliability function,the procedure allows constructing the continuous joint prior distribution of Gumbel parameters as well as the posterior estimates of the mean and standard deviation of the estimated reliability function（or the cumulative density function） at any given value of the exposure variable.It is possible to quickly depict extreme event by using the simple Bayesian estimation in reliability and risk assessment.

关 键 词：可靠性与风险评估 贝叶斯估计 BETA分布 Gumbel分布 

分 类 号：O212.8[理学—概率论与数理统计] O213.2[理学—数学]