基于Gibbs抽样算法的三参数威布尔分布Bayes估计  

BAYESIAN ANALYSIS OF THREE-PARAMETER WEIBULL DISTRIBUTION BASED ON GIBBS SAMPLING ALGORITHM

作　　者：刘飞[1] 王祖尧[1] 窦毅芳[1] 张为华 

机构地区：[1]国防科技大学航天与材料工程学院,长沙410008

出　　处：《机械强度》2007年第3期429-432,共4页Journal of Mechanical Strength

基　　金：国家"863"计划(2003AA765030)资助项目~~

摘　　要：由于三参数威布尔分布概率密度函数较为复杂,后验分布的积分计算成为进行Bayes估计的主要障碍。利用Gibbs抽样算法研究Bayes估计的计算问题。首先描述Gibbs抽样算法的特点,在定数截尾寿命试验情形下,推导无先验信息的参数联合后验分布,然后,结合取舍抽样方法,设计计算参数Bayes估计的Gibbs抽样方案,最后给出一个算例。结果表明,与传统的数值积分法相比较,Gibbs抽样算法更加简便直接,更适于计算可靠性指标的Bayes估计。Because the probability density function of three-parameter Weibull distribution is complicated, the integral computations for posterior distribution have served as the main obstacle to implement Bayes analysis. The computational problem for posterior distribution is researched through the Gibbs samphng algorithm. Firstly, the characteristics of the Gibbs samphng are described. For type Ⅱ censored dada, the parameter joint posterior distribution is deduced for the non-information prior distribution. Then, combining with the adaptive rejection sampling （ARS）, the Gibbs sampling project is designed to compute the parameter Bayesian estimators. Lastly, the example is demonstrated. The results show that using Gibbs samphng algorithm to evaluate the Bayesian estimators is mote convenient and straightforward than the numerical integration method. And the Gibbs sampling algorithm is apt to evaluate the Bayesian estimators of the reliability indexes.

关 键 词：三参数威布尔分布 BAYES估计 GIBBS抽样 取舍抽样 可靠度 失效率 

分 类 号：TB114.3[理学—概率论与数理统计]