Weibull分布定时截尾寿命试验参数的近似联合置信域  

Simultaneous Confidence Region of Parameters for Weibull Distribution under Fix-Time Censored Test

作　　者：邹林全[1] 

机构地区：[1]常州技术师范学院经济管理系,常州213001

出　　处：《南京航空航天大学学报》2001年第2期194-196,共3页Journal of Nanjing University of Aeronautics & Astronautics

摘　　要：研究了 Weibull分布大样本定时截尾寿命试验 ,利用一种新的途径给出了试验参数的近似联合置信域。设产品寿命 X服从 Weibull分布 ,对 n个受试样本 x1 ,x2 ,… ,xn 进行定时 (时间为 t0 )截尾试验 ,得到观察数据 Si=min( xi,t0 ) ,i=1 ,2 ,… ,n。利用似然方程 ,分别得到参数 λ,b的极大似然估计 λ和 b。进一步考察联合分布 ( λ,b) ,可以用二元正态分布来近似。再利用多元正态分布与 X2 分布的关系 ,可以推导出未知参数 u=(λ,b)的置信度为 1 -α的联合置信区域 ( x-u)′I0 ( x-u)≤The fix time censored test of Weibull distribution is studied. By using a new method, the simultaneous confidence region of parameters is obtained. Suppose that the lifetime x of product is of W(λ,b) distribution, then we censor the data x i with fix time t 0 , and S i= min (x i,t 0) is available,( i=1,2,…,n ). When the maximum likelihood eguation is solved, the maximum likelihood estimator ( , ) of the parameter ( λ,b ) can be obtained. The simultaneous distribution of ( , ) is asymptotically convergent to two dimensional normal distribution . By using the relation between mutiple dimension normal distribution and X 2 distribution, the following conclusion is obtained,i.e.,when the confidence level is 1- α ,the simultaneous confidence region is the ellipse: (-u)′I 0(-u)≤x 2 α , where u=(λ,b) .

关 键 词：可行性 定时截尾试验 WEIBULL分布 极大似然估计 二元正态分布 联合置信域 

分 类 号：O213.2[理学—概率论与数理统计] TB114.3[理学—数学]