逐步Ⅱ型删失数据下BurrⅢ分布形状参数的估计

Estimation of Shape Parameter of Burr III Distribution under Progressive Type II Censoring Data

基于逐步Ⅱ型删失数据,假设在每一阶段退出试验的样品是随机的情况下,对BurrⅢ分布中的形状参数进行估计。定义了BurrⅢ分布形状参数的极大似然估计、EM估计和贝叶斯估计三种估计方法的估计式。同时,给出了EM估计的近似置信区间与贝叶斯估计的HPD置信区间。此外,利用Monte-Carlo模拟,对上述三种估计方法的效果进行了对比分析。模拟结果表明,在均方误差(MSE)准则下,贝叶斯估计优于EM估计,更优于极大似然估计,同时两种置信区间的区间长度近似。

Based on the gradually typeⅡcensored data,the shape parameters in BurrⅢdistribution are estimated under the assumption that the samples exiting the test at each stage are random.The estimation formulas of maximum likelihood estimation,EMestimation and Bayesian estimation of BurrⅢdistribution shape parameters are defined.At the same time,the approximate confidence interval of EMestimation and the HPD confidence interval of Bayesian estimation are given.In addition,Monte Carlo simulation is used to com-pare and analyze the effects of the above three estimation methods.The simulation results showthat under theMean Square Error(MSE)criterion,Bayesian estimation is better than EMestimation and maximumlikelihood estimation,and the interval lengths of the two con-fidence intervals are approximate.