Weibull分布形状参数的收缩估计

Shrinkage Estimation for the Shape Parameter of Weibull Distribution under Type Ⅱ Censoring

本文研究两参数Weibull分布在Ⅱ形截尾场合下形状参数的收缩估计．提出了形状参数的四个不同的收缩估计，在Minimax遗憾准则下得到了最优收缩系数．通过对这四个收缩信计的效的研究，可知他们在适当的先验信息下都优于原来的估计，其中基于近似无偏估计所得的形状参数的无编估计是比较理想的估计量．

In this paper,We consider four shrinkage estimators of the Weibull Shape parameter underType Ⅱcensoring when the prior information of the shape parameters available, The optimalshrinkage cofficients of the above four shrinkage estimators are obtained with the minimax regretcriterion. The efficiency of the four shrinkage estimators of the Weibull shape parameters showsthat they are all better than their original ones in the sense of mean square error when there is theappropriate prior iuformation of the Weibull shape parameter. By comparing these four shrinkageestimators one another, we have recommended that the usual BLUE of the Weibull shape parametercan be replaced by shrinkage cstimator based on the approximate unbiased estimator.