广义Weibull分布参数的收缩估计

Shrinkage Estimation of Generalized Weibull Parameter in Censored Samples

在右删失样本下,研究了双参数广义Weibull分布参数的极大似然估计。针对在小样本或高度删失样本下参数估计效果差的问题,引入了收缩估计方法,将先验信息与样本信息相结合,用于改善参数估计。分别在单参数和双参数含有先验信息两种情形下,给出了分布参数的收缩估计。以定数截尾样本为例,利用Monte-Carlo方法对收缩估计与极大似然估计进行了比较,模拟结果表明在一定的条件下,收缩估计具有更优的统计性质。数值算例表明,在小样本或高度截尾样本下,双参数广义Weibull分布参数的收缩估计具有较好的效果。

The estimation of two parameter generalized Weibull model was studied under type Ⅱ censored samples. To draw better inferences, the shrinkage estimation was introduced to combine the sample information with the relevant prior information. Then two different shrinkage estimations of the generalized Weibull parameter were proposed in two cases of different prior information, Compared with the maximize likelihood estimation, the relative efficiency of the shrinkage estimations was studied by Monte- Carlo simulation. And the result shows that the shrinkage estimations are better under center conditions, especially when the sample size is small or samples are highly censored. The illustrative example shows that the shrinkage estimations of the generalized Weibull parameter are available for reliability analysis.