定数截尾试验下两参数Weibull分布尺度参数的最优稳健Bayes估计

以Г-后验期望损失作为标准,研究了定数截尾试验下两参数W e ibu ll分布尺度参数θ的最优稳健Bayes估计问题.假设尺度参数θ的先验分布在分布族Г上变化,形状参数β已知时,在0-1损失下,得到了θ的最优稳健区间估计,在均方损失下得到θ的最优稳健点估计及区间估计;β未知时,得到了θ的最优稳健点估计及区间估计.最后给出了数值例子,说明了方法的有效性.

The Optimal Robust Bayes Estimation of Scale-Parameter for the Two-parameter Weibull Distribution under the Type- Ⅱ Censoring Life Test

The problems of the Optimal robust Bayes estimation of Scale-Parameter for the Two-parameter Weibull distribution under the Type-Ⅱ censoring Life Test are discussed using the Г-posterior expected loss as the criterion.It is assumed that the prior distribution of Scale-Parameter θ is in a conjugate prior class.When the shape-parameter β is known,the optimal robust interval of θ is obtained under the 0-1 loss function and the optimal robust point estimation and interval of θ are obtained under the squared error loss function.Also,we consider the optimal robust point estimation and interval of θ when β is unknown.At last,examples are given,which indicate that the method is effective.