指数分布定数截尾数据下刻度参数的经验Bayes估计

Empirical Bayes estimation for scale parameter on type-Ⅱ censored samples in exponential distribution

在指数分布定数截尾情形下,当先验分布中的超参数部分未知时,在加权平方损失下构造了刻度参数的参数型经验Bayes(PEB)估计,研究了其在均方误差(MSE)准则下相对于一致最小方差无偏估计(UMVUE)的优良性,并获得了PEB估计的大样本性质.当先验分布中的超参数完全未知时,通过数值模拟比较了PEB估计和UMVUE的均方误差,获得了其优良性.最后,通过数值模拟的结果,获得了PEB区间估计的优良性.

We consider type-Ⅱ censored samples of the exponential distribution.In the case that the hyper-parameters of prior distribution are partly unknown,we construct the parametic empirical Bayes（PEB） estimation for scale parameter with the weighted square-error loss function,study the superiority of PEB estimation over the uniformly minimum variance unbiased estimation（UMVUE） in terms of the mean-square error（MSE） criterion,and obtain its large sample properties.In the case that the hyper-parameters of prior distribution are all unknown,we get the superiority of PEB estimation over UMVUE by comparing the simulated MSE.Finally,we show the superiority of PEB interval estimation by simulation results.