关键词: 刻度参数, 指数分布, PEB 估计, MSE准则, 收敛速度

Abstract:

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.

Key words: scale parameter, exponential distribution, PEB estimation, MSE criterion, convergence rate