Empirical Bayes estimators for Weibull parts

Based on progressively type-II censored trials, the estimators and their properties of Weibull parts are discussed. The uniformly minimum variance unbiased estimator (UMVUE), Bayesian estimators and empirical Bayesian estimators for the parameter, reliability and hazard functions are obtained under Linex loss function. And we prove the empirical Bayesian estimator is asymptotic optimality. At last, the statistical performances are compared through the mean squared error (MSE) based on Monte Carlo simulation study. According to these comparisons, it is suggested that the empirical Bayesian estimators have high-precision.