Optimal Property of Parametric Estimation under Progressively First-Failure-Censored Samples

Under the symmetric loss functions, by means of progressively first-failure-censored samples, the paper studies the uniformly minimum variance unbiased estimation (UMVUE), Bayes estimation and parametric empirical Bayes estimation (PEB) based on two-parameter Pareto distribution. According to the code of mean squared error (MSE), the gradualism of parametric Bayes and PEB estimation is investigated by applying risk function and by comparing the optimal property between UMVUE and PEB estimations to obtain their convergence rate. Based on the same confidence level, parametric interval estimation in classical and Bayes statistics is analyzed. A conclusion can be made that the precision of interval estimation in Bayes statics is higher than that in classical statics by means of numerical simulation.