关于三参数Pareto分布的参数估计问题

在逐步增加首失效截尾样本下,研究三参数Pareto分布族形状参数的一致最小方差无偏估计(UMVUE),在对称平方损失函数下,讨论其Bayes估计和参数型经验Bayes(PEB)估计;按照均方误差(MSE)准则,比较UMVUE与PEB估计的小样本性质;根据形状参数的风险,导出其Bayes估计与PEB估计的大样本性质,并获得它们的收敛速度o(n-1)。

ESTIMATION OF THREE-PARAMETER PARETO DISTRIBUTION UNDER PROGRESSIVELY FIRST-FAILURE-CENSORED DATA

We derive the uniformly minimum variance unbiased estimation (UMVUE) of shape parameter of the three-parameter Pareto distribution family based on progressive first-failure-censoring samples. Furthermore, the Bayesian estimation and the parameter-type empirical Bayes (PEB) estimation have been obtained under the symmetric loss function. The small sample properties of UMVUE and the PEB estimation are compared under the mean-square error (MSE) criterion. The large sample properties of the Bayesian estimation and the PEB estimation of the parameters are proved according to the risk of the shape parameter and the convergence rate o(n^-1) is obtained. The interval estimations of the parameters in classical statistics and Bayesian statistics are discussed respectively under the same or similar credible level. At last, the precision of the Bayesian interval estimation is better than in classical statistics is illustrated by some numerical simulation results.