在刻度平方损失函数下, 采用定数截尾样本,研究三参数 Burr分布族形状参数的一致最小方差无偏估计(UMVUE),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估计的优良性.给出参数的PEB估计相对于它的Bayes估计的大样本性质,并获得其收敛速度$o(n^{-1})$.

We derive the uniformly minimum variance unbiased estimation (UMVUE),the Bayes estimation and the parameter-type empirical Bayes (PEB) estimation of
shape parameter under the square loss function in scale and the fixed number trun-cation sample. The excellent properties of these estimations are ompared under the mean- square eo(MSE) criterion. The large sample properties of the PEB estima- tion of the parameters relative to its Bayes estimation are proved and the convergence rate o(n−1) is obtained. At last, some numerical simulation results of the precision and the level of coverage of the confidence interval of the UMVUE and the PEB estimation of the parameters are discussed.