中文摘要：

研究BurrI分布族形状参数的一致最小方差无偏估计（UMVUE）、以及在刻度平方损失下的Bayes估计和参数型经验Bayes（PEB）估计.在均方误差（MSE）准则下比较UMVUE与PEB估计的优良性.给出了参数的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）.对参数PEB估计的置信区间进行了数值模拟分析.

英文摘要：

The uniformly minimum variance unbiased estimation （UMVUE） and the Bayes estimation under the square loss in scale and the parameter-type empirical Bayes （PEB）estimation of shape parameter of the BurrI distribution family are studied in this paper.The fine properties of UMVUE and PEB estimations under the mean-square error（MSE） criterion are compared.The large sample properties of the PEB estimation of the parameters relative to its Bayes estimation are presented and the convergence rate o（n-1） is obtained.Finally the numerical simulation of the confidence interval of the PEB estimation of the parameters is demonstrated.