逐步增加Ⅱ型截尾下Pareto分布形状参数的Bayes估计

Bayes Estimation of the Shape Parameter of Pareto Distribution under the Gradually Increasing of TypeⅡTruncation

基于逐步增加Ⅱ型截尾样本,首先得出Pareto分布形状参数的极大似然估计,考虑两个损失函数和形状参数的两个先验分布,得出该分布形状参数的4个Bayes估计。由数值模拟结果发现,上述四个Bayes估计值的均方误差均小于极大似然估计值,其中,当损失函数为二次损失函数,形状参数的先验分布为共轭先验分布时的Bayes估计的均方误差较小,估计效果更理想,且实例分析与数值模拟结果相符。其次在二次损失函数下,针对形状参数先验分布选取共轭先验分布,给出Pareto分布形状参数的多层Bayes估计和E-Bayes估计。

Based on gradually increasing typeⅡtruncated samples.Firstly,obtain the maximum likelihood estimation of the Pareto distribution shape parameter,considering the two loss functions and the two prior distributions of shape parameters,four Bayes estimation of the distribution shape parameter is concluded.It is found from the numerical simulation results that the mean square error of the four Bayes estimates is less than the maxi⁃mum likelihood estimate.Among them,when the loss function is a quadratic loss function and the prior distribution of the shape parameter is a conjugate prior distribution,the mean square error of the Bayes estimate is smaller,and the estimation effect is more ideal,and the example analysis is consistent with the numerical simulation re⁃sults.Secondly,under the quadratic loss function,the conjugate prior distribution is selected for the prior distribu⁃tion of the shape parameters,and the multi-layer Bayes estimation and E-Bayes estimation of the shape parameters of the Pareto distribution are given.