Pareto分布形状参数的最小风险同变估计  

Minimum Risk Equivariant Estimator of Pareto Distribution Shape Parameter

作　　者：徐宝[1] 王宇廷[1] 马艺光 

机构地区：[1]吉林师范大学数学学院,中国四平136000

出　　处：《湖南师范大学自然科学学报》2017年第6期76-79,86,共5页Journal of Natural Science of Hunan Normal University

基　　金：国家自然科学基金资助项目(11571138)

摘　　要：在加权p,q对称损失函数下,对实际中广泛应用的两参数Pareto分布,当刻度参数已知时,用参数估计方法,研究了形状参数的最小风险同变估计的形式和性质.得到了最小风险同变估计的一般形式,又经由该参数的广义Bayes估计,得到了最小风险同变估计的精确形式,并证明了这一最小风险同变估计具有最小最大性,从而它也是该参数的最小最大估计,由此将Pareto分布形状参数的最小风险同变估计、广义Bayes估计以及最小最大估计联系起来.For the Pareto distribution, in the present work, the form and property of the minimum risk equiva- riant estimator for shape parameters with known local parameters were investigated under weighted p, q symmetric entropy loss by the method of parameter estimation. The general form of the minimum risk equivariant estimator was obtained, and the exact form of the minimum risk equivariant estimator was found using the general Bayes estimator of shape parameter. The minimaxity of this minimum risk equivariant estimator was proved. The relationships among the general Bayes estimator, the minimum risk equivariant estimator, and the minimax estimator have been established.

关 键 词：PARETO分布 最小风险同变估计 BAYES估计 最小最大估计 

分 类 号：O212.8[理学—概率论与数理统计]