基于Gibbs抽样算法的两参数Pareto分布的Bayes估计  

Bayesian estimation of two-parameter pareto distribution under linex loss function

作　　者：李凡群[1] 韦善然 LI Fanqun;WEI Shanran(Institute of Statistics and Applied Mathematics,Anhui University of Finance and Economics,Bengbu Anhui 233000,China)

机构地区：[1]安徽财经大学统计与应用数学学院,安徽蚌埠233000

出　　处：《阜阳师范大学学报（自然科学版）》2023年第4期8-13,共6页Journal of Fuyang Normal University:Natural Science

基　　金：安徽省哲学社会科学规划项目(AHSKF2020D06)。

摘　　要：本文在非正常先验分布下讨论了基于Linex非对称损失函数的两参数Pareto分布的Bayes估计,证明了Linex损失函数下的Bayes估计是可容许的,并利用Gibbs抽样算法进行了Bayes估计实现;通过数值模拟,比较了极大似然估计与Bayes估计的风险。结果表明:Pareto分布的尺度参数的Bayes估计效率一致高于极大似然估计;在小样本情形下,当损失函数的尺度参数大于0时,Pareto分布的形状参数的Bayes估计的效率高于极大似然估计。This paper discusses the Bayesian estimation of a two-parameter Pareto distribution based on the Linex asymmetric loss function under non-normal priors.It proves the admissibility of Bayesian estimation with the Linex loss function and implements the Bayesian estimation using Gibbs sampling algorithm.Through numerical simulations,it compares the risks of maximum likelihood estimation and Bayesian estimation.The results show that the Bayesian estimation of the scale parameter of the Pareto distribution consistently outperforms the maximum likelihood estimation.In the case of small samples,when the scale parameter of the loss function is greater than O,the Bayesian estimation of the shape parameter of the Pareto distribution is more efficient than the maximum likelihood estimation.

关 键 词：PARETO分布 极大似然估计 BAYES估计 GIBBS抽样 LINEX损失 

分 类 号：O211.62[理学—概率论与数理统计]