双参数指数分布尺度参数的近似贝叶斯估计  

Approximate Bayes Estimation of Scale Parameter of Two-parameter Exponential Distribution

作　　者：张良超 温利民[1] Zhang Liangchao;Wen Limin(School of Mathematics and Statistics,Jiangxi Normal University,Nanchang 330022,China)

机构地区：[1]江西师范大学数学与统计学院,南昌330022

出　　处：《统计与决策》2022年第13期52-57,共6页Statistics & Decision

基　　金：国家自然科学基金资助项目(71761019);江西省自然科学基金资助项目(20202BABL201001);江西省研究生创新基金资助项目(YC2019-S125)。

摘　　要：文章针对双参数指数分布,讨论了其尺度参数的参数估计问题:建立了尺度参数的贝叶斯模型,定义了尺度参数的信度估计、二次贝叶斯估计与贝叶斯估计,并证明了这些估计的大样本性质。两种近似贝叶斯估计都具有解析解的形式,在均方误差准则下,二次贝叶斯估计优于经典的信度估计,更优于极大似然估计。最后,通过MCMC方法比较了这些估计的均方误差,并验证了估计的收敛速度。Aimed at two-parameter exponential distribution, this paper discusses the parameter estimation of scale parameter: The Bayesian model of scale parameter is constructed;credibility estimation, quadratic Bayesian estimation and Bayesian estimation of scale parameter are defined, and the large sample properties of these estimations are proved. Both approximate Bayes estimation have analytic solution form. Under the mean square error criterion, quadratic Bayesian estimation is better than the classical credibility estimation and even better than the maximum likelihood estimation. Finally, the paper uses the MCMC method to compare the mean square error of these estimations and verifies the convergence rate of these estimations.

关 键 词：双参数指数分布 近似贝叶斯估计 信度估计 MCMC方法 

分 类 号：O212.8[理学—概率论与数理统计]