Pareto分布形状参数的E-Bayes估计和多层Bayes估计及其应用The E-Bayesian estimation and hierarchical Bayesian estimation of shape parameter for Pareto distribution and its applications
韩明;
摘要(Abstract):
给出了参数的E-Bayes估计的定义,对Pareto分布在尺度参数已知时,在平方损失下给出了形状参数的E-Bayes估计和多层Bayes估计,并且用Monte Carlo方法给出了模拟算例.最后,结合高尔夫球手收入数据的实际问题进行了计算,结果表明本文提出的方法可行且便于应用.
关键词(KeyWords): Pareto分布;E-Bayes估计;多层Bayes估计;尺度参数;形状参数
基金项目(Foundation): 宁波市自然科学基金(2013A610108)
作者(Authors): 韩明;
参考文献(References):
- [1]Lindley D V,Smith A F M.Bayes estimaters for the linear model[J].Journal of the Royal Statistical Society,Series B,1972,34:1-41.
- [2]韩明.多层先验分布的构造及其应用[J].运筹与管理,1997,6(3):31-40.
- [3]Ando T,Zellner A.Hierarchical Bayesian analysis of the seemingly unrelated regression and simultaneous equations models using a combination of direct monte Carlo and importance sampling techniques[J].Bayesian Analysis,2010,5(1):65-96.
- [4]Andrieu C,Thoms J.A tutorial on adaptive MCMC[J].Statistics and Computing,2008,18(4):343-373.
- [5]Arnold B C.Pareto Distributions[M].2nd ed.London/Boca Raton:Chapman and Hall/CRC,2015.
- [6]韩明.贝叶斯统计学及其应用[M].上海:同济大学出版社,2015.
- [7]康会光,师义民.LINEX损失下Pareto分布参数的经验Bayes估计[J].纯粹数学与应用数学,2001,17(2):169-171.
- [8]韦程东,韦师,苏韩.复合LINEX对称损失下Pareto分布形状参数的E-Bayes估计及其应用[J].统计与决策,2009,17:7-9.
- [9]韩明.Pascal分布的参数估计[J].纯粹数学与应用数学,2006,22(4):510-515.
- [10]Berger J O.Statistical Decision Theory and Bayesian Analysis[M].2nd ed.New York:Springer-Verlag,1985.
- [11]Han M.E-Bayesian estimation of failure probability and its application[J].Mathematical and Computer Modelling,2007,45:1272-1279.
- [12]Han M.E-Bayesian estimation of the reliability derived from binomial distribution[J].Applied Mathematical Modelling,2011,35:2419-2424.