复合LINEX对称损失下广义Pareto分布形状参数θ的Bayes估计
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摘要
广义Pareto分布已被应用在社会学、保险精算学等众多领域,有着非常重要的实际应用价值.该文主要研究了复合LINEX对称损失函数下尺度参数已知,先验分布为伽马分布时,广义Pareto分布形状参数的Bayes估计和E-Bayes估计,给出了二者的精确表达式.最后对参数的Bayes估计和E-Bayes估计进行了数值模拟检验,检验结果说明了估计的合理性.
The generalized Pareto distribution has been applied in many fields such as sociology,insurance actuarial science,etc.It has very important practical application value for the society.In this paper,the Bayesian and E-Bayesian estimation of the shape parameters of the generalized Pareto distribution is mainly studied when the scale parameters of the composite LINEX loss function are known and the prior distribution is a gamma distribution.The exact expressions of these two estimates are given.Finally,the Bayes estimation and E-Bayes estimation of the parameters are tested by numerical simulation,which shows the rationality of the estimation.
The generalized Pareto distribution has been applied in many fields such as sociology,insurance actuarial science,etc.It has very important practical application value for the society.In this paper,the Bayesian and E-Bayesian estimation of the shape parameters of the generalized Pareto distribution is mainly studied when the scale parameters of the composite LINEX loss function are known and the prior distribution is a gamma distribution.The exact expressions of these two estimates are given.Finally,the Bayes estimation and E-Bayes estimation of the parameters are tested by numerical simulation,which shows the rationality of the estimation.
引文
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[2]井晓培,周菊玲.Mlinex损失函数下广义Pareto分布的Bayes估计[J].鲁东大学学报(自然科学版),2015,31(2):210-213.
[3]单国栋.基于删失数据的广义Pareto分布的Bayes分析[J].长春大学学报,2008,18(8):1-4.
[4]张月,井晓培,周菊玲.广义Pareto分布参数的经验Bayes估计的收敛速度[J].数学的实践与认识,2016,46(20):187-192.
[5]Srivastava R S,Kumar V,Rao A K.Bayesian estimation of the shape parameter and reliability of generalized Pareto distribution using precautionary loss function with censoring[J].South East Asian J Math&Math Sci,2004,2(2):47-56.
[6]张睿.复合LINEX损失下的参数估计[D].大连:大连理工大学,2007.
[7]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估计及应用[J].统计与决策,2009,17:7-9.
[8]韩明.Pascal分布的参数估计[J].纯粹数学与应用数学,2006,2(4):510-514.
[2]井晓培,周菊玲.Mlinex损失函数下广义Pareto分布的Bayes估计[J].鲁东大学学报(自然科学版),2015,31(2):210-213.
[3]单国栋.基于删失数据的广义Pareto分布的Bayes分析[J].长春大学学报,2008,18(8):1-4.
[4]张月,井晓培,周菊玲.广义Pareto分布参数的经验Bayes估计的收敛速度[J].数学的实践与认识,2016,46(20):187-192.
[5]Srivastava R S,Kumar V,Rao A K.Bayesian estimation of the shape parameter and reliability of generalized Pareto distribution using precautionary loss function with censoring[J].South East Asian J Math&Math Sci,2004,2(2):47-56.
[6]张睿.复合LINEX损失下的参数估计[D].大连:大连理工大学,2007.
[7]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估计及应用[J].统计与决策,2009,17:7-9.
[8]韩明.Pascal分布的参数估计[J].纯粹数学与应用数学,2006,2(4):510-514.