指数分布抽样基本定理及在四参数二元Marshall-Olkin型指数分布参数估计中的应用
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摘要
本文提出指数分布抽样基本定理,四参数二元Marshall-Olkin型指数分布的参数估计中,从参数的识别性分析着手,获得了一个用可识最小值函数表示的分布函数表达式,进而得到了二元指数分布的一个特征;以二元指数分布随机变量样本与二元可识最小值随机变量样本的等价性,获得了基于二元可识最小值随机变量样本参数的最大似然估计,并应用指数分布抽样基本定理,得到了四参数二元Marshall-Olkin型指数分布参数的一致最小方差无偏估计。
This article raises the sampling theorem of exponential distribution,and applies it into parameter estimation of four-parameter bivariate exponential distribution of Marshall and Olkin. Through the analysis of parameter identification,it obtains an expression,in which,the distribution function is denoted by the identifiable minimum formula,hence,the Characterization of four-parameter bivariate exponential distribution of Marshall and Olkin is devived. Therefore,depending on the random sampling equivalence of bivariate exponential distribution and bivariate identifiable minimum value,it gets the maximum likelihood estimation of the parameter,which is based on the random sampling of bivariate identifiable minimum value,applies the fundamental sampling theorem of exponential distribution,and obtains the uniformly minimum variance unbiased estimator( UMVUE) of the parameter of four-parameter bivariate exponential distribution of Marshall and Olkin.
This article raises the sampling theorem of exponential distribution,and applies it into parameter estimation of four-parameter bivariate exponential distribution of Marshall and Olkin. Through the analysis of parameter identification,it obtains an expression,in which,the distribution function is denoted by the identifiable minimum formula,hence,the Characterization of four-parameter bivariate exponential distribution of Marshall and Olkin is devived. Therefore,depending on the random sampling equivalence of bivariate exponential distribution and bivariate identifiable minimum value,it gets the maximum likelihood estimation of the parameter,which is based on the random sampling of bivariate identifiable minimum value,applies the fundamental sampling theorem of exponential distribution,and obtains the uniformly minimum variance unbiased estimator( UMVUE) of the parameter of four-parameter bivariate exponential distribution of Marshall and Olkin.
引文
[1]Marshall A W,Olkin I.A multivariate exponential distribution[J].Journal of American Statistical Association,1967,62(1):30-44.
[2]Arnold B C.Parameter restimation for a multivariate exponential distribution[J].Journal of American Statistical Association,1968,63:848-852.
[3]Proschan F,Sullo P.Estimating The Parameters of A Bivariate Exponential Distribution in Several Sampling Situations[a].In:Proschan F,Serfling R F Reliability and Biometry,SIAM,Philadelphia,1974,423-440.
[4]Proschan F,Sullo P.Estimating the parameters of a multivariate exponential distribution[J],J.Amer.statist.Assoc.1976,71:465-472.
[5]Basu A P,Ghosh J K.Identifiability of the multinorma and other distributions under competing risks model[J].Journal of Multivariate Analysis,1978,8(3):413-429.
[6]李国安.混合分布的性及其应用[J].宁波大学学报(理工版),1993,6(2):28-38.
[7]李国安.多元Marshall-Olkin型指数分布的特征及其参数估计[J].工程数学学报,2005,22(6):1055-1062.
[8]Juan Li,Weixing Song,Jianhong Shi.Parametric bootstrap simultaneous confidence intervals for differences of means from several two-parameter exponential distributions[J].Statistics and Probability Letters,2015,106:39-45.
[9]Weinman D G.A multivariate extension of the exponential distribution[D]:[Ph.D.thesis].Phoenix:State University,1966.
[10]Cramer E,Kamps U.The UMVUE of P(X [11]李国安.二元Weinman型指数分布的特征及其应用[J].数学研究与评论,2005,25(2):337-340.
[12]李国安.多元Weinman型指数分布的特征及其参数估计[J].宁波大学学报(理工版),2009,22(1):81-84.
[13]Yamato H.Uniformly minimum variance unbiased estimation for symmetric normal distributions[J].Journal of multivariate analysis,1990,34,227-237.
[2]Arnold B C.Parameter restimation for a multivariate exponential distribution[J].Journal of American Statistical Association,1968,63:848-852.
[3]Proschan F,Sullo P.Estimating The Parameters of A Bivariate Exponential Distribution in Several Sampling Situations[a].In:Proschan F,Serfling R F Reliability and Biometry,SIAM,Philadelphia,1974,423-440.
[4]Proschan F,Sullo P.Estimating the parameters of a multivariate exponential distribution[J],J.Amer.statist.Assoc.1976,71:465-472.
[5]Basu A P,Ghosh J K.Identifiability of the multinorma and other distributions under competing risks model[J].Journal of Multivariate Analysis,1978,8(3):413-429.
[6]李国安.混合分布的性及其应用[J].宁波大学学报(理工版),1993,6(2):28-38.
[7]李国安.多元Marshall-Olkin型指数分布的特征及其参数估计[J].工程数学学报,2005,22(6):1055-1062.
[8]Juan Li,Weixing Song,Jianhong Shi.Parametric bootstrap simultaneous confidence intervals for differences of means from several two-parameter exponential distributions[J].Statistics and Probability Letters,2015,106:39-45.
[9]Weinman D G.A multivariate extension of the exponential distribution[D]:[Ph.D.thesis].Phoenix:State University,1966.
[10]Cramer E,Kamps U.The UMVUE of P(X
[12]李国安.多元Weinman型指数分布的特征及其参数估计[J].宁波大学学报(理工版),2009,22(1):81-84.
[13]Yamato H.Uniformly minimum variance unbiased estimation for symmetric normal distributions[J].Journal of multivariate analysis,1990,34,227-237.