删失样本及完全样本下含位置参数的多元指数分布的参数估计
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摘要
首先归纳出指数分布抽样基本定理;通过分布的识别性分析及参数的识别性分析,导出了串联系统下多元Marshall-Olkin型指数分布的一个识别特征,并由此得到了基于删失样本的含位置参数的多元Marshall-Olkin型指数分布参数的最大似然估计及一致最小方差无偏估计;通过密度分拆重组技术,还导出了随机系统下多元Marshall-Olkin型指数分布的一个特征,并由此得到了基于完全样本的含位置参数的二元Marshall-Olkin型指数分布参数的最大似然估计及无偏估计.
The fundamental sampling theorem of exponential distribution is concluded in this paper. Through identifiability analysis of the distributions and analysis of parameter identification, an identifiable characteristic of multivariate MarshallOlkin exponential distribution is derived based on series system, thus, the maximum likelihood estimator and uniformly minimum variance unbiased estimator of the multivariate Marshall-Olkin exponential distribution with location parameter under censored samples are obtained. Through the analysis of partition and reorganization of density, also a characteristic of multivariate Marshall-Olkin exponential distribution is derived based on random system, hence, the maximum likelihood estimator and unbiased estimator of the bivariate Marshall-Olkin exponential distribution with location parameter under complete samples are obtained.
The fundamental sampling theorem of exponential distribution is concluded in this paper. Through identifiability analysis of the distributions and analysis of parameter identification, an identifiable characteristic of multivariate MarshallOlkin exponential distribution is derived based on series system, thus, the maximum likelihood estimator and uniformly minimum variance unbiased estimator of the multivariate Marshall-Olkin exponential distribution with location parameter under censored samples are obtained. Through the analysis of partition and reorganization of density, also a characteristic of multivariate Marshall-Olkin exponential distribution is derived based on random system, hence, the maximum likelihood estimator and unbiased estimator of the bivariate Marshall-Olkin exponential distribution with location parameter under complete samples are obtained.
引文
[1]Marshall A W,Olkin I.A multivariate exponential distribution.Journal of American Statistical Association,1967,62(1):30-44.
[2]Arnold B C.Parameter estimation for a multivariate exponential distribution.Journal of American Statistical Association,1968,63:848-852.
[3]Bemis B M,Bain L J,Higgins J J.Estimation and hypothesis testing for the parameters of a bivariate exponential distribution.Journal of the American Statistical Association,1972,67:927-929.
[4]Bhattacharyya G K,Johnson R A.On a test of independence in a bivariate exponential distribution.Journal of the American Statistical Association,1972,68:704-706.
[5]Proschan F,Sullo P.Estimating the parameters of a multivariate exponential distribution.Journal of the American Statistical Association,1976,71:465-472.
[6]Block H W.A characterization of a bivariate exponential distribution.The Annals of Statisticics,1977,5:808-812.
[7]李国安.混合分布的识别性及其应用.宁波大学学报(理工版),1993,6(2):28-38.(Li G A.Identifiability of multivariate mixed distribution and its applications.Journal of Ningbo University,1993,6(2):28-38.)
[8]李国安.多元Marshall~Olkin型指数分布的特征及其参数估计.工程数学学报,2005,22(6):1055-1062.(Li G A.A characterization of the multivariate Marshall-Olkin exponential distibution and its parameter estimation.Chinese Journal of Engineering Mathematics,2005,22(6):1055-1062.)
[9]李国安.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.统计研究,2016,33(7):98-102.(Li G A.Sampling fundamental theorem for exponential distribution with application to parameter estimation in the four-parameter bivariate exponential distribution of Marshall and Olkin.Statistical Research,2016,33(7):98-102.)
[10]Lin G D,Lai C D,Govindaraju K.Correlation structure of the Marshall-Olkin bivariate exponential distribution.Statistical Methodology,2016,29:1-9.
[11]Basu A P,Ghosh J K.Identifiability of the multinorma and other distributions under competing risks model.Journal of Multiva,riate Analysis,1978,8(3):413-429.
[12]Yamato H.Uniformly minimum variance unbiased estimation for symmetric normal distributions.Journal of Multiva-riate Analysis,1990,34:227-237.
[13]Bacchi B,Bacciu G,Kottegoda N T.Bivariate exponential model applied to intensities and durations of extreme rainfall.Journal of Hydrology,1994,155(1-2):225-236.
[14]Dargahi-Noubary G R,Razzaghi M.Earthquake hazard assessment based on bivariate exponential distributions.Reliability Engineering&System Safety,1994,44(2):153-166.
[15]Nadarajah S,Kotz S.Reliability models based on bivariate exponential distributions.Probabilistic Engineering Mechanics,2006,21(4):338-351.
[16]Marshall A W,Olkin I.A new method for adding a parameter to a family of distributions with application to the exponential and Weibull families.Biometrika,1997,84(3):641-652.
[17]Nagaraja H N,He Q Y.Fisher information in censored samples from the marshall-olkin bivariate exponential distribution.Communications in Statistics—Theory and Methods,2015,44(19):4172-4184.
[18]Pasari S,Dikshit O.Three-parameter generalized exponential distribution in earthquake recurrence interval estimation.Natural Hazards,2014,73(2):639-656.
[19]Gupta R D,Kundu D.Generalized exponential distributions.Australian and New Zealand Journal of Statistics,1999,41:173-188
[20]Kundu D,Gupta R D.Bivariate generalized exponential distributions.Journal of Multivariate Analysis,2009,100(4):581-593.
[2]Arnold B C.Parameter estimation for a multivariate exponential distribution.Journal of American Statistical Association,1968,63:848-852.
[3]Bemis B M,Bain L J,Higgins J J.Estimation and hypothesis testing for the parameters of a bivariate exponential distribution.Journal of the American Statistical Association,1972,67:927-929.
[4]Bhattacharyya G K,Johnson R A.On a test of independence in a bivariate exponential distribution.Journal of the American Statistical Association,1972,68:704-706.
[5]Proschan F,Sullo P.Estimating the parameters of a multivariate exponential distribution.Journal of the American Statistical Association,1976,71:465-472.
[6]Block H W.A characterization of a bivariate exponential distribution.The Annals of Statisticics,1977,5:808-812.
[7]李国安.混合分布的识别性及其应用.宁波大学学报(理工版),1993,6(2):28-38.(Li G A.Identifiability of multivariate mixed distribution and its applications.Journal of Ningbo University,1993,6(2):28-38.)
[8]李国安.多元Marshall~Olkin型指数分布的特征及其参数估计.工程数学学报,2005,22(6):1055-1062.(Li G A.A characterization of the multivariate Marshall-Olkin exponential distibution and its parameter estimation.Chinese Journal of Engineering Mathematics,2005,22(6):1055-1062.)
[9]李国安.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.统计研究,2016,33(7):98-102.(Li G A.Sampling fundamental theorem for exponential distribution with application to parameter estimation in the four-parameter bivariate exponential distribution of Marshall and Olkin.Statistical Research,2016,33(7):98-102.)
[10]Lin G D,Lai C D,Govindaraju K.Correlation structure of the Marshall-Olkin bivariate exponential distribution.Statistical Methodology,2016,29:1-9.
[11]Basu A P,Ghosh J K.Identifiability of the multinorma and other distributions under competing risks model.Journal of Multiva,riate Analysis,1978,8(3):413-429.
[12]Yamato H.Uniformly minimum variance unbiased estimation for symmetric normal distributions.Journal of Multiva-riate Analysis,1990,34:227-237.
[13]Bacchi B,Bacciu G,Kottegoda N T.Bivariate exponential model applied to intensities and durations of extreme rainfall.Journal of Hydrology,1994,155(1-2):225-236.
[14]Dargahi-Noubary G R,Razzaghi M.Earthquake hazard assessment based on bivariate exponential distributions.Reliability Engineering&System Safety,1994,44(2):153-166.
[15]Nadarajah S,Kotz S.Reliability models based on bivariate exponential distributions.Probabilistic Engineering Mechanics,2006,21(4):338-351.
[16]Marshall A W,Olkin I.A new method for adding a parameter to a family of distributions with application to the exponential and Weibull families.Biometrika,1997,84(3):641-652.
[17]Nagaraja H N,He Q Y.Fisher information in censored samples from the marshall-olkin bivariate exponential distribution.Communications in Statistics—Theory and Methods,2015,44(19):4172-4184.
[18]Pasari S,Dikshit O.Three-parameter generalized exponential distribution in earthquake recurrence interval estimation.Natural Hazards,2014,73(2):639-656.
[19]Gupta R D,Kundu D.Generalized exponential distributions.Australian and New Zealand Journal of Statistics,1999,41:173-188
[20]Kundu D,Gupta R D.Bivariate generalized exponential distributions.Journal of Multivariate Analysis,2009,100(4):581-593.