一类新的二参数二元混合型指数分布的参数估计及相关结构
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摘要
本文继续文[13]的工作,针对二元Marshall-Olkin型指数分布随机结构模型,取掉一个服从指数分布的随机变量,从而导出一类二参数二元混合型指数分布,并由此研究了它的特征和参数估计及相关结构;通过密度分拆重组技术,本文导出了一类二参数二元混合型指数分布的一个特征,据此,获得了基于总体(X,Y)完全样本的参数的最大似然估计及一致最小方差无偏估计,计算了两个随机变量之间的相关系数,证明了其相关系数的取值落在(0,1)区间内.
This paper continues the work of[13],in accordance with stochastic structuremodel of the bivariate exponential distribution of Marshall-Olkin,a new mixed two-parameter bivariate exponential distribution is given and its characterization and parameter estimation or correlation are discussed,as well as the maximum likelihood estimator,uniformly minimum variance unbiased estimation of parameters,and correlation coefficient.It is also proved that the value of the correlation coefficient is between zero and one.
This paper continues the work of[13],in accordance with stochastic structuremodel of the bivariate exponential distribution of Marshall-Olkin,a new mixed two-parameter bivariate exponential distribution is given and its characterization and parameter estimation or correlation are discussed,as well as the maximum likelihood estimator,uniformly minimum variance unbiased estimation of parameters,and correlation coefficient.It is also proved that the value of the correlation coefficient is between zero and one.
引文
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[2]李国安,李晶晶.二元Cuadra-Auge型帕累托分布的相关性及渐近独立性[J].高等数学研究,2017,2014:13-16.
[3]李国安,李晶晶,二元Cuadra-Auge帕累托分布参数的一致最小方差无偏估计[J].大学数学,2017,33(1):86-89.
[4]Weinman D G.A multivariate extension of the exponential distribution[J].Ph.D.thesis,Arizona State University,1966.
[5]Cramer E,Kamps U.The UMVUE of P(X [6]李国安.二元Weinman指数分布的特征及其应用[J],数学研究与评论,2005,25(2):337-340.
[7]李国安.二元Weinman型指数分布随机变量之和、差、积、商及比率的分布[J].大学数学,2015,31(5):114-119.
[8]李国安,李建峰.满意度市场调查中最小样本量的计算公式[J].高等数学研究,2016,19(1):101-103.
[9]Krishna H,Pundir P S.A Bivariate Geometric Distribution with Applications to Reliability[J].Communications in Statistics-Theory and Methods,2009,38(7):1079-1093.
[10]李国安,李建峰.一个新的二参数二元几何分布及其多元推广[J].宁波大学学报,2017,30(1):59-63.
[11]Ferguson T S.A class of symmetric bivariate uniform distribution[J].Statistical Papers,1995,36(1):31-40.
[12]Marshall A W,Olkin I.A multivariate exponential distribution[J].Journal of American Statistical Association,1967,62(1):30-44.
[13]李国安.一类可用于相依数据处理的新的二元统计分布[J].高等数学研究,2018,21(14):56-58.
[14]Arnold B C.Parameter estimation for a multivariate exponential distribution[J].Journal of American Statistical Association,1968,63:848-852.
[15]Proschan F,Sullo P.Estimating the parameters of a multivariate exponential distribution[J],J.Amer.statist.Assoc.1976,71:465-472
[16]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.
[2]李国安,李晶晶.二元Cuadra-Auge型帕累托分布的相关性及渐近独立性[J].高等数学研究,2017,2014:13-16.
[3]李国安,李晶晶,二元Cuadra-Auge帕累托分布参数的一致最小方差无偏估计[J].大学数学,2017,33(1):86-89.
[4]Weinman D G.A multivariate extension of the exponential distribution[J].Ph.D.thesis,Arizona State University,1966.
[5]Cramer E,Kamps U.The UMVUE of P(X
[7]李国安.二元Weinman型指数分布随机变量之和、差、积、商及比率的分布[J].大学数学,2015,31(5):114-119.
[8]李国安,李建峰.满意度市场调查中最小样本量的计算公式[J].高等数学研究,2016,19(1):101-103.
[9]Krishna H,Pundir P S.A Bivariate Geometric Distribution with Applications to Reliability[J].Communications in Statistics-Theory and Methods,2009,38(7):1079-1093.
[10]李国安,李建峰.一个新的二参数二元几何分布及其多元推广[J].宁波大学学报,2017,30(1):59-63.
[11]Ferguson T S.A class of symmetric bivariate uniform distribution[J].Statistical Papers,1995,36(1):31-40.
[12]Marshall A W,Olkin I.A multivariate exponential distribution[J].Journal of American Statistical Association,1967,62(1):30-44.
[13]李国安.一类可用于相依数据处理的新的二元统计分布[J].高等数学研究,2018,21(14):56-58.
[14]Arnold B C.Parameter estimation for a multivariate exponential distribution[J].Journal of American Statistical Association,1968,63:848-852.
[15]Proschan F,Sullo P.Estimating the parameters of a multivariate exponential distribution[J],J.Amer.statist.Assoc.1976,71:465-472
[16]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.