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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

李国安   

  • 出版日期:2016-07-15 发布日期:2016-07-06

parameter estimation in the four-parameter bivariate exponential distribution of Marshall and Olkin

Li Guoan   

  • Online:2016-07-15 Published:2016-07-06

摘要:

本文提出指数分布抽样基本定理,并把它应用到四参数二元Marshall—Olkin型指数分布的参数估计中,从参数的识别性分析着手,获得了一个分布函数用可识最小值函数表示的一个表达式,进而得到了二元指数分布的一个特征,从而,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的参数的最大似然估计,并由此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。

关键词: 指数分布抽样基本定理;四参数二元Marshall&mdash, Olkin型指数分布;特征;最大似然估计;一致最小方差无偏估计

Abstract:

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.

Key words: fundamental sampling theorem for exponential distribution, four-parameter bivariate exponential distribution of Marshall and Olkin, characterization, maximum likelihood estimator, uniformly minimum variance unbiased estimation