| PARAMETER ESTIMATION OF EXPONENTIAL DISTRIBUTION |
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| 引用本文： | XUHaiyan FEIHeliang. PARAMETER ESTIMATION OF EXPONENTIAL DISTRIBUTION[J]. 系统科学与复杂性, 2005, 18(1): 86-94 |
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| 作者姓名： | XUHaiyan FEIHeliang |
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| 作者单位： | MathematicsandScienceCollege,ShanghaiNormalUniversity,Shanghai200234,China |
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| 基金项目： | ThisresearchissupportedbytheNationalNaturalScienceFoundationofChina(10271079)theSpecialFoundationforMajorSpecialtiesofShanghaiEducationCommittee. |
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| 摘 要： | Because of the importance of grouped data, many scholars have been devoted to the study of this kind of data. But, few documents have been concerned with the thresh-old parameter. In this paper, we assume that the threshold parameter is smaller than the first observing point. Then, on the basis of the two-parameter exponential distribution, the maximum likelihood estimations of both parameters are given, the sufficient and necessary conditions for their existence and uniqueness are argued, and the asymptotic properties of the estimations are also presented, according to which approximate confidence intervals of the parameters are derived. At the same time, the estimation of the parameters is generalized, and some methods are introduced to get explicit expressions of these generalized estimations. Also, a special case where the first failure time of the units is observed is considered.
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| 关 键 词： | 参数估计 指数分配 区间估计 分组数据 极大似然估计 渐近性质 |
PARAMETER ESTIMATION OF EXPONENTIAL DISTRIBUTION |
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| XU Haiyan FEI Heliang. PARAMETER ESTIMATION OF EXPONENTIAL DISTRIBUTION[J]. Journal of Systems Science and Complexity, 2005, 18(1): 86-94 |
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| Authors: | XU Haiyan FEI Heliang |
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| Abstract: | Because of the importance of grouped data, many scholars have been devoted to the study of this kind of data. But, few documents have been concerned with the threshold parameter. In this paper, we assume that the threshold parameter is smaller than the first observing point. Then, on the basis of the two-parameter exponential distribution, the maximum likelihood estimations of both parameters are given, the sufficient and necessary conditions for their existence and uniqueness are argued, and the asymptotic properties of the estimations are also presented, according to which approximate confidence intervals of the parameters are derived. At the same time, the estimation of the parameters is generalized, and some methods are introduced to get explicit expressions of these generalized estimations. Also, a special case where the first failure time of the units is observed is considered. |
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| Keywords: | Exponential distribution grouped data maximum likelihood estimate (MLE) asymptotic property interval estimation. |
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