| Fiducial inference in the pivotal family of distributions |
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| 作者姓名： | XU Xingzhong & LI Guoying |
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| 作者单位： | XU Xingzhong & LI Guoying Department of Mathematics，Beijing Institute of Technology，Beijing 100081，China; Academy of Mathematics and Systems Science，Chinese Academy of Sciences，Beijing 100080，China |
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| 摘 要： | In this paper a family, called the pivotal family, of distributions is considered. A pivotal family is determined by a generalized pivotal model. Analytical results show that a great many parametric families of distributions are pivotal. In a pivotal family of distributions a general method of deriving fiducial distributions of parameters is proposed. In the method a fiducial model plays an important role. A fiducial model is a function of a random variable with a known distribution, called the pivotal random element, when the observation of a statistic is given. The method of this paper includes some other methods of deriving fiducial distributions. Specially the first fiducial distribution given by Fisher can be derived by the method. For the monotone likelihood ratio family of distributions, which is a pivotal family, the fiducial distributions have a frequentist property in the Neyman-Pearson view. Fiducial distributions of regular parametric functions also have the above frequentist property. Some advantages of the fiducial inference are exhibited in four applications of the fiducial distribution. Many examples are given, in which the fiducial distributions cannot be derived by the existing methods.
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| 收稿时间： | 9 January 2005 |
| 修稿时间： | 16 September 2005 |
Fiducial inference in the pivotal family of distributions |
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| XU Xingzhong & LI Guoying.Fiducial inference in the pivotal family of distributions[J].Science in China(Mathematics),2006,49(3):410-432. |
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| Authors: | XU Xingzhong LI Guoying |
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| Institution: | 1. Department of Mathematics, Beijing Institute of Technology, Beijing 100081, China
2. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080, China |
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| Abstract: | In this paper a family, called the pivotal family, of distributions is considered. A pivotal family is determined by a generalized pivotal model. Analytical results show that a great many parametric families of distributions are pivotal. In a pivotal family of distributions a general method of deriving fiducial distributions of parameters is proposed. In the method a fiducial model plays an important role. A fiducial model is a function of a random variable with a known distribution, called the pivotal random element, when the observation of a statistic is given. The method of this paper includes some other methods of deriving fiducial distributions. Specially the first fiducial distribution given by Fisher can be derived by the method. For the monotone likelihood ratio family of distributions, which is a pivotal family, the fiducial distributions have a frequentist property in the Neyman-Pearson view. Fiducial distributions of regular parametric functions also have the above frequentist property. Some advantages of the fiducial inference are exhibited in four applications of the fiducial distribution. Many examples are given, in which the fiducial distributions cannot be derived by the existing methods. |
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| Keywords: | confidence bounds fiducial distributions fiducial model frequentist prop-erty generalized pivotal model pivotal family of distributions testing hypotheses |
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