Characterizations based on regression assumptions of order statistics |
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| Authors: | Wen-Jang Huang Nan-Cheng Su |
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| Institution: | 1. Department of Applied Mathematics, National University of Kaohsiung, Kaohsiung 81148, Taiwan, Republic of Chinahuangwj@nuk.edu.tw;3. Department of Statistics, National Taipei University, New Taipei City 23741, Taiwan, Republic of China |
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| Abstract: | Let X(1)≤X(2)≤···≤X(n) be the order statistics from independent and identically distributed random variables {Xi, 1≤i≤n} with a common absolutely continuous distribution function. In this work, first a new characterization of distributions based on order statistics is presented. Next, we review some conditional expectation properties of order statistics, which can be used to establish some equivalent forms for conditional expectations for sum of random variables based on order statistics. Using these equivalent forms, some known results can be extended immediately. |
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| Keywords: | characterization exponential distribution gamma distribution inverse gamma distribution normal distribution order statistics regression function student t-distribution uniform distribution |
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