Mean-variance bounds for order statistics from dependent DFR,IFR, DFRA and IFRA samples |
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| Institution: | 1. Capital One Bank, United States;2. McCombs School of Business, University of Texas at Austin, United States;3. Department of Mathematics, University of Texas at Austin, United States;1. Department of Mathematics, Graduate School of Science, Kyoto University, Sakyo-ku, Kyoto 606-8502, Japan;2. Department of Probability and Statistics, Centro de Investigación en Matemáticas, A.C. Calle Jalisco s/n. C.P. 36240, Guanajuato, Mexico;3. Department of Mathematics, Faculty of Engineering Science, Kansai University, 3-3-35 Yamate-cho, Suita-shi, Osaka 564-8680, Japan;1. School of Risk and Actuarial Studies, Business School and UNSW Data Science Hub, UNSW Sydney, Sydney NSW-2052, Australia;2. Actuarial Research Centre, Department of Statistics, University of Haifa, Mount Carmel, Haifa 31905, Israel;3. Faculty of Sciences, Holon Institute of Technology, Holon 5810201, Israel;1. School of Mathematical Sciences, Xiamen University, Fujian, 361005, PR China;2. College of Mathematics and Statistics, Chongqing University, Chongqing, 401331, PR China |
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| Abstract: | For arbitrarily dependent identically distributed samples with DFR, IFR, DFRA and IFRA distributions, we determine the best attainable upper bounds for the expectation of arbitrary order statistics in terms of the expectation and variance of the parent distribution. Analogous results are concluded for spacings and some other L-estimates. |
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