On variances and covariances of a kind of extreme order statistics |
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| Authors: | Jinliang Wang Changshou Deng Jiangfeng Li Mingfa Zhou |
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| Institution: | 1. Department of Science, Jiujiang University, Jiangxi Province, P.R. Chinawjlwyk@126.com;3. Department of Information and Technology, Jiujiang University, Jiangxi Province, P.R. China;4. Department of Science, Jiujiang University, Jiangxi Province, P.R. China |
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| Abstract: | ABSTRACTFor a random sample from a population with a continuous density function over its bounded support, when the sample size turns to infinity, we explore the uniform integrability of normalized extreme order statistics, for which we obtain limit equivalent expressions of variances. Moreover, we prove that the covariance of the minimum and the maximum of the sample can be bounded by two expressions that are same order infinitesimals. Examples with simulated results are provided to demonstrate the application of our theorems. |
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| Keywords: | Order statistics Uniform integrability UMVUE |
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