Analysis of Order Statistics from Distributions with Regularly Varying Tails |
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| Authors: | Yu Huang Yongling Li Maochao Xu |
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| Affiliation: | 1. Hebei Engineering Research Center of Simulation &2. Optimized Control for Power Generation, North China Electric Power University, Baoding, P.R. China;3. Department of Mathematics, Illinois State University, Normal, Illinois, USA |
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| Abstract: | In this article, necessary conditions for comparing order statistics from distributions with regularly varying tails are discussed in terms of various stochastic orders. A necessary and sufficient condition for stochastically comparing tail behaviors of order statistics is derived. The main results generalize and recover some results in Kleiber (2002 Kleiber, C. (2002). Variability ordering of heavy-tailed distributions with applications to order statistics. Statist. Probab. Lett. 58:381388.[Crossref], [Web of Science ®] , [Google Scholar], 2004 Kleiber, C. (2004). Lorenz ordering of order statistics from log-logistic and related distributions. J. Statist. Plann. Infer. 120:2004.[Crossref], [Web of Science ®] , [Google Scholar]). Extensions to coherent systems are mentioned as well. |
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| Keywords: | Coherent systems Increasing and convex (concave) order Lorenz order Order statistics regular variation. |
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