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On the dependence between the extreme order statistics in the proportional hazards model |
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| Authors: | Ali Dolati Subhash C Kochar |
| Institution: | a Department of Mathematics, Faculty of Science, Yazd University, Yazd 89195-741, Iran b Département de mathématiques et de statistique, Université Laval, Québec, Canada G1K 7P4 c Department of Mathematics and Statistics, Portland State University, Portland, OR 97207-0751, USA |
| Abstract: | Let X1,…,Xn be a random sample from an absolutely continuous distribution with non-negative support, and let Y1,…,Yn be mutually independent lifetimes with proportional hazard rates. Let also X(1)<?<X(n) and Y(1)<?<Y(n) be their associated order statistics. It is shown that the pair (X(1),X(n)) is then more dependent than the pair (Y(1),Y(n)), in the sense of the right-tail increasing ordering of Avérous and Dortet-Bernadet LTD and RTI dependence orderings, Canad. J. Statist. 28 (2000) 151-157]. Elementary consequences of this fact are highlighted. |
| Keywords: | 60E15 62G30 62H20 |
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