Inequalities for order statistics of samples from distributions with monotone hazard rate


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A number of inequalities relating the mathematical expectations of order statistics or functions of order statistics in the case where the sample is taken from a distribution with monotone hazard rate function are presented. These inequalities can be applied in reliability theory and other areas of probability theory and mathematical statistics. In particular, in the paper, they are used to obtain new characterizations of the exponential distribution.

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V. Ushakov

Faculty of Computational Mathematics and Cybernetics; Institute of of Informatics Problems, Federal Research Center “Computer Science and Control,”

编辑信件的主要联系方式.
Email: vgushakov@mail.ru
俄罗斯联邦, Moscow, 119991; ul. Vavilova 44 korp. 2, Moscow, 119333

N. Ushakov

Institute of Microelectronics Technology and High Purity Materials; Norwegian Science and Technology University

Email: vgushakov@mail.ru
俄罗斯联邦, ul. Akademika Osip’yana 6, Chernogolovka, Moscow oblast, 142432; Trondheim

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