Hazard rate ordering of the second-order statistics from multiple-outlier PHR samples |
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| Authors: | Xiong Cai Yiying Zhang |
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| Institution: | 1. School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou, People's Republic of China;2. Department of Statistics and Actuarial Science, The University of Hong Kong, Pokfulam, Hong Kong |
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| Abstract: | In this paper, we compare the hazard rate functions of the second-order statistics arising from two sets of independent multiple-outlier proportional hazard rates (PHR) samples. It is proved that the submajorization order between the sample size vectors together with the supermajorization order between the hazard rate vectors imply the hazard rate ordering between the corresponding second-order statistics from multiple-outlier PHR random variables. The results established here provide theoretical guidance both for the winner's price for the bid in the second-price reverse auction in auction theory and fail-safe system design in reliability. Some numerical examples are also provided for illustration. |
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| Keywords: | Hazard rate ordering multiple-outlier PHR models majorization order second-order statistics |
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