On extreme order statistics from heterogeneous Weibull variables |
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Authors: | Peng Zhao Yiying Zhang Jianfei Qiao |
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Affiliation: | 1. School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou 221116, People's Republic of China;2. Department of Statistics and Actuarial Science, The University of Hong Kong, Pokfulam Road, Hong Kong, People's Republic of China;3. School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, People's Republic of China |
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Abstract: | In this paper, we focus on stochastic comparisons of extreme order statistics from heterogeneous independent/interdependent Weibull samples. Specifically, we study extreme order statistics from Weibull distributions with (i) common shape parameter but different scale parameters, and (ii) common scale parameter but different shape parameters. Several new comparison results in terms of the likelihood ratio order, reversed hazard rate order and usual stochastic order are studied in those scenarios. The results established here strengthen and generalize some of the results known in the literature including Khaledi and Kochar [Weibull distribution: some stochastic comparisons. J Statist Plann Inference. 2006;136:3121–3129], Fang and Zhang [Stochastic comparisons of series systems with heterogeneous Weibull components. Statist Probab Lett. 2013;83:1649–1653], Torrado [Comparisons of smallest order statistics from Weibull distributions with different scale and shape parameters. J Korean Statist Soc. 2015;44:68–76] and Torrado and Kochar [Stochastic order relations among parallel systems from Weibull distributions. J Appl Probab. 2015;52:102–116]. Some numerical examples are also provided for illustration. |
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Keywords: | Stochastic orders majorization Weibull distribution Archimedean survival copula heterogeneous samples |
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