位置尺度样本构成极值顺序统计量的扩散序和星序

Dispersive and Star Orders on Extreme Order Statistics from Location-Scale Samples

  • 摘要: 顺序统计量在可靠性、拍卖和保险精算等领域有着广泛的应用.本文将讨论位置尺度分布族样本构成的极值顺序统计量的随机序,研究发现极值顺序统计量的随机序与位置参数无关,仅与尺度参数有关.同时,我们建立了尺度参数影响最大顺序统计量的扩散序和星序,也给出了最小顺序统计量的扩散序和星序成立的充分条件.最后,借助数值算例验证了理论结果的有效性.

     

    Abstract: Order statistics are of significant importance in various fields, including reliability, auctions, and actuarial science. This paper explores the stochastic orderings of extreme order statistics within the location-scale samples. Our findings demonstrate that the stochastic orderings of extreme order statistics is independent of the location parameter and is influenced solely by the scale parameter. Meanwhile, we further establish the conditions under which the scale parameter induces dispersive order and star order on the maximum order statistic, and provide sufficient conditions for these orders to hold for the minimum order statistic. Finally, Numerical examples are presented to validate the effectiveness of the theoretical findings.

     

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