发表机构
Shanghai University of International Business and Economics; Illinois State University; Jiangsu Normal University（上海对外经贸大学; 伊利诺伊州立大学; 江苏师范大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明在凸变换序下，齐次次序统计量小于异质对应量，异质性更强地拉伸上分位数，并扩展到Weibull等比例风险族，刻画了异质性对分布形状的影响。
AI 中文摘要
设X1,...,Xn为具有任意正速率（不一定相等）的独立指数随机变量，设Y1,...,Yn为独立同分布的指数随机变量。我们证明，对于每个次序统计量，齐次次序统计量在凸变换序意义下小于其异质对应量。我们的结果表明，相对于齐次基准，异质性对上分位数的影响强于对下分位数的影响，而齐次次序统计量在凸变换意义下老化更快。我们进一步将比较扩展到包含Weibull、Lomax和Burr XII分布的比例风险族。我们给出了比较得以保持的显式条件，并证明了在Weibull族内形状限制是紧的。这些结果刻画了分量异质性如何改变次序统计量的分布形状，而不仅仅是位置或尺度效应。
英文摘要
Let X1,...,Xn be independent exponential random variables with arbitrary positive, not necessarily equal, rates, and let Y1,\ldots,Yn be independent and identically distributed exponential random variables. We prove that, for every order statistic, the homogeneous order statistic is smaller than its heterogeneous counterpart in the convex transform order. Our results show that, relative to the homogeneous benchmark, heterogeneity stretches upper quantiles more strongly than lower quantiles, while the homogeneous order statistic ages faster in the convex-transform sense. We further extend the comparison to a proportional-hazards family that includes Weibull, Lomax, and Burr XII distributions. We give explicit conditions under which the comparison is preserved and show that the shape restriction is sharp within the Weibull family. These results characterize how component heterogeneity changes the distributional shape of order statistics beyond effects on location or scale.
