来自变换序族的期望次序统计量的不等式与界
Inequalities and bounds for expected order statistics from transform-ordered families
AI总结：
本文提出一种基于变换序建立i.i.d.次序统计量随机序的方法，并利用Jensen不等式在凸序族中推导出随机变量超过次序统计量期望值的概率界。
摘要：
我们引入一种在独立同分布情形下建立次序统计量之间随机序的综合方法。该方法依赖于如下假设：基础分布通过一个变换序与某个参考分布相联系。值得注意的是，该方法具有广泛的适用性，尤其是因为若干著名的非参数分布族可以利用相关的变换序来定义，包括凸变换序和星形变换序。在凸序族的情形下，我们证明应用Jensen不等式能够推导出一个随机变量超过其相应次序统计量期望值的概率的界。
英文摘要：
We introduce a comprehensive method for establishing stochastic orders among order statistics in the i.i.d. case. This approach relies on the assumption that the underlying distribution is linked to a reference distribution through a transform order. Notably, this method exhibits broad applicability, particularly since several well-known nonparametric distribution families can be defined using relevant transform orders, including the convex and the star transform orders. In the context of convex-ordered families, we demonstrate that applying Jensen's inequality enables the derivation of bounds for the probability that a random variable exceeds the expected value of its corresponding order statistic.
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