In this paper, we discuss stochastic comparison of the largest order statistics arising from two sets of dependent distribution-free random variables with respect to multivariate chain majorization, where the dependency structure can be defined by Archimedean copulas. When a distribution-free model with possibly two parameter vectors has its matrix of parameters changing to another matrix of parameters in a certain mathematical sense, we obtain the first sample maxima is larger than the second sample maxima with respect to the usual stochastic order, based on certain conditions. Applications of our results for scale proportional reverse hazards model, exponentiated gamma distribution, Gompertz–Makeham distribution, and location-scale model, are also given. Meanwhile, we provide two numerical examples to illustrate the results established here.

中文翻译：

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来自相关分布自由随机变量的样本最大值的通常随机排序

在本文中，我们讨论了关于多元链主要化的两组相关无分布随机变量产生的最大阶统计量的随机比较，其中依赖结构可以由阿基米德联结函数定义。当一个可能有两个参数向量的无分布模型在某种数学意义上将其参数矩阵变为另一个参数矩阵时，我们得到第一个样本最大值大于第二个样本最大值相对于通常的随机顺序，基于在某些条件下。还给出了我们的结果在尺度比例逆向风险模型、取幂伽玛分布、Gompertz-Makeham 分布和位置尺度模型中的应用。同时，我们提供了两个数值示例来说明此处建立的结果。