A new class of random vectors is introduced, where the components are obtained through trend-transforms of independent random variables. Such a vector is called trend-transformed independent vector. The new class includes many models from the previous literature, such as sequential and intermediate order statistics, or the vectors formed by the first arrival times in classical counting processes such as trend renewal/extended Pólya/non-homogeneous pure-birth processes. This allows to treat all these different models in a unified way. New multivariate stochastic comparison results are obtained between trend-transformed independent vectors with different parameters, which are shown to enlarge previous results from the literature.

中文翻译：

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趋势转换的独立向量：构建和随机比较结果

引入了一类新的随机向量，其中的分量是通过独立随机变量的趋势变换获得的。这样的向量称为趋势变换独立向量。新类包括许多来自先前文献的模型，例如顺序和中间顺序统计，或者由经典计数过程中的首次到达时间形成的向量，例如趋势更新/扩展 Pólya/非同质纯出生过程。这允许以统一的方式处理所有这些不同的模型。在具有不同参数的趋势转换独立向量之间获得了新的多变量随机比较结果，这表明扩大了先前文献中的结果。