Majorisation, also called rearrangement inequalities, yields a type of stochastic ordering in which two or more distributions can be then compared. This method provides a representation of the peakedness of probability distributions and is also independent of the location of probabilities. These properties make majorisation a good candidate as a theory for uncertainty. We demonstrate that this approach is also dimension free by obtaining univariate decreasing rearrangements from multivariate distributions, thus we can consider the ordering of two, or more, distributions with different support. We present operations including inverse mixing and maximise/minimise to combine and analyse uncertainties associated with different distribution functions. We illustrate these methods for empirical examples with applications to scenario analysis and simulations.

中文翻译：

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专业化作为不确定性的理论

大化，也称为重排不等式，产生一种随机排序，其中可以比较两个或多个分布。该方法提供了概率分布峰值的表示，并且与概率的位置无关。这些属性使专业化成为不确定性理论的良好候选者。我们通过从多元分布中获得单变量递减重排来证明这种方法也是无维度的，因此我们可以考虑两个或多个具有不同支持的分布的排序。我们提出了包括逆混合和最大化/最小化在内的操作，以组合和分析与不同分布函数相关的不确定性。