Almost stochastic dominance has been receiving a great amount of attention in the financial and economic literatures. In this paper, we characterize the properties of almost first-order stochastic dominance (AFSD) via distorted expectations and investigate the conditions under which AFSD is preserved under a distortion transform. The main results are also applied to establish stochastic comparisons of order statistics and receiver operating characteristic curves via AFSD.

中文翻译：

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扭曲预期几乎是一阶随机主导

几乎随机的支配地位在金融和经济文献中受到了广泛的关注。在本文中，我们通过扭曲的期望来表征几乎一阶随机优势（AFSD）的特性，并研究了在扭曲变换下保留 AFSD 的条件。主要结果还用于通过 AFSD 建立订单统计和接收器操作特征曲线的随机比较。