We study a generalized family of stochastic orders, semiparametrized by a distortion function H, namely H-distorted stochastic dominance, which may determine a continuum of dominance relations from the first- to the second-order stochastic dominance (and beyond). Such a family is especially suitable for representing a decision maker's preferences in terms of risk aversion and may be used in those situations in which a strong order does not have enough discriminative power, whilst a weaker one is poorly representative of some classes of decision makers. In particular, we focus on the class of power distortion functions, yielding power-distorted stochastic dominance, which seems to be particularly appealing owing to its computational simplicity and some interesting statistical interpretations. Finally, we characterize distorted stochastic dominance in terms of distortion functions yielding isotonic classes of distorted expectations.

中文翻译：

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扭曲的随机优势：一个广义的随机顺序族

我们研究了一个广义的随机阶族，由失真函数 H 半参数化，即 H 失真的随机优势，它可以确定从一阶到二阶随机优势（及以后）的连续支配关系。这样的族特别适合代表决策者在风险规避方面的偏好，可用于强命令没有足够辨别力的情况，而较弱的命令不能很好地代表某些类别的决策者。特别是，我们专注于功率失真函数的类别，产生功率失真的随机优势，由于其计算简单性和一些有趣的统计解释，这似乎特别有吸引力。最后，