畸变随机优势：随机序的广义族
Distorted stochastic dominance: a generalized family of stochastic orders
摘要：
我们研究了一个广义家庭的随机订单，半参数化的失真函数H，即H-扭曲的随机优势，这可能会决定一个连续的优势关系，从第一至第二阶随机优势（及以上）。这样一个家庭是特别适合代表决策者的偏好，在风险规避方面，并可用于在这些情况下，一个强的顺序没有足够的判别力，而一个较弱的是不好的代表某些类别的决策者。特别是，我们专注于一类的功率失真函数，产生功率失真的随机优势，这似乎是特别有吸引力的，由于其计算简单和一些有趣的统计解释。最后，我们扭曲的随机优势的失真函数产生的扭曲的期望保序类的特征。
英文摘要：
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.
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