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Cumulative distribution functions, p-boxes and decisions under risk

机译：累积分布函数，p-box和风险决策

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Our concern is with the problem of decision making in the face of incomplete or imprecise probabilistic information. We particularly focus on the use of the Cumulative Distribution Function (CDF) and the related idea of a p-box. After first describing the CDF we consider the problem of choosing between two uncertain alternatives based on their representation using CDFs. We introduce the idea of dominance as a primary rule for choosing between CDFs. Since this condition is often not satisfied, we provide a rule based on a comparison of the integrals of the CDF. We show how this is related to the expected value. The p-box, which is seen as an imprecise CDF, is introduced. We then consider the problem of choosing between alternatives whose payoffs are represented as p-boxes.
机译：我们关注的是面对不完整或不准确的概率信息进行决策的问题。我们特别关注累积分布函数（CDF）的使用和p盒的相关概念。在首先描述CDF之后，我们考虑基于两个不确定替代方案在CDF上的表示来进行选择的问题。我们介绍了支配地位的概念，作为在CDF之间进行选择的主要规则。由于通常不满足此条件，因此我们提供了基于CDF积分比较的规则。我们展示了这与期望值的关系。介绍了p-box，它被视为不精确的CDF。然后，我们考虑在收益表示为p-box的替代方案之间进行选择的问题。

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