Stochastic Dominance and Transformations of Random Variables
Stochastic Dominance and Transformations of Random Variables
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DOI：
10.1007/978-1-4613-8922-4_3
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发表时间：
1989
期刊：
影响因子：
--
通讯作者：
Jack Meyer
中科院分区：
文献类型：
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作者：
Jack Meyer
在过去的20年里，经济学家使用随机优势（SD）一词来描述一组特定的随机变量排序规则。这些规则适用于随机变量对，并通过指定它们的累积分布函数（CDF）之间的差必须满足的条件来指示何时一个比另一个排名更高。各种SD排名程序已被用于实证和理论分析。一阶随机优势、二阶随机优势以及Rothschild和Stiglitz关于风险递增的定义都是典型的例子，大量的实证研究都使用这些SD规则来确定选择集中哪些元素在两两随机优势和凸随机优势意义下都是非劣势的（有效的）。此外，涉及随机性的理论研究通常确定在特定SD定义下用主导随机参数的随机参数替换随机参数的效果。在这些应用中，SD定义可以直接使用而无需修改。这是可能的，因为比较选择集中的随机变量可以通过比较它们的CDF来进行;同样，在决策模型中用另一个随机变量替换一个随机变量是通过在期望效用计算中用另一个CDF替换一个CDF来完成的。因此，在这些应用中可以不加修改地使用各种SD排序标准。
During the past twenty years, the term stochastic dominance (SD) has been used by economists to describe a particular set of rules for ranking random variables. These rules apply to pairs of random variables, and indicate when one is to be ranked higher than the other by specifying a condition which the difference between their cumulative distribution functions (CDF) must satisfy. Various SD ranking procedures have been employed in both empirical and theoretical analysis. First degree stochastic dominance, second degree stochastic dominance, and Rothschild and Stiglitz'definition of increasing risk are prominent examples.A variety of empirical studies have used these SD rules to determine which elements in a choice set are undominated (efficient) in both the pairwise and convex stochastic dominance senses. In addition, theoretical studies involving randomness have often determined the effect of replacing a random parameter by one which dominates it under a particular SD definition. In each of these applications, the SD definitions can be used directly without modification. This is possible since comparing the random variables in a choice set can be carried out by comparing their CDFs; also, replacing one random variable by another in a decision model is accomplished by replacing one CDF with another in the expected utility calculation. Thus, the various SD ranking criteria can be used without modification in these applications.