Positive Dependence Orders: A Survey
Notions of positive dependence of two random variables X and Y have been introduced in the literature in an effort to mathematically describe the property that “large (respectively, small) values of X go together with large (respectively, small) values of Y.” Some of these notions are based on some comparison of the joint distribution of X and Y with their distribution under the theoretical assumption that X and Y are independent. Often such a comparison can be extended to general pairs of bivariate distributions with given marginals. This fact led researchers to introduce various notions of positive dependence orders. These orders are designed to compare the strength of positive dependence of the two underlying bivariate distributions. In this survey we describe some such notions.
KeywordsRandom Vector Joint Distribution Independent Random Variable Bivariate Distribution Dependence Order
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