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Relations Between Stochastic Orderings and generalized Stochastic Precedence

The concept of "stochastic precedence" between two real-valued random variables has often emerged in different applied frameworks. In this paper we consider a slightly more general, and completely natural, concept of stochastic precedence and analyze its relations with the notions of stochastic ordering. Such a study leads us to introducing some special classes of bivariate copulas. Motivations for our study can arise from different fields. In particular we consider the frame of Target-Based Approach in decisions under risk. This approach has been mainly developed under the assumption of stochastic independence between "Prospects" and "Targets". Our analysis concerns the case of stochastic dependence.