Relations Between Stochastic Orderings and generalized Stochastic Precedence

TL;DR

This paper explores the relationship between stochastic precedence and stochastic orderings, introducing new classes of copulas, with applications in decision-making under risk involving dependent prospects and targets.

Contribution

It generalizes stochastic precedence, analyzes its connection with stochastic orderings, and introduces copula classes relevant for dependent variables in decision models.

Findings

Established links between stochastic precedence and stochastic orderings.

Introduced new classes of copulas for dependent variables.

Applied findings to decision-making frameworks under risk.

Abstract

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.