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Weak Dependence Notions and Their Mutual Relationships

Jorge Navarro (), Franco Pellerey () and Miguel A. Sordo ()
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Jorge Navarro: Facultad de Matemáticas, Universidad de Murcia, Campus de Espinardo, 30100 Murcia, Spain
Franco Pellerey: Dipartimento di Scienze Matematiche, Politecnico di Torino, Duca degli Abruzzi 24, 10129 Torino, Italy
Miguel A. Sordo: Departamento de Estadítica e I. O., Universidad de Cádiz, C/Duque de Nájera 8, 11002 Cádiz, Spain

Mathematics, 2020, vol. 9, issue 1, 1-27

Abstract: New weak notions of positive dependence between the components X and Y of a random pair ( X , Y ) have been considered in recent papers that deal with the effects of dependence on conditional residual lifetimes and conditional inactivity times. The purpose of this paper is to provide a structured framework for the definition and description of these notions, and other new ones, and to describe their mutual relationships. An exhaustive review of some well-know notions of dependence, with a complete description of the equivalent definitions and reciprocal relationships, some of them expressed in terms of the properties of the copula or survival copula of ( X , Y ) , is also provided.

Keywords: dependence notions; stochastic orders; copulas; total positivity (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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