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Weak Dependence Notions and Their Mutual Relationships

Author

Listed:
  • Jorge Navarro

    (Facultad de Matemáticas, Universidad de Murcia, Campus de Espinardo, 30100 Murcia, Spain)

  • Franco Pellerey

    (Dipartimento di Scienze Matematiche, Politecnico di Torino, C.so 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)

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.

Suggested Citation

  • Jorge Navarro & Franco Pellerey & Miguel A. Sordo, 2020. "Weak Dependence Notions and Their Mutual Relationships," Mathematics, MDPI, vol. 9(1), pages 1-27, December.
    • Handle: RePEc:gam:jmathe:v:9:y:2020:i:1:p:81-:d:473186
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    References listed on IDEAS

    as
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    5. Longobardi, Maria & Pellerey, Franco, 2019. "On the role of dependence in residual lifetimes," Statistics & Probability Letters, Elsevier, vol. 153(C), pages 56-64.
    6. Belzunce, Félix & Martínez-Riquelme, Carolina & Ruiz, José M., 2013. "On sufficient conditions for mean residual life and related orders," Computational Statistics & Data Analysis, Elsevier, vol. 61(C), pages 199-210.
    7. Jorge Navarro & Nuria Torrado & Yolanda del Águila, 2018. "Comparisons Between Largest Order Statistics from Multiple-outlier Models with Dependence," Methodology and Computing in Applied Probability, Springer, vol. 20(1), pages 411-433, March.
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    Cited by:

    1. Ortega-Jiménez, Patricia & Pellerey, Franco & Sordo, Miguel A. & Suárez-Llorens, Alfonso, 2024. "Probability equivalent level for CoVaR and VaR," Insurance: Mathematics and Economics, Elsevier, vol. 115(C), pages 22-35.

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