IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2020i1p81-d473186.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/1/81/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/1/81/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Dhaene, Jan & Goovaerts, Marc J., 1996. "Dependency of Risks and Stop-Loss Order1," ASTIN Bulletin, Cambridge University Press, vol. 26(2), pages 201-212, November.
    2. Schechtman, E. & Yitzhaki, S., 1999. "On the proper bounds of the Gini correlation," Economics Letters, Elsevier, vol. 63(2), pages 133-138, May.
    3. 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.
    4. 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.
    5. George Kimeldorf & Allan Sampson, 1989. "A framework for positive dependence," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 41(1), pages 31-45, March.
    6. Rodríguez-Lallena, José Antonio & Úbeda-Flores, Manuel, 2004. "A new class of bivariate copulas," Statistics & Probability Letters, Elsevier, vol. 66(3), pages 315-325, February.
    7. Longobardi, Maria & Pellerey, Franco, 2019. "On the role of dependence in residual lifetimes," Statistics & Probability Letters, Elsevier, vol. 153(C), pages 56-64.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Antonio Di Crescenzo & Abdolsaeed Toomaj, 2022. "Weighted Mean Inactivity Time Function with Applications," Mathematics, MDPI, vol. 10(16), pages 1-30, August.
    2. Denuit, Michel & Lefevre, Claude & Mesfioui, M'hamed, 1999. "A class of bivariate stochastic orderings, with applications in actuarial sciences," Insurance: Mathematics and Economics, Elsevier, vol. 24(1-2), pages 31-50, March.
    3. Fabrizio Durante & Roberto Ghiselli-Ricci, 2012. "Supermigrative copulas and positive dependence," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 96(3), pages 327-342, July.
    4. Goovaerts, M. J. & Dhaene, J., 1999. "Supermodular ordering and stochastic annuities," Insurance: Mathematics and Economics, Elsevier, vol. 24(3), pages 281-290, May.
    5. Mansour Shrahili & Mohamed Kayid, 2023. "Stochastic Orderings of the Idle Time of Inactive Standby Systems," Mathematics, MDPI, vol. 11(20), pages 1-21, October.
    6. Torrado, Nuria, 2022. "Optimal component-type allocation and replacement time policies for parallel systems having multi-types dependent components," Reliability Engineering and System Safety, Elsevier, vol. 224(C).
    7. Yeo, Keng Leong & Valdez, Emiliano A., 2006. "Claim dependence with common effects in credibility models," Insurance: Mathematics and Economics, Elsevier, vol. 38(3), pages 609-629, June.
    8. Frostig, Esther, 2006. "On risk dependence and mrl ordering," Statistics & Probability Letters, Elsevier, vol. 76(3), pages 231-243, February.
    9. Mukhtar M. Salah & M. El-Morshedy & M. S. Eliwa & Haitham M. Yousof, 2020. "Expanded Fréchet Model: Mathematical Properties, Copula, Different Estimation Methods, Applications and Validation Testing," Mathematics, MDPI, vol. 8(11), pages 1-29, November.
    10. Serfling, Robert & Xiao, Peng, 2007. "A contribution to multivariate L-moments: L-comoment matrices," Journal of Multivariate Analysis, Elsevier, vol. 98(9), pages 1765-1781, October.
    11. Kaas, Rob & Tang, Qihe, 2005. "A large deviation result for aggregate claims with dependent claim occurrences," Insurance: Mathematics and Economics, Elsevier, vol. 36(3), pages 251-259, June.
    12. Li, Chen & Li, Xiaohu, 2021. "On stochastic dependence in residual lifetime and inactivity time with some applications," Statistics & Probability Letters, Elsevier, vol. 177(C).
    13. Loisel, Stéphane & Trufin, Julien, 2014. "Properties of a risk measure derived from the expected area in red," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 191-199.
    14. Yoel Finkel & Yevgeny Artsev & Shlomo Yitzhaki, 2006. "Inequality measurement and the time structure of household income in Israel," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 4(2), pages 153-179, August.
    15. J. Christopher Westland, 2015. "Economics of eBay’s buyer protection plan," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 1(1), pages 1-20, December.
    16. Kaas, Rob & Laeven, Roger J.A. & Nelsen, Roger B., 2009. "Worst VaR scenarios with given marginals and measures of association," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 146-158, April.
    17. Joachim R. Frick & Jan Goebel & Edna Schechtman & Gert G. Wagner & Shlomo Yitzhaki, 2006. "Using Analysis of Gini (ANOGI) for Detecting Whether Two Subsamples Represent the Same Universe," Sociological Methods & Research, , vol. 34(4), pages 427-468, May.
    18. Navarro, Jorge & Fernández-Martínez, Pedro, 2021. "Redundancy in systems with heterogeneous dependent components," European Journal of Operational Research, Elsevier, vol. 290(2), pages 766-778.
    19. Ortega-Jiménez, P. & Sordo, M.A. & Suárez-Llorens, A., 2021. "Stochastic orders and multivariate measures of risk contagion," Insurance: Mathematics and Economics, Elsevier, vol. 96(C), pages 199-207.
    20. Albers, Willem, 1999. "Stop-loss premiums under dependence," Insurance: Mathematics and Economics, Elsevier, vol. 24(3), pages 173-185, May.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:9:y:2020:i:1:p:81-:d:473186. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.