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A Characterization of Quasi-copulas

Author

Listed:
  • Genest, C.
  • Quesada Molina, J. J.
  • Rodriguez Lallena, J. A.
  • Sempi, C.

Abstract

The notion of quasi-copula was introduced by C. Alsina, R. B. Nelsen, and B. Schweizer (Statist. Probab. Lett.(1993), 85-89) and was used by these authors and others to characterize operations on distribution functions that can or cannot be derived from operations on random variables. In this paper, the concept of quasi-copula is characterized in simpler operational terms and the result is used to show that absolutely continuous quasi-copulas are not necessarily copulas, thereby answering in the negative an open question of the above mentioned authors.

Suggested Citation

  • Genest, C. & Quesada Molina, J. J. & Rodriguez Lallena, J. A. & Sempi, C., 1999. "A Characterization of Quasi-copulas," Journal of Multivariate Analysis, Elsevier, vol. 69(2), pages 193-205, May.
    • Handle: RePEc:eee:jmvana:v:69:y:1999:i:2:p:193-205
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    References listed on IDEAS

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    1. Alsina, Claudi & Nelsen, Roger B. & Schweizer, Berthold, 1993. "On the characterization of a class of binary operations on distribution functions," Statistics & Probability Letters, Elsevier, vol. 17(2), pages 85-89, May.
    2. Parrini, Carl P. & Sklar, Martin J., 1983. "New Thinking about the Marker, 1896–1904: Some American Economists on Investment and the Theory of Surplus Captial," The Journal of Economic History, Cambridge University Press, vol. 43(3), pages 559-578, September.
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    Cited by:

    1. Fabrizio Durante & Erich Klement & Carlo Sempi & Manuel Úbeda-Flores, 2010. "Measures of non-exchangeability for bivariate random vectors," Statistical Papers, Springer, vol. 51(3), pages 687-699, September.
    2. Quesada Molina, Jose Juan & Sempi, Carlo, 2005. "Discrete quasi-copulas," Insurance: Mathematics and Economics, Elsevier, vol. 37(1), pages 27-41, August.
    3. Stefan Aulbach & Verena Bayer & Michael Falk, 2012. "A multivariate piecing-together approach with an application to operational loss data," Papers 1205.1617, arXiv.org.
    4. Nelsen, Roger B. & Molina, José Juan Quesada & Lallena, José Antonio Rodríguez & Flores, Manuel Úbeda, 2004. "Best-possible bounds on sets of bivariate distribution functions," Journal of Multivariate Analysis, Elsevier, vol. 90(2), pages 348-358, August.
    5. Fabrizio Durante & Juan Fernández-Sánchez & Wolfgang Trutschnig & Manuel Úbeda-Flores, 2020. "On the Size of Subclasses of Quasi-Copulas and Their Dedekind–MacNeille Completion," Mathematics, MDPI, vol. 8(12), pages 1-11, December.
    6. Michel Grabisch & Jean-Luc Marichal & Radko Mesiar & Endre Pap, 2011. "Aggregation functions: construction methods, conjunctive, disjunctive and mixed classes," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00539032, HAL.
    7. Durante Fabrizio & Puccetti Giovanni & Scherer Matthias & Vanduffel Steven, 2017. "My introduction to copulas: An interview with Roger Nelsen," Dependence Modeling, De Gruyter, vol. 5(1), pages 88-98, January.
    8. Cuculescu, Ioan & Theodorescu, Radu, 2003. "Are copulas unimodal?," Journal of Multivariate Analysis, Elsevier, vol. 86(1), pages 48-71, July.
    9. Mesiar, R. & Kolesárová, A. & Bustince, H. & Dimuro, G.P. & Bedregal, B.C., 2016. "Fusion functions based discrete Choquet-like integrals," European Journal of Operational Research, Elsevier, vol. 252(2), pages 601-609.
    10. Chiburis, Richard C., 2010. "Semiparametric bounds on treatment effects," Journal of Econometrics, Elsevier, vol. 159(2), pages 267-275, December.
    11. Durante Fabrizio & Fernández-Sánchez Juan & Trutschnig Wolfgang, 2014. "Solution to an open problem about a transformation on the space of copulas," Dependence Modeling, De Gruyter, vol. 2(1), pages 1-8, November.
    12. Genest Christian & Scherer Matthias, 2020. "The gentleman copulist: An interview with Carlo Sempi," Dependence Modeling, De Gruyter, vol. 8(1), pages 34-44, January.
    13. Bernard Carole & Liu Yuntao & MacGillivray Niall & Zhang Jinyuan, 2013. "Bounds on Capital Requirements For Bivariate Risk with Given Marginals and Partial Information on the Dependence," Dependence Modeling, De Gruyter, vol. 1(2013), pages 37-53, October.
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    15. Genest Christian & Scherer Matthias, 2020. "The gentleman copulist: An interview with Carlo Sempi," Dependence Modeling, De Gruyter, vol. 8(1), pages 34-44, January.
    16. Thibaut Lux & Antonis Papapantoleon, 2016. "Improved Fr\'echet$-$Hoeffding bounds on $d$-copulas and applications in model-free finance," Papers 1602.08894, arXiv.org, revised Jun 2017.
    17. Ali E. Abbas, 2009. "Multiattribute Utility Copulas," Operations Research, INFORMS, vol. 57(6), pages 1367-1383, December.
    18. Saminger-Platz Susanne & De Jesús Arias-García José & Mesiar Radko & Klement Erich Peter, 2017. "Characterizations of bivariate conic, extreme value, and Archimax copulas," Dependence Modeling, De Gruyter, vol. 5(1), pages 45-58, January.
    19. Nelsen, Roger B. & Quesada-Molina, José Juan & Rodri­guez-Lallena, José Antonio & Úbeda-Flores, Manuel, 2008. "On the construction of copulas and quasi-copulas with given diagonal sections," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 473-483, April.
    20. Aulbach, Stefan & Falk, Michael & Hofmann, Martin, 2012. "The multivariate Piecing-Together approach revisited," Journal of Multivariate Analysis, Elsevier, vol. 110(C), pages 161-170.

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