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A Characterization of Quasi-copulas


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


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

    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.
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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. 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.
    4. 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, Sciendo, vol. 1, pages 37-53, October.
    5. Thibaut Lux & Antonis Papapantoleon, 2016. "Improved Fr\'echet$-$Hoeffding bounds on $d$-copulas and applications in model-free finance," Papers 1602.08894,, revised Jun 2017.
    6. 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.
    7. Stefan Aulbach & Verena Bayer & Michael Falk, 2012. "A multivariate piecing-together approach with an application to operational loss data," Papers 1205.1617,
    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. repec:bpj:demode:v:6:y:2018:i:1:p:139-155:n:9 is not listed on IDEAS
    12. 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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