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A class of multivariate copulas based on products of bivariate copulas

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  • Mazo, Gildas
  • Girard, Stéphane
  • Forbes, Florence

Abstract

Copulas are a useful tool to model multivariate distributions. While there exist various families of bivariate copulas, much less work has been done when the dimension is higher. We propose a class of multivariate copulas based on products of transformed bivariate copulas. The analytical forms of the copulas within this class allow to naturally associate a graphical structure which helps to visualize the dependencies and to compute the full joint likelihood even in high dimension. Numerical experiments are conducted both on simulated and real data thanks to a dedicated R package.

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  • Mazo, Gildas & Girard, Stéphane & Forbes, Florence, 2015. "A class of multivariate copulas based on products of bivariate copulas," Journal of Multivariate Analysis, Elsevier, vol. 140(C), pages 363-376.
    • Handle: RePEc:eee:jmvana:v:140:y:2015:i:c:p:363-376
    DOI: 10.1016/j.jmva.2015.06.001
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    References listed on IDEAS

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    8. Ivan Kojadinovic & Jun Yan, 2012. "A Non-parametric Test of Exchangeability for Extreme-Value and Left-Tail Decreasing Bivariate Copulas," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 39(3), pages 480-496, September.
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    Cited by:

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    3. Saminger-Platz Susanne & Klement Erich Peter & Arias-García José De Jesús & Mesiar Radko, 2017. "Characterizations of bivariate conic, extreme value, and Archimax copulas," Dependence Modeling, De Gruyter, vol. 5(1), pages 45-58, January.
    4. Savinov, Evgeniy & Shamraeva, Victoria, 2023. "On a Rosenblatt-type transformation of multivariate copulas," Econometrics and Statistics, Elsevier, vol. 25(C), pages 39-48.
    5. Zhang, Yi & Gomes, António Topa & Beer, Michael & Neumann, Ingo & Nackenhorst, Udo & Kim, Chul-Woo, 2019. "Reliability analysis with consideration of asymmetrically dependent variables: Discussion and application to geotechnical examples," Reliability Engineering and System Safety, Elsevier, vol. 185(C), pages 261-277.
    6. Gregory, Alastair, 2019. "A streaming algorithm for bivariate empirical copulas," Computational Statistics & Data Analysis, Elsevier, vol. 135(C), pages 56-69.
    7. Shyamal Ghosh & Prajamitra Bhuyan & Maxim Finkelstein, 2022. "On a bivariate copula for modeling negative dependence: application to New York air quality data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 31(5), pages 1329-1353, December.

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