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Lorenz-generated bivariate Archimedean copulas

Author

Listed:
  • Fontanari Andrea

    (Applied Probability Group, EEMCS Faculty, Delft University of Technology, Building 28, Van Mourik Broekmanweg 6, 2628 XE Delft, TheNetherlands, Phone: +31.152.782.589)

  • Cirillo Pasquale

    (M Open Forecasting Center and Institute For the Future, University of Nicosia)

  • Oosterlee Cornelis W.

    (Numerical Analysis, DIAM, Delft University of Technology,Mekelweg 4, 2628 CD Delft, the Netherland)

Abstract

A novel generating mechanism for non-strict bivariate Archimedean copulas via the Lorenz curve of a non-negative random variable is proposed. Lorenz curves have been extensively studied in economics and statistics to characterize wealth inequality and tail risk. In this paper, these curves are seen as integral transforms generating increasing convex functions in the unit square. Many of the properties of these “Lorenz copulas”, from tail dependence and stochastic ordering, to their Kendall distribution function and the size of the singular part, depend on simple features of the random variable associated to the generating Lorenz curve. For instance, by selecting random variables with a lower bound at zero it is possible to create copulas with asymptotic upper tail dependence. An “alchemy” of Lorenz curves that can be used as general framework to build multiparametric families of copulas is also discussed.

Suggested Citation

  • Fontanari Andrea & Cirillo Pasquale & Oosterlee Cornelis W., 2020. "Lorenz-generated bivariate Archimedean copulas," Dependence Modeling, De Gruyter, vol. 8(1), pages 186-209, January.
    • Handle: RePEc:vrs:demode:v:8:y:2020:i:1:p:186-209:n:11
    DOI: 10.1515/demo-2020-0011
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    References listed on IDEAS

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    Cited by:

    1. Pasquale Cirillo & Andrea Fontanari, 2025. "From Inequality to Extremes and Back: A Lorenz Representation of the Pickands Dependence Function," Mathematics, MDPI, vol. 13(13), pages 1-28, June.

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