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From Inequality to Extremes and Back: A Lorenz Representation of the Pickands Dependence Function

Author

Listed:
  • Pasquale Cirillo

    (ZHAW School of Management and Law, Theaterstrasse 17, 8401 Winterthur, Switzerland)

  • Andrea Fontanari

    (Optiver BV, Strawinskylaan 3095, 1077ZX Amsterdam, The Netherlands)

Abstract

We establish a correspondence between Lorenz curves and Pickands dependence functions, thereby reframing the construction of any bivariate extreme-value copula as an inequality problem. We discuss the conditions under which a Lorenz curve generates a closed-form Pickands model, considerably expanding the small set of tractable parametrizations currently available. Furthermore, the Pickands measure-generating function M can be written explicitly in terms of the quantile function underlying the Lorenz curve, providing a constructive route to model specification. Finally, classical inequality indices like the Gini coincide with scale-free, rotation-invariant indices of global upper-tail dependence, thereby complementing local coefficients such as the upper tail dependence index λ U .

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:13:p:2047-:d:1683715
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    References listed on IDEAS

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