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

Pasquale Cirillo () and Andrea Fontanari
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Pasquale Cirillo: ZHAW School of Management and Law, Theaterstrasse 17, 8401 Winterthur, Switzerland
Andrea Fontanari: Optiver BV, Strawinskylaan 3095, 1077ZX Amsterdam, The Netherlands

Mathematics, 2025, vol. 13, issue 13, 1-28

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 .

Keywords: Lorenz curve; pickands dependence function; extreme-value copula; inequality measures; tail dependence (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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