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, 1-29

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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