From Inequality to Extremes and Back: A Lorenz Representation of the Pickands Dependence Function
Year: 2025
Type: article
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 λU.
Source: Mathematics
DOI: 10.3390/math13132047
Authors: Pasquale Cirillo, Andrea Fontanari
Institution: ZHAW Zurich University of Applied Sciences
Language: English
Subfield: Finance
Domain: Social Sciences
Open Access status: gold
Estimated APC paid: $3,137
OpenAlex ID: W4411492903