A note on the view of the Pickands dependence function as a Lorenz curve

Abstract

The goal of this note is to introduce a new way of representing and characterizing the Pickands dependence function in the bivariate framework, using the Lorenz curve, a well-know tool in wealth inequality studies.

We first notice that the Pickands dependence function is nothing but a Lorenz curve in a particular coordinate system. Once this connection is established, we can use the representation of the Lorenz curve as integral of the quantile function of positive random variables to obtain a simple way to generate Pickands dependence functions, and to characterize their measure generating function.

The new Lorenz representation also allows to import in the Pickands framework all the set of concentration measures usually found in the inequality studies literature, giving them brand new interpretations in terms of extremal dependence.

Keywords: Extremal copula, Pickands function, Lorenz Curve, Inequality Indices

JEL Classification: C10, C13