Lorenz-Generated Bivariate Archimedean Copulas
22 Pages Posted: 7 Jun 2019 Last revised: 26 Jun 2020
Date Written: February 24, 2020
An alternative generating mechanism for non-strict bivariate Archimedean copulas via the Lorenz curve of a positive random variable is proposed. Lorenz curves have been extensively studied in economics and statistics to characterize wealth inequality and tail risk. In this paper, these curves are seen as integral transforms generating increasing convex functions in the unit square.
Many of the properties of these "Lorenz copulas", from tail dependence and stochastic ordering, to their Kendall distribution function and the size of the singular part, depend on simple features of the random variable associated to the generating Lorenz curve. For instance, by selecting random variables with lower bound at zero it is possible to create copulas with asymptotic upper tail dependence.
An "alchemy" of Lorenz curves that can be used as general framework to build multiparametric families of copulas is also discussed.
Keywords: Copula, Lorenz Curve, Lorenz Copula, Kendall's tau, Generator
JEL Classification: C10, C46
Suggested Citation: Suggested Citation