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BY 4.0 license Open Access Published by De Gruyter Open Access October 1, 2020

Lorenz-generated bivariate Archimedean copulas

Andrea Fontanari EMAIL logo , Pasquale Cirillo and Cornelis W. Oosterlee
From the journal Dependence Modeling

Abstract

A novel generating mechanism for non-strict bivariate Archimedean copulas via the Lorenz curve of a non-negative 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 a 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.

MSC 2010: 62H05; 62H10

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Received: 2020-02-25
Accepted: 2020-08-03
Published Online: 2020-10-01

© 2020 Andrea Fontanari et al., published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

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