Construction of copulas with hairpin support

Chamizo Lorente, Fernando; Fernández-Sánchez, Juan; Úbeda-Flores, Manuel

UAM_Biblioteca

Author

Chamizo Lorente, Fernando

; Fernández-Sánchez, Juan; Úbeda-Flores, Manuel

Entity

UAM. Departamento de Matemáticas

Publisher

Springer

Date

2021-05-29

Citation

Mediterranean Journal of Mathematics 18.4 (2021): 155

ISSN

1660-5446 (print); 1660-5454 (online)

DOI

10.1007/s00009-021-01803-8

Funded by

The authors acknowledge the comments of the reviewer. The first author is partially supported by the MTM2017-83496-P grant of the MICINN (Spain) and the “Severo Ochoa Programme for Centres of Excellence in R&D” (SEV2015-0554)

Project

Gobierno de España. MTM2017-83496-P

Editor's Version

https://doi.org/10.1007/s00009-021-01803-8

Subjects

1-Lipschitz; Copula; Hairpin; Primary 60E05; Secondary 62E10; Matemáticas

URI

http://hdl.handle.net/10486/700633

Note

“This is a post-peer-review, pre-copyedit version of an article published in Mediterranean Journal of Mathematics. The final authenticated version is available online at: http://dx.doi.org/10.1007/s00009-021-01803-8”

Rights

Abstract

Consider a nondecreasing homeomorphisms f defined on [0, 1] such that f(x) < x for all x ∈]0, 1[. In this paper, we provide necessary and sufficient conditions for such f to be part of a C-hairpin that concentrates the mass of a bivariate copula. In addition, we study when copulas of this kind come from modular functions. Finally, under certain conditions, we give a multidimensional method that generalizes the bivariate case and allows to construct extreme points in the set of multidimensional copulas

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