Journal
MEDITERRANEAN JOURNAL OF MATHEMATICS
Volume 18, Issue 4, Pages -Publisher
SPRINGER BASEL AG
DOI: 10.1007/s00009-021-01803-8
Keywords
1-Lipschitz; copula; hairpin
Categories
Funding
- MICINN (Spain) [MTM2017-83496-P]
- Severo Ochoa Programme for Centres of Excellence in RD [SEV-2015-0554]
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This paper investigates necessary and sufficient conditions for a nondecreasing homeomorphisms f defined on [0, 1] such that f(x) < x for all x in ]0, 1[ to be part of a C-hairpin that concentrates the mass of a bivariate copula. It also explores when copulas of this kind come from modular functions, and provides a multidimensional method to construct extreme points in the set of multidimensional copulas under certain conditions.
Consider a nondecreasing homeomorphisms f defined on [0, 1] such that f(x) < x for all x is an element of]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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