Copulas With Given Diagonal Sections: Novel Constructions and Applications

Abstract

In this paper, we present some methods for constructing copulas with a given diagonal section that are not necessarily symmetric. An interesting application for the construction of copulas with given tail dependence coefficients is, hence, provided.

A New Characterization of Bivariate Copulas

“…Γ = {(x, x) | x ∈ I}: see (Durante et al, 2007a;Nelsen et al, 2008). Moreover, it also applies to all the cases where two copulas A and A coincides on a given Γ being the graph of a continuous and strictly increasing function of I.…”

Copula Theory: An Introduction

“…• copulas with given horizontal and/or vertical sections: see [48,110,167,170,196]; • copulas with given diagonal sections: see [34,35,44,47,59,101,102,134,154]; • copulas with given affine sections [109,164]. 8 Copula theory: what's the future?…”

Biconic aggregation functions with a given diagonal or opposite diagonal section

“…is the greatest symmetric copula with diagonal section δ [12,14,26]. Similarly, the opposite diagonal section of a [0, 1]…”

“…Diagonal and opposite diagonal functions have been used recently to construct several subclasses of aggregation functions such as quasi-copulas and copulas [5,7,11,12,13,14,20].…”