Issue: 2024/Vol.34/No.3, Pages 61-86
DIVERSE COPULAS THROUGH DURANTE’S METHOD. EXPLORING PARAMETRIC FUNCTIONS
Christophe Chesneau
Cite as: C. Chesneau. Diverse copulas through Durante’s method. Exploring parametric functions. Operations Research and Decisions 2024: 34(3), 61-86. DOI 10.37190/ord240304
Abstract
This article unveils the often underestimated potential of a copula methodology introduced by Durante in 2009. It highlights the remarkable ability of the method to generate a broad spectrum of copulas by exploiting various parametric functions. Our exploration encompasses a collection of power-like, exponential-like, trigonometric-like, logarithmic-like, hyperbolic-like and error-like functions, each dependent on one, two, or three parameters, effectively satisfying the necessary assumptions of Durante’s method. The proofs provided rely on suitable differentiation, comprehensive factorizations, and judicious application of mathematical inequalities. In the vast repertoire of copulas derived from this methodology, we present three distinct series of eight new copulas, supported by a graphical analysis of their respective densities. This theoretical study not only expands the understanding of copula generation but also introduces a new perspective on their construction in various contexts.
Keywords: copula, Durante’s method, dependence modeling, copula density, correlation
Received: 15 November 2023 Accepted: 3 July 2024
Published online: 17 October 2024