The construction of multivariate distributions with arbitrary margins has been a problem of interest to statisticians for many years, but nowadays, by virtue of Sklar’s theorem, this problem can be reduced to the construction of a copula. However, there is no general method for constructing a copula. In order to provide a partial solution to this problem, we present in this article, a construction of a new class of ratio-type copulas called a class of copulas with horizontal or vertical section of a homographic function. Indeed, the horizontal section of the copulas of this class can be considered as a homographic function of variable u whose coefficients are functions of v (formula (8)) and the vertical section can be considered as a homographic function of variable v whose coefficients are functions of u (formula (9)). This class can be also considered as a generalization of Ali-Mikhail-Haq family of copulas. We present some examples of copulas in this class.

copulas, AMH copula, horizontal section, vertical section, homographic function

Received: July 9, 2024; Revised: July 14, 2024; Accepted: August 12, 2024; Published: September 14, 2024

How to cite this article: Remi Guillaume Bagré, Herman Tiemtoré and Vini Yves Bernadin Loyara, Construction of a class of copulas with horizontal or vertical section of a homographic function, International Journal of Numerical Methods and Applications 24(2) (2024), 219-236. https://doi.org/10.17654/0975045224014

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

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