CONSTRUCTION OF A CLASS OF COPULAS WITH HORIZONTAL OR VERTICAL SECTION OF A HOMOGRAPHIC FUNCTION

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. Received: July 9, 2024Revised: July 14, 2024Accepted: August 12, 2024