Some new developments on variable-power copulas

Abstract

This article aims to contribute to the theory of variable-power copulas. In the first part, we discuss and study two unexplored variable-power copulas based on a modification of the function "x 1/y y 1/x ". Their originality in definition offers interesting alternative options to the existing variablepower copulas. However, these copulas have a strong limitation: they are free of any parameters, making them rigid in the functional sense. In light of this, the second part is devoted to some parametric versions of them, still belonging to the variable-power copulas family. They have the feature of being original and of recovering the independence copula for some values of the parameter. Their properties are investigated. Introduction.Copula theory, initially introduced by Sklar [14], has become a vital tool for analyzing multivariate data and characterizing the dependence structure between random variables. The main functions, called copulas, provide a means to separate the marginal distributions from the dependence structure, allowing practitioners to model and estimate the joint distribution independently. This flexibility has enabled copulas to find applications in a wide range of fields, including finance (see [9]), insurance (see [7]), environmental sciences (see [1]), and many others. The main theoretical and applied background on copulas can be found in [12,5], and recent advancements are described in [15,16,3,4,2,11,13,6,18].Nowadays, the need for new copula constructions arises due to several reasons. Firstly, existing copula families may lack the flexibility to model dependence structures with asymmetric tail behavior or extreme values, which