Some new developments on variable-power copulas

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 variable-power 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.