International Journal of Emerging Multidisciplinaries: Mathematics

Corresponding Author

Christophe Chesneau

Document Type

Research Article

Subject Areas

Applied Mathematics and Computations


Convex sums of copulas, multivariate analysis, unit distributions


A two-dimensional copula is a function that accurately depicts the pattern of dependence between two quantitative variables. The demand for new two-dimensional copulas is as strong as ever, driven by the emergence of contemporary data from various sources. This paper makes a contribution to this area by presenting a novel modification of the well-known convex sums of copulas method. This modification is based on a thorough duplication-parameter technique: we transform one parameter into two, and we apply the classical convex sums method to only one of these parameters in the unit distribution setting. The main goals are (i) to solve the parameter dimension reduction problem of the classical convex sums approach and (ii) to create new two-dimensional copulas with immediate knowledge of their admissible parameter values. To demonstrate the interest in this new method, we provide a large number of original examples with various functionalities. The theoretical framework for developing news dependence models under statistical scenarios is thus laid out in this paper.

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