Browse Journals

Copulas are multi-dimensional functions used to describe the dependence or association between variables separately from their marginal distributions. Among the numerous types of copulas, the strict Archimedean copulas are the most popular. However, the same short list of Archimedean copulas always attracts attention; a lot of strict Archimedean copulas are often discarded because they have limited tail dependence or insufficient flexibility in their shapes. In this article, we attempt to rehabilitate some of the understudied strict Archimedean copulas by making their properties more attractive via new functional modifications depending on several parameters. For each of them, the main contribution is theoretical; it consists of determining the range of admissible values for the involved parameters. Then, we concentrate on the two that show the greatest promise, which have the advantages of simple expressions and adaptable dependence qualities as a result of various tuning configurations. The first one extends the famous Clayton copula and depends on three complementary parameters. It has the particularity of allowing negative dependence, which was not the case with the original Clayton copula. The second one can be presented as a new two-parameter trigonometric copula. We investigate several of their main properties, such as symmetry, tail dependence, and correlation; the median correlation and tau of Kendall are considered. The theoretical results are supported by graphics and numerical tables. 

Archimedean copulas, parametric transformation, symmetry, orrelation, statistical modelling.