Diagonal copulas of archimedean class

In this paper the concept of diagonal copulas is introduced and its properties are examined. It is shown that for the Archimedean class, the diagonal copula uniquely determines the corresponding copula. This fact helps to reduce the dimension and makes it easier to understand the underlying dependence structure without losing any information. Therefore diagonal copulas can be used in various stages of dependence model building, selection, fitting and diagnostics. In this paper we consider some of the possibilities on estimation, test of hypotheses and graphical data analysis.