Constructions of copulas with given diagonal (and opposite diagonal) sections and some generalizations

Abstract

We review various methods for constructing bivariate copulas with given diagonal sections from seminal work to the most recent research on copulas with given diagonal and opposite diagonal sections. A survey on a generalization of copulas with given diagonal plane sections in higher dimensions and other sections that generalize the diagonal and opposite diagonal sections is of particular interest.

Keywords

• copula
• diagonal section
• track section
• primary 60e05
• secondary 62e10