On the Classes of copulas and Quasi-copulas with a Given Diagonal Section

Condition (C3) is called the 2–increasing property of C, and VC ([x1, x2]× [y1, y2]) is called the C–volume of the rectangle [x1, x2]× [y1, y2]. According to Sklar’s Theorem, copulas are functions that express the rankinvariant dependence between a pair of continuous random variables and, as such, they have been largely used in statistical applications . In particular, examples of copulas are given by M(x, y) = min{x, y}, Π(x, y) = xy and W (x, y) =