Mathematical Analysis and Computational Approximation of Extremal Points of the Subset of Copulas

Copulas, as a new tool for statistical analysis, are studied in depth. One of the most notable aspects of this study is the geometric perspective, particularly the concept of regeneration via extreme points and the well-known result in functional analysis: the Krein–Milman theorem. The practical value of such a theoretical study is highlighted by a very interesting illustration in biomedical analysis. As the effective determination of all extremal points is quasi-impossible, we suggest an implementation method to approximate those of a finite and countable set. Computer implementations have demonstrated the effectiveness of the adopted approach.