Introduction to the Special Issue in Axioms Titled Current Research on Mathematical Inequalities

Abstract

The importance of inequalities in Mathematics is beautifully summarized in a citation attributed to Respected Professor Andrey Nikolaevich Kolmogorov. [...]

Some new developments on variable-power copulas

“…Let us call the copula in (2) the variable-power 1 (VP1) copula. To the best of our knowledge, it provides a new member of the variable-power copulas family (see [3,4]). It is worth noting that the VP1 copula and the function in (1) are related as follows:…”

“…This flexibility has enabled copulas to find applications in a wide range of fields, including finance (see [9]), insurance (see [7]), environmental sciences (see [1]), and many others. The main theoretical and applied background on copulas can be found in [12,5], and recent advancements are described in [15,16,3,4,2,11,13,6,18].…”

“…This flexibility has enabled copulas to find applications in a wide range of fields, including finance (see [9]), insurance (see [7]), environmental sciences (see [1]), and many others. The main theoretical and applied background on copulas can be found in [12,5], and recent advancements are described in [15,16,3,4,2,11,13,6,18].Nowadays, the need for new copula constructions arises due to several reasons. Firstly, existing copula families may lack the flexibility to model dependence structures with asymmetric tail behavior or extreme values, which…”

“…Clearly, if P (x, y) = Q(x, y) = 1, the independence copula is obtained, i.e., C op (x, y) = xy = Π(x, y). The case where P (x, y) = 1 and Q(x, y) is a function only depending on x is explored in [4]. A collection of new two-dimensional variable-power copulas was obtained, providing a perspective on dependence models beyond the standard scheme.…”