Symmetry and dependence properties within a semiparametric family of bivariate copulas

TL;DR

This paper investigates a semiparametric family of bivariate copulas, exploring how univariate functions influence their symmetry and dependence properties, and providing bounds on association measures like Kendall's Tau and Spearman's Rho.

Contribution

It introduces a new semiparametric family of copulas and derives bounds on dependence measures based on the generating functions.

Findings

Bounds on Kendall's Tau and Spearman's Rho established

Characterization of symmetry and dependence properties

Examples of generating functions reaching the bounds

Abstract

In this paper, we study a semiparametric family of bivariate copulas. The family is generated by an univariate function, determining the symmetry (radial symmetry, joint symmetry) and dependence property (quadrant dependence, total positivity, ...) of the copulas. We provide bounds on different measures of association (such as Kendall's Tau, Spearman's Rho) for this family and several choices of generating functions allowing to reach these bounds.