The bivariate $K$-finite normal mixture "blanket" copula

TL;DR

This paper introduces a new bivariate copula based on finite mixtures of normal distributions, offering enhanced flexibility to model diverse and asymmetric dependence structures in data.

Contribution

It proposes a novel copula family that captures complex dependence patterns using mixture models, extending the capabilities of existing parametric copulas.

Findings

The copula can model various dependence patterns, including asymmetric ones.

Theoretical properties of the copula are established.

Illustrations on astrophysics and agriculture data demonstrate its practical effectiveness.

Abstract

There exist many bivariate parametric copulas to model bivariate data with different dependence features. We propose a new bivariate parametric copula family that cannot only handle various dependence patterns that appear in the existing parametric bivariate copula families, but also provides a more enriched dependence structure. The proposed copula construction exploits finite mixtures of bivariate normal distributions. The mixing operation, the distinct correlation and mean parameters at each mixture component introduce quite a flexible dependence. The new parametric copula is theoretically investigated, compared with a set of classical bivariate parametric copulas and illustrated on two empirical examples from astrophysics and agriculture where some of the variables have peculiar and asymmetric dependence, respectively.