Bivariate Modelling of Stochastic Features: A Convex Mixture Copula Approach

Harris Odoi Yemoh; Emmanuel Kojo Aidoo; Maxwell Akwasi Boateng; Felix Okoe Mettle; Akoto Yaw Omari-Sasu

Harris Odoi Yemoh Kwame Nkrumah University of Science and Technology https://orcid.org/0009-0000-3441-3741
Emmanuel Kojo Aidoo Ashesi University https://orcid.org/0000-0001-8054-841X
Maxwell Akwasi Boateng Kwame Nkrumah University of Science and Technology https://orcid.org/0000-0003-4895-4754
Felix Okoe Mettle University of Ghana, Legon https://orcid.org/0000-0003-2160-0198
Akoto Yaw Omari-Sasu Kwame Nkrumah University of Science and Technology https://orcid.org/0000-0002-1655-1515

Keywords: Clayton Copula, Joe Copula, Convex Mixture, Dependence Parameter, Mixing Parameter

Abstract

The Clayton and Joe copulas serve as mathematical constructs utilised within copula theory to explicate the interrelationships among stochastic variables. Renowned for their efficacy in capturing extreme tail occurrences, these copulas are recognised members of the Archimedean copula family. Their utility spans diverse domains: genetics, neuroscience, finance, insurance, hydrology, environmental research, telecommunications, and reliability engineering. To augment their flexibility, we present in this discourse an elevated mixture of the Clayton and Joe copulas, denoted as the CJM copula. This convex mixture offers a direct linear interpolation between the Clayton and Joe copulas, modulated by a blending parameter. Such integration facilitates a more nuanced depiction of the copula density function. We scrutinise its attributes, including determining the blending parameter, Kendall’s tau, and quadrant-dependent coefficients, while introducing three innovative copulas: the x-flipping CJM, y-flipping CJM, and survival CJM copulas. The collective discoveries significantly contribute to advancing the theoretical underpinnings governing copula-based modelling methodologies and their ensuing applications.