The trivariate wrapped Cauchy copula

TL;DR

This paper introduces a new trivariate wrapped Cauchy copula for modeling data on the three-dimensional torus, featuring simple density, adjustable dependence, and easy estimation, with applications in protein bioinformatics.

Contribution

It presents a novel trivariate copula with flexible dependence modeling, simple form, and practical estimation methods, expanding tools for circular and toroidal data analysis.

Findings

The copula has a simple density and desirable modality properties.

Parameters allow for adjustable dependence between variable pairs.

The model can be easily simulated and estimated from data.

Abstract

In this paper, we propose a new flexible distribution for data on the three-dimensional torus which we call a trivariate wrapped Cauchy copula. Our trivariate copula has several attractive properties. It has a simple form of density and desirable modality properties. Its parameters allow for an adjustable degree of dependence between every pair of variables and these can be easily estimated. The conditional distributions of the model are well studied bivariate wrapped Cauchy distributions. Furthermore, the distribution can be easily simulated. Parameter estimation via maximum likelihood for the distribution is given and we highlight the simple implementation procedure to obtain these estimates. We illustrate our trivariate wrapped Cauchy copula on data from protein bioinformatics of conformational angles.