Modelling toroidal and cylindrical data via the trivariate wrapped Cauchy copula with non-uniform marginals

TL;DR

This paper introduces a flexible trivariate wrapped Cauchy copula model with non-uniform marginals, suitable for complex angular and linear data, demonstrated on bioinformatics and climate science datasets.

Contribution

It develops a new trivariate wrapped Cauchy copula with non-uniform marginals and a parameter estimation method, advancing modeling of complex trivariate data.

Findings

Model outperforms competitors in analyzing trivariate data

Effective for toroidal and cylindrical datasets

Demonstrated on bioinformatics and climate data

Abstract

In this paper, we propose a new flexible family of distributions for data that consist of three angles, two angles and one linear component, or one angle and two linear components. To achieve this, we equip the recently proposed trivariate wrapped Cauchy copula with non-uniform marginals and develop a parameter estimation procedure. We compare our model to its main competitors for analyzing trivariate data and provide some evidence of its advantages. We illustrate our new model using toroidal data from protein bioinformatics of conformational angles, and cylindrical data from climate science related to buoy in the Adriatic Sea. The paper is motivated by these real trivariate datasets.