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

2025-11-13

AI Summary

This paper addresses the statistical modeling of hybrid circular–linear data—comprising multiple angular (e.g., directional) and linear variables (e.g., 3-angle, 2-angle-1-linear, or 1-angle-2-linear configurations). Methodologically, it introduces a novel flexible distribution family by generalizing the trivariate wrapped Cauchy copula to non-uniform marginal settings: the copula structure is constructed via a wrapped Cauchy kernel and coupled with arbitrary continuous marginal distributions, enabling parameter estimation via maximum likelihood. The key contribution lies in unifying the modeling of toroidal and cylindrical data structures, thereby substantially enhancing flexibility and adaptability for multivariate circular–linear dependence. Empirical evaluation on protein dihedral angle data and Adriatic Sea buoy climate measurements demonstrates superior goodness-of-fit and greater practical utility compared to existing approaches.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Probabilistic Circuits and Graphical Models
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Mining multimedia, multimodal, multilingual, cross-lingual Web data
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems

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.

Problem

• Modeling trivariate data with mixed angular and linear components
• Developing wrapped Cauchy copula with non-uniform marginal distributions
• Addressing toroidal and cylindrical data from protein and climate science

Innovation

• Uses trivariate wrapped Cauchy copula
• Incorporates non-uniform marginal distributions
• Models toroidal and cylindrical data types