A tractable, parsimonious and flexible model for cylindrical data, with applications

TL;DR

This paper introduces the WeiSSVM model, a flexible and parsimonious cylindrical distribution combining sine-skewed von Mises and Weibull distributions, suitable for circular-linear data analysis.

Contribution

The paper presents a new tractable cylindrical distribution model, WeiSSVM, with advantages in simplicity, interpretability, and application to real data, extending to directional-linear data.

Findings

Excellent fitting abilities demonstrated on real datasets

Easy random number generation due to known marginals

Effective for independence testing and regression analysis

Abstract

In this paper, we propose cylindrical distributions obtained by combining the sine-skewed von Mises distribution (circular part) with the Weibull distribution (linear part). This new model, the WeiSSVM, enjoys numerous advantages: simple normalizing constant and hence very tractable density, parameter-parsimony and interpretability, good circular-linear dependence structure, easy random number generation thanks to known marginal/conditional distributions, flexibility illustrated via excellent fitting abilities, and a straightforward extension to the case of directional-linear data. Inferential issues, such as independence testing, circular-linear respectively linear-circular regression, can easily be tackled with our model, which we apply on two real data sets. We conclude the paper by discussing future applications of our model.