A flexible family of distributions on the cylinder

TL;DR

This paper introduces a new flexible family of generalized t-distributions on the cylinder, capable of modeling various data shapes and asymmetries, with applications demonstrated on real cylindrical data.

Contribution

It proposes a novel family of distributions on the cylinder derived from trivariate t-distributions, enhancing modeling flexibility for cylindrical data.

Findings

The distribution can be unimodal or bimodal.

It can be symmetric or asymmetric.

It fits real cylindrical data effectively.

Abstract

We propose a flexible family of distributions, generalized $t$-distributions, on the cylinder which is obtained as a conditional distribution of a trivariate $t$ distribution. The new distribution has unimodality or bimodality, symmetry or asymmetry, depending on the values of parameters and flexibly fits the cylindrical data. The circular marginal of this distribution is distributed as a generalized $t$-distribution on the circle. Some other properties are also investigated. The proposed distribution is applied to the real cylindrical data.