A flexible family of distributions on the cylinder

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.