On the Foundations of Dependency Models and Parameters for Random Variables on Cylinder R 3

Abstract

Abtsrcat

Directional data often deal with observations on circles, spheres, cylinders, torus, etc. The notion of dependency between the variables involved and the development of related models and dependency parameters are of fundamental importance in this area. Here we develop a method of obtaining regression curves on manifold (cylinder) on R³ based on a differential geometric approach. With an aim to develop statistical inference procedures, we propose useful distribution on the cylinder for which the dependency parameter can be elegantly elucidated, and demonstrate how this parameter can be estimated in practice.