Directional Distributions

Various practical situations give rise to observations that are directions, and this has led to the field of directional statistics. Especially in recent years, new applications of this area have emerged, such as in structural bioinformatics, machine learning and cosmology. Consequently, various new directional distributions have appeared in the literature including on the circle, sphere, cylinder, torus, among others. These distributions take into account the underlying manifold. In this article, we provide a thorough review of the most important directional distributions with their main properties. Wherever relevant, we also give some indication of the particular application area which has led to a specific distribution.