Probability Distributions in Directional Statistics: A Review

Abstract

Angular data arise in environmental science and meteorology as wind direction, in ecology as animal movement, and in molecular science as dihedral angle, etc. Also, the time of an event may be viewed as an angle on a 24 hour clock. Cardioid, von Mises and wrapped Cauchy distributions as symmetric distributions on the circle are well known in the literature. This article reviews recent developments, mainly after 2000, in the distribution theory for directional data which include angular observations. The topics include new symmetric distributions which contain cardioid, von Mises and wrapped Cauchy distributions as special cases, asymmetric distributions, distributions on the (hyper-) sphere, torus, cylinder and disc, together with their applications.