A small circle distribution on the sphere

Abstract

A new distribution is proposed as a model for measurements of direction that cluster near a small circle, i.e. parallel of latitude, on the sphere. It is a generalization of both the Fisher-von Mises and Dimroth-Watson distributions. Methods of estimation and inference are discussed and an approximation that is valid for large values of the shape parameter is introduced. The use of the distribution is illustrated by the analysis of artificially generated data