The von Mises–Fisher Matrix Distribution in Orientation Statistics

Summary When n distinguishable directions in p dimensions are required to describe each orientation, Downs (1972) has extended the von Mises–Fisher distribution. We obtain the normalizing constant which leads to the investigation of various basic properties of the distribution. In particular, an explicit expression for the first population moment as well as the asymptotic distribution of the basic statistics are provided. The estimation problem, important testing problems, and exact sampling distributions are dealt with, and some techniques are applied to a set of vectorcardiogram data. An extension of the distribution is also proposed.