The Statistics of Orientation Data

Abstract

This paper provides the key references for, and a summary of, statistical methods for describing and analyzing orientation data. Most of the paper is concerned with the author's approximate analysis of variance procedures for unit vectors in two and three dimensions. The procedures are based on probability density proportional to exp (κ cos θ), where κ is an accuracy parameter and θ is the angle between the true and the observed directions. A brief account of the theory for exp ($$κ cos^{2}θ$$) and its generalization is given; this may be useful for axial data.