Abstract

Analogues of the normal distribution in Euclidean space for orientations represented by Rodrigues parameters are discussed. It is emphasized that different characterizations of the normal distribution in Euclidean space lead to different distributions in other spaces, none of which is mathematically superior to any other one. Particular analogues of the normal distribution are the Bingham distribution on S+4 for the purposes of mathematical statistics, and the Brownian motion distribution on S+4 in terms of probability theory and stochastic processes. It is reminded of the fact that a simple analogue of the central limit theorem in Euclidean space does not exist for the hyperspheres SP and projective hyperplanes HP−1=S+4.