The Theory of Concentrated Fisher-Von Mises Distributions.

The density of the Fisher-von-Mises distribution is proportional to exp kappa micron prime x where x and the modal vector microns are unit vectors in IRq times kappa equal to or greater than 0 is called the concentration parameter. The distribution of statistics for testing hypotheses about the modal vectors of m distributions simplify greatly as the concentration parameters tend to infinity. The non-null distributions are obtained for statistics appropriate when kappa 1,..., kappa m are known but tend to infinity and are unknown but equal to kappa which tends to infinity.