Large Sample Theory of the Fisher-Von Mises Distribution.

The Fisher-von-Mises distribution has probability density proportional to exp kappa micron prime x where x and microns are points on the surface of the unit ball in q dimensions. Kappa greater than or equal to 0 is a concentration parameter and micron the mean or modal direction. This paper makes a self-contained study of estimation and testing problems when the sample sizes are large. Earlier work used approximations based on eta finite and kappa large. Some of these results are shown to be true for all kappa if eta yields infinity. New tests are given by comparing the kappas and the microns of different populations the latter tests do not assume that all populations have the same kappas. Further, power functions are given for the proposed tests. Because the random vectors are of unit length we may expect these asymptotic distributions to be accurate approximations even with quite small sample sizes. Author