This site provides programs and machine readable data for the paper "Properties and applications of Fisher distribution on the rotation group" by Tomonari Sei(清), Hiroki Shibata(柴田), Akimichi Takemura(竹村), Katsuyoshi Ohara(小原), Nobuki Takayama(高山).


We study properties of Fisher distribution (von Mises-Fisher distribution, matrix Langevin distribution) on the rotation group SO(3). In particular we apply the holonomic gradient descent method, introduced in Holonomic Gradient Descent and its Application to the Fisher-Bingham Integral and a method of series expansion for evaluating the normalizing constant of the distribution and for computing the maximum likelihood estimate. The rotation group can be identified with the Stiefel manifold of two orthonormal vectors. Therefore from the viewpoint of statistical modeling, it is of interest to compare Fisher distributions on these manifolds. We illustrate the difference with an example of near-earth objects data. Programs and machine readable data are for the R (a system for statistics) and the Risa/Asir (a computer algebra system).

Programs and Data for V_2(R^3) (Stiefel manifold)

Programs and Data for SO(3)