ABSTRACT
This chapter discusses distributions which have been studied by James, Herz, Khatri, Roux, Downs, van der Merwe and Roux, Khatri and Mardia, Mardia and Khatri, de Waal, and Chikuse. Patil, Boswell, Ratnaparkhi and Roux have also written a classified bibliography of statistical distributions which include matrix variate distributions. The chapter defines Bingham matrix distribution which is the obvious analogue on the Stiefel manifold of Bingham's antipodally symmetric distribution on sphere. The Bingham matrix distribution is a special case of the generalized von Mises-Fisher matrix variate distribution introduced by Khatri and Mardia. The Bingham matrix distribution on the Stiefel manifold has been generalized by Prentice. He has also obtained the large sample maximum likelihood estimators and uniformity test. The Bingham matrix distribution is an antipodally symmetric distribution. The chapter gives hypergeometric function distributions of two types.
