Multivariate Normal Distributions Parametrized as a Riemannian Symmetric Space

The construction of a distance function between probability distributions is of importance in mathematical statistics and its applications. The distance function based on the Fisher information metric has been studied by a number of statisticians, especially in the case of the multivariate normal distribution (Gaussian) on Rn. It turns out that, except in the case n=1, where the Fisher metric describes the hyperbolic plane, it is difficult to …