On Closed-Form expressions for the Fisher-Rao Distance

Henrique K. Miyamoto, Fábio C. C. Meneghetti, Sueli I. R. Costa

Published 2023-04-28Version 1

The Fisher-Rao distance is the geodesic distance between probability distributions in a statistical manifold equipped with the Fisher metric, which is the natural choice of Riemannian metric on such manifolds. Finding closed-form expressions for the Fisher-Rao distance is a non-trivial task, and those are available only for a few families of probability distributions. In this survey, we collect explicit examples of known Fisher-Rao distances for both discrete (binomial, Poisson, geometric, negative binomial, categorical, multinomial, negative multinomial) and continuous distributions (exponential, Gaussian, log-Gaussian, Pareto). We expand this list by deducing those expressions for Rayleigh, Erlang, Laplace, Cauchy and power function distributions.