  The Fisher-Rao distance is the geodesic distance between probability
distributions in a statistical manifold equipped with the Fisher metric, which
is a natural choice of Riemannian metric on such manifolds. It has recently
been applied to supervised and unsupervised problems in machine learning, in
various contexts. Finding closed-form expressions for the Fisher-Rao distance
is generally a non-trivial task, and those are only available for a few
families of probability distributions. In this survey, we collect examples of
closed-form expressions for the Fisher-Rao distance of both discrete and
continuous distributions, aiming to present them in a unified and accessible
language. In doing so, we also: illustrate the relation between negative
multinomial distributions and the hyperbolic model, include a few new examples,
and write a few more in the standard form of elliptical distributions.
