{
  "id": "2304.14885",
  "version": "v1",
  "published": "2023-04-28T14:46:12.000Z",
  "updated": "2023-04-28T14:46:12.000Z",
  "title": "On Closed-Form expressions for the Fisher-Rao Distance",
  "authors": [
    "Henrique K. Miyamoto",
    "Fábio C. C. Meneghetti",
    "Sueli I. R. Costa"
  ],
  "comment": "26 pages",
  "categories": [
    "math.ST",
    "cs.IT",
    "math.DG",
    "math.IT",
    "stat.TH"
  ],
  "abstract": "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-04-28T14:46:12.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "fisher-rao distance",
      "probability distributions",
      "power function distributions",
      "collect explicit examples",
      "geodesic distance"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}