Fisher-Rao Geometry and Jeffreys Prior for Pareto Distribution
Statistics Theory
2022-03-25 v1 Statistics Theory
Abstract
In this paper, we investigate the Fisher-Rao geometry of the two-parameter family of Pareto distribution. We prove that its geometrical structure is isometric to the Poincar\'e upper half-plane model, and then study the corresponding geometrical features by presenting explicit expressions for connection, curvature and geodesics. It is then applied to Bayesian inference by considering the Jeffreys prior determined by the volume form. In addition, the posterior distribution from the prior is computed, providing a systematic method to the Bayesian inference for Pareto distribution.
Keywords
Cite
@article{arxiv.1907.06006,
title = {Fisher-Rao Geometry and Jeffreys Prior for Pareto Distribution},
author = {Mingming Li and Huafei Sun and Linyu Peng},
journal= {arXiv preprint arXiv:1907.06006},
year = {2022}
}