Fisher–Rao geometry and Jeffreys prior for Pareto distribution

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 Poincaré 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:

• Fisher–Rao metric
• Jeffreys prior
• Bayesian inference
• Pareto distribution

Additional information

Funding

H. Sun is supported by the National Natural Science Foundation of China (Nos. 61179031, 10932002). L. Peng is supported by the MEXT “Top Global University Project”, JST-CREST and Waseda University Grant for Special Research Projects (Nos. 2019C-179, 2019E-036, 2019R-081).