# Fisher-Rao Geometry and Jeffreys Prior for Pareto Distribution

## TL;DR

This paper explores the Fisher-Rao geometric structure of the Pareto distribution, revealing its isometry to the Poincaré model, and applies this to Bayesian inference using the Jeffreys prior.

## Contribution

It establishes the Fisher-Rao geometry of the Pareto distribution and develops a systematic Bayesian inference method based on the Jeffreys prior.

## Key findings

- Fisher-Rao geometry of Pareto is isometric to Poincaré upper half-plane
- Explicit expressions for connection, curvature, and geodesics are provided
- Bayesian inference is systematically performed using the Jeffreys prior

## 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.