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Fisher–Rao geometry and Jeffreys prior for Pareto distribution

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  • Mingming Li
  • Huafei Sun
  • Linyu Peng

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.

Suggested Citation

  • Mingming Li & Huafei Sun & Linyu Peng, 2022. "Fisher–Rao geometry and Jeffreys prior for Pareto distribution," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 51(6), pages 1895-1910, March.
    • Handle: RePEc:taf:lstaxx:v:51:y:2022:i:6:p:1895-1910
    DOI: 10.1080/03610926.2020.1771593
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