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.

中文翻译：

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帕累托分布的 Fisher-Rao 几何和 Jeffreys 先验

在本文中，我们研究了帕累托分布的双参数族的 Fisher-Rao 几何。我们证明其几何结构与Poincar\'e上半平面模型是等距的，然后通过给出连接、曲率和测地线的显式表达式来研究相应的几何特征。然后通过考虑由体积形式确定的 Jeffreys 先验，将其应用于贝叶斯推理。此外，计算了先验的后验分布，为帕累托分布的贝叶斯推理提供了一种系统方法。