On the geometric structure ofsome statistical manifolds

TL;DR

This paper explores the geometric properties of statistical manifolds, specifically the generalized normal distribution manifold with constant lpha-Gaussian curvature and the construction of lpha-flat manifolds in any dimension.

Contribution

It introduces the geometric structure of the generalized normal distribution manifold and constructs lpha-flat manifolds in arbitrary dimensions, advancing the understanding of information geometry.

Findings

The generalized normal distribution manifold has constant lpha-Gaussian curvature.

Construction of lpha-flat manifolds in any positive integer dimension.

Provides insights into the geometric properties of statistical models.

Abstract

In information geometry, one of the basic problem is to study the geomet-ric properties of statistical manifold. In this paper, we study the geometricstructure of the generalized normal distribution manifold and show that it has constant {\alpha}-Gaussian curvature. Then for any positive integerp, we con-struct ap-dimensional statistical manifold that is {\alpha}-flat.