$\kappa$-exponential models from the geometrical viewpoint

TL;DR

This paper explores the geometric structure of $ppa$-exponential models within statistical manifolds, analyzing algebraic properties and defining charts for positive densities using Kaniadakis' deformed exponential.

Contribution

It introduces a geometric framework for $ppa$-exponential models and defines a chart for positive densities, advancing the understanding of deformed exponential families.

Findings

Algebraic features of $ppa$-exponential models analyzed

A chart for positive densities is constructed

Representation of densities via centered $ppa$-log likelihood

Abstract

We discuss the use of Kaniadakis' $\kappa$-exponential in the construction of a statistical manifold modelled on Lebesgue spaces of real random variables. Some algebraic features of the deformed exponential models are considered. A chart is defined for each strictly positive densities; every other strictly positive density in a suitable neighborhood of the reference probability is represented by the centered $\Kln$ likelihood