Eur. Phys. J. B 70, 29-37 (2009)
https://doi.org/10.1140/epjb/e2009-00154-y

κ-exponential models from the geometrical viewpoint

Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy

Corresponding author: ^a giovanni.pistone@polito.it

Received: 3 January 2009
Revised: 26 March 2009
Published online: 5 May 2009

Abstract

We discuss the use of Kaniadakis' κ-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 ln_κ likelihood.