κ-exponential models from the geometrical viewpoint
Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy
Corresponding author: a firstname.lastname@example.org
Revised: 26 March 2009
Published online: 5 May 2009
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 lnκ likelihood.
PACS: 05.20.-y – Classical statistical mechanics / 02.50.Cw – Probability theory / 02.70.Rr – General statistical methods
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2009