$\kappa$-exponential models from the geometrical viewpoint

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

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• Relativistic kinetics and power-law tailed distributions
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• On the Kaniadakis distributions applied in statistical physics and natural sciences
• On $\phi$-families of probability distributions
• Marginal Polytope of a Deformed Exponential Family
• Maximum entropy generation in open systems: the Fourth Law?
• Irreversibility and maximum generation in $\kappa$-generalized statistical mechanics