κ-exponential models from the geometrical viewpoint

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.

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