2014-11-072013http://hdl.handle.net/10784/4401For the family of non-parametric q-exponential statistical models, in a former paper, written by the same authors, a differentiable Banach manifold modelled on Lebesgue spaces of real random variables has been built. In this paper, the geometry induced on this manifold is characterized by q-divergence functionals. This geometry turns out to be a generalization of the geometry given by Fisher information metric and Levi-Civita connections. Moreover, the classical Amari’s α-connections appears as special case of the q −connections ∇ (q). The main result is the expected one, namely the zero curvature of the manifold.enginfo:eu-repo/semantics/bookPartinfo:eu-repo/semantics/restrictedAccessq-ExponentialBanach ManifoldGeometryAcceso restringido2014-11-07Quiceno, H. R.Loaiza, Gabriel