2015-04-242013-02G. Loaiza, H.R. Quiceno, A -exponential statistical Banach manifold, Journal of Mathematical Analysis and Applications, Volume 398, Issue 2, 15 February 2013, Pages 466-476, ISSN 0022-247X, http://dx.doi.org/10.1016/j.jmaa.2012.08.046. (http://www.sciencedirect.com/science/article/pii/S0022247X12006981)0022-247Xhttp://hdl.handle.net/10784/5245Letµbe a given probability measure andMµ the set ofµ-equivalent strictly positive probability densities -- In this paper we construct a Banach manifold on Mµ, modeled on the space L∞(p · µ) where p is a reference density, for the non-parametric q-exponential statistical models (Tsallis’s deformed exponential), where 0 < q < 1 is any real number -- This family is characterized by the fact that when q → 1, then the non-parametric exponential models are obtained and the manifold constructed by Pistone and Sempi is recovered, up to continuous embeddings on the modeling space -- The coordinate mappings of the manifold are given in terms of Csiszár’s Φ-divergences; the tangent vectors are identified with the one-dimensional q-exponential models and q-deformations of the score functionLetµbe a given probability measure andMµ the set ofµ-equivalent strictly positive probability densities -- In this paper we construct a Banach manifold on Mµ, modeled on the space L∞(p · µ) where p is a reference density, for the non-parametric q-exponential statistical models (Tsallis’s deformed exponential), where 0 < q < 1 is any real number -- This family is characterized by the fact that when q → 1, then the non-parametric exponential models are obtained and the manifold constructed by Pistone and Sempi is recovered, up to continuous embeddings on the modeling space -- The coordinate mappings of the manifold are given in terms of Csiszár’s Φ-divergences; the tangent vectors are identified with the one-dimensional q-exponential models and q-deformations of the score functionengCopyright © 2012 Elsevier Ltd. All rights reserved.articleinfo:eu-repo/semantics/restrictedAccessTEORÍA DE LA INFORMACIÓNENTROPÍA (TEORÍA DE LA INFORMACIÓN)ESPACIOS DE BANACHFÍSICA CUÁNTICAANÁLISIS MATEMÁTICOGEOMETRÍA DIFERENCIALFUNCIONES ANALÍTICASInformation theoryEntropy (information theory)Banach spacesQuantum physicalMathematical analysisGeometry, differentialAnalytic functionsEspacios de OrliczAcceso restringido2015-04-24Quiceno Echavarría, Héctor RománLoaiza Ossa, Gabriel Ignacio10.1016/j.jmaa.2012.08.046