A Deformed Exponential Statistical Manifold
Departamento de Matemática, Universidade Regional do Cariri, Juazeiro do Norte-CE 63041-145, Brazil
Departamento de Ciências Naturais, Matemática e Estatística, Universidade Federal Rural do Semi-Árido, Mossoró-RN 59625-900, Brazil
Curso de Engenharia de Computação, Campus Sobral, Universidade Federal do Ceará, Sobral-CE 62042-280, Brazil
Departamento de Engenharia de Teleinformática, Universidade Federal do Ceará, Fortaleza-CE 60020-181, Brazil
Author to whom correspondence should be addressed.
Received: 19 April 2019 / Revised: 12 May 2019 / Accepted: 13 May 2019 / Published: 15 May 2019
PDF [348 KB, uploaded 15 May 2019]
a probability measure and
the set of
-equivalent strictly positive probability densities. To endow
with a structure of a
-Banach manifold we use the
-connection by an open arc, where
is a deformed exponential function which assumes zero until a certain point and from then on is strictly increasing. This deformed exponential function has as particular cases the q
-deformed exponential and
-exponential functions. Moreover, we find the tangent space of
at a point p
, and as a consequence the tangent bundle of
. We define a divergence using the q
-exponential function and we prove that this divergence is related to the q
-divergence already known from the literature. We also show that q
-exponential functions can be used to generalize of Rényi divergence.
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MDPI and ACS Style
Josué Vieira, F.L.; Félix de Andrade, L.H.; Facundo Vigelis, R.; Casimiro Cavalcante, C. A Deformed Exponential Statistical Manifold. Entropy 2019, 21, 496.
Josué Vieira FL, Félix de Andrade LH, Facundo Vigelis R, Casimiro Cavalcante C. A Deformed Exponential Statistical Manifold. Entropy. 2019; 21(5):496.
Josué Vieira, Francisca L.; Félix de Andrade, Luiza H.; Facundo Vigelis, Rui; Casimiro Cavalcante, Charles. 2019. "A Deformed Exponential Statistical Manifold." Entropy 21, no. 5: 496.
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