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metadata.dc.type: Artigo de Periódico
Title in Portuguese: A deformed exponential statistical manifold
Author: Vieira, Francisca Leidmar Josué
Andrade, Luiza Helena Félix de
Vigelis, Rui Facundo
Cavalcante, Charles Casimiro
Issue Date: 2019
Publisher: Entropy
Keywords: Deformed exponential manifold
Statistical manifold
Information geometry
Exponential arcs
Citation: CAVALCANTE, C. C. et al. A deformed exponential statistical manifold. Entropy, vol. 21, n. 5, p. 496, 2019
Abstract: Consider μ a probability measure and Pμ the set of μ -equivalent strictly positive probability densities. To endow Pμ with a structure of a C∞ -Banach manifold we use the φ -connection by an open arc, where φ 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 κ -exponential functions. Moreover, we find the tangent space of Pμ at a point p, and as a consequence the tangent bundle of Pμ . 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 and κ -exponential functions can be used to generalize of Rényi divergence.
ISSN: 1099-4300
Appears in Collections:DETE - Artigos publicados em revista científica

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