Abstract
Consider 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 and -exponential functions can be used to generalize of Rényi divergence.
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