Hiroshi Matsuzoe

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A deformed exponential family is a generalization of exponential families. Since the useful classes of power law tailed distributions are described by the deformed exponential families, they are important objects in the theory of complex systems. Though the deformed exponential families are defined by deformed exponential functions, these functions do not(More)
We explore the information geometric structures among the thermodynamic potentials in the κ-thermostatistics, which is a generalized thermostatistics based on the κ-deformed entropy. We show that there exists two different kinds of dualistic Hessian structures: one is associated with the κ-escort expectations and the other with the standard expectations.(More)
Academic Editors: Frédéric Barbaresco and Frank Nielsen Received: 26 October 2016; Accepted: 19 December 2016; Published: 25 December 2016 Abstract: In the theory of complex systems, long tailed probability distributions are often discussed. For such a probability distribution, a deformed expectation with respect to an escort distribution is more useful(More)
This paper studies geometrical structure of the manifold of escort probability distributions and shows its new applicability to information science. In order to realize escort probabilities we use a conformal transformation that flattens so-called alpha-geometry of the space of discrete probability distributions, which well characterizes nonadditive(More)
The McKay bivariate gamma distribution has marginal gamma densities with positive covariance and recently its information geometry as a 3-manifold has been provided. Here we derive: natural coordinates, explicit expressions for the α-connections, mutually dual foliations and an affine embedding in Euclidean R. We compute also the Kullback-Leibler divergence(More)