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- Hiroshi Matsuzoe
- 2005

For the space of gamma distributions with Fisher metric and exponential connections, natural coordinate systems, potential functions and an affine immersion in R3 are provided.

- Hiroshi Matsuzoe, Masayuki Henmi
- GSI
- 2013

- Hiroshi Matsuzoe, Tatsuaki Wada
- Entropy
- 2015

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)

- Tatsuaki Wada, Hiroshi Matsuzoe, Antonio Maria Scarfone
- Entropy
- 2015

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)

- Hiroshi Matsuzoe
- ETVC
- 2008

- Monta Sakamoto, Hiroshi Matsuzoe
- GSI
- 2015

- Hiroshi Matsuzoe
- Entropy
- 2017

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)

- Atsumi Ohara, Hiroshi Matsuzoe, Shun-ichi Amari
- ArXiv
- 2010

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)

- Khadiga Arwini, Hiroshi Matsuzoe
- 2003

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)