Abstract
An exponential family is an important class of statistical models in statistical sciences. In information geometry, it is known that an exponential family naturally has dualistic Hessian structures. A deformed exponential family is a statistical model which is a generalization of exponential families. A deformed exponential family naturally has two kinds of dualistic Hessian structures. In this paper, such Hessian geometries are summarized.In addition, a deformed exponential family has a generalized conformal structure of statistical manifolds. In the case of q-exponential family, which is a special class of deformed exponential families, the family naturally has two kinds of different Riemannian metrics which are obtained from conformal transformations of Hessian metrics. Then it is showed that a q-exponential family is a Riemannian manifold of constant curvature.
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