Heavily tailed probability distributions are important objects in anomalous statistical physics. For such probability distributions, expectations do not exist in general. Therefore, an escort distribution and an escort expectation have been introduced. In this paper, by generalizing such escort distributions, a sequence of escort distributions is introduced. For a deformed exponential family, we study the fundamental properties of statistical manifold structures derived from the sequence of escort expectations.
CITATION STYLE
Matsuzoe, H., Scarfone, A. M., & Wada, T. (2017). A sequential structure of statistical manifolds on deformed exponential family. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 10589 LNCS, pp. 223–230). Springer Verlag. https://doi.org/10.1007/978-3-319-68445-1_26
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