Abstract
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.
H. Matsuzoe—This research was partially supported by JSPS (Japan Society for the Promotion of Science), KAKENHI (Grants-in-Aid for Scientific Research) Grant Numbers JP26108003, JP15K04842 and JP16KT0132.
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Matsuzoe, H., Scarfone, A.M., Wada, T. (2017). A Sequential Structure of Statistical Manifolds on Deformed Exponential Family. In: Nielsen, F., Barbaresco, F. (eds) Geometric Science of Information. GSI 2017. Lecture Notes in Computer Science(), vol 10589. Springer, Cham. https://doi.org/10.1007/978-3-319-68445-1_26
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DOI: https://doi.org/10.1007/978-3-319-68445-1_26
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