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Open AccessArticle

A Sequence of Escort Distributions and Generalizations of Expectations on q-Exponential Family

Department of Computer Science and Engineering, Nagoya Institute of Technology, Nagoya 466-8555, Japan
Academic Editors: Frédéric Barbaresco and Frank Nielsen
Entropy 2017, 19(1), 7; https://doi.org/10.3390/e19010007
Received: 26 October 2016 / Revised: 16 December 2016 / Accepted: 19 December 2016 / Published: 25 December 2016
(This article belongs to the Special Issue Differential Geometrical Theory of Statistics)
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 than the standard expectation. In this paper, by generalizing such escort distributions, a sequence of escort distributions is introduced. As a consequence, it is shown that deformed expectations with respect to sequential escort distributions effectively work for anomalous statistics. In particular, it is shown that a Fisher metric on a q-exponential family can be obtained from the escort expectation with respect to the second escort distribution, and a cubic form (or an Amari–Chentsov tensor field, equivalently) is obtained from the escort expectation with respect to the third escort distribution. View Full-Text
Keywords: escort distribution; escort expectation; statistical manifold; deformed exponential family; Tsallis statistics; information geometry escort distribution; escort expectation; statistical manifold; deformed exponential family; Tsallis statistics; information geometry
MDPI and ACS Style

Matsuzoe, H. A Sequence of Escort Distributions and Generalizations of Expectations on q-Exponential Family. Entropy 2017, 19, 7.

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