{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,6]],"date-time":"2026-06-06T16:16:49Z","timestamp":1780762609100,"version":"3.54.1"},"reference-count":27,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2016,12,25]],"date-time":"2016-12-25T00:00:00Z","timestamp":1482624000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>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\u2013Chentsov tensor field, equivalently) is obtained from the escort expectation with respect to the third escort distribution.<\/jats:p>","DOI":"10.3390\/e19010007","type":"journal-article","created":{"date-parts":[[2016,12,28]],"date-time":"2016-12-28T11:22:14Z","timestamp":1482924134000},"page":"7","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["A Sequence of Escort Distributions and Generalizations of Expectations on q-Exponential Family"],"prefix":"10.3390","volume":"19","author":[{"given":"Hiroshi","family":"Matsuzoe","sequence":"first","affiliation":[{"name":"Department of Computer Science and Engineering, Nagoya Institute of Technology, Nagoya 466-8555, Japan"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2016,12,25]]},"reference":[{"key":"ref_1","unstructured":"Tsallis, C. 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