{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,16]],"date-time":"2026-01-16T04:34:01Z","timestamp":1768538041731,"version":"3.49.0"},"reference-count":26,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2020,2,23]],"date-time":"2020-02-23T00:00:00Z","timestamp":1582416000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Recently, Tahmasebi and Eskandarzadeh introduced a new extended cumulative entropy (ECE). In this paper, we present results on shift-dependent measure of ECE and its dynamic past version. These results contain stochastic order, upper and lower bounds, the symmetry property and some relationships with other reliability functions. We also discuss some properties of conditional weighted ECE under some assumptions. Finally, we propose a nonparametric estimator of this new measure and study its practical results in blind image quality assessment.<\/jats:p>","DOI":"10.3390\/sym12020316","type":"journal-article","created":{"date-parts":[[2020,2,26]],"date-time":"2020-02-26T04:18:29Z","timestamp":1582690709000},"page":"316","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["A Shift-Dependent Measure of Extended Cumulative Entropy and Its Applications in Blind Image Quality Assessment"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4025-6791","authenticated-orcid":false,"given":"Saeid","family":"Tahmasebi","sequence":"first","affiliation":[{"name":"Department of Statistics, Persian Gulf University, Bushehr 7516913817, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ahmad","family":"Keshavarz","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering and the ICT Research Institute, Persian Gulf University, Bushehr 7516913817, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6772-5167","authenticated-orcid":false,"given":"Maria","family":"Longobardi","sequence":"additional","affiliation":[{"name":"Dipartimento di Matematica e Applicazioni Universita di Napoli Federico II, I-80126 Napoli, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9538-0648","authenticated-orcid":false,"given":"Reza","family":"Mohammadi","sequence":"additional","affiliation":[{"name":"Department of Operation Management, Amsterdam Business School, University of Amsterdam, 1018 TV Amsterdam, The Netherlands"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,2,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1002\/j.1538-7305.1948.tb01338.x","article-title":"Mathematical theory of communication","volume":"27","author":"Shannon","year":"1948","journal-title":"Bell Syst. 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