{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,11]],"date-time":"2026-06-11T23:24:41Z","timestamp":1781220281276,"version":"3.54.1"},"reference-count":33,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2021,12,21]],"date-time":"2021-12-21T00:00:00Z","timestamp":1640044800000},"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>Tsallis introduced a non-logarithmic generalization of Shannon entropy, namely Tsallis entropy, which is non-extensive. Sati and Gupta proposed cumulative residual information based on this non-extensive entropy measure, namely cumulative residual Tsallis entropy (CRTE), and its dynamic version, namely dynamic cumulative residual Tsallis entropy (DCRTE). In the present paper, we propose non-parametric kernel type estimators for CRTE and DCRTE where the considered observations exhibit an \u03c1-mixing dependence condition. Asymptotic properties of the estimators were established under suitable regularity conditions. A numerical evaluation of the proposed estimator is exhibited and a Monte Carlo simulation study was carried out.<\/jats:p>","DOI":"10.3390\/e24010009","type":"journal-article","created":{"date-parts":[[2021,12,22]],"date-time":"2021-12-22T01:08:09Z","timestamp":1640135289000},"page":"9","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Kernel Estimation of Cumulative Residual Tsallis Entropy and Its Dynamic Version under \u03c1-Mixing Dependent Data"],"prefix":"10.3390","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5999-1588","authenticated-orcid":false,"given":"Muhammed Rasheed","family":"Irshad","sequence":"first","affiliation":[{"name":"Department of Statistics, Cochin University of Science and Technology, Cochin 682 022, India"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1138-740X","authenticated-orcid":false,"given":"Radhakumari","family":"Maya","sequence":"additional","affiliation":[{"name":"Department of Statistics, Govt. College for Women, Trivandrum 695 014, India"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3569-4052","authenticated-orcid":false,"given":"Francesco","family":"Buono","sequence":"additional","affiliation":[{"name":"Dipartimento di Matematica e Applicazioni \u201cRenato Caccioppoli\u201d, Universit\u00e0 degli Studi di Napoli Federico II, 80138 Naples, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6772-5167","authenticated-orcid":false,"given":"Maria","family":"Longobardi","sequence":"additional","affiliation":[{"name":"Dipartimento di Biologia, Universit\u00e0 degli Studi di Napoli Federico II, 80138 Naples, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2021,12,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1002\/j.1538-7305.1948.tb01338.x","article-title":"A mathematical theory of communication","volume":"27","author":"Shannon","year":"1948","journal-title":"Bell Syst. 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