{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T09:10:23Z","timestamp":1777367423185,"version":"3.51.4"},"reference-count":42,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2022,1,13]],"date-time":"2022-01-13T00:00:00Z","timestamp":1642032000000},"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>A large family of new \u03b1-weighted group entropy functionals is defined and associated Fisher-like metrics are considered. All these notions are well-suited semi-Riemannian tools for the geometrization of entropy-related statistical models, where they may act as sensitive controlling invariants. The main result of the paper establishes a link between such a metric and a canonical one. A sufficient condition is found, in order that the two metrics be conformal (or homothetic). In particular, we recover a recent result, established for \u03b1=1 and for non-weighted relative group entropies. Our conformality condition is \u201cuniversal\u201d, in the sense that it does not depend on the group exponential.<\/jats:p>","DOI":"10.3390\/e24010120","type":"journal-article","created":{"date-parts":[[2022,1,13]],"date-time":"2022-01-13T10:57:37Z","timestamp":1642071457000},"page":"120","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Weighted Relative Group Entropies and Associated Fisher Metrics"],"prefix":"10.3390","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1339-995X","authenticated-orcid":false,"given":"Iulia-Elena","family":"Hirica","sequence":"first","affiliation":[{"name":"Faculty of Mathematics and Computer Science, University of Bucharest, Academiei 14, 010014 Bucharest, Romania"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3059-9707","authenticated-orcid":false,"given":"Cristina-Liliana","family":"Pripoae","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics, Bucharest University of Economic Studies, Piata Romana 6, 010374 Bucharest, Romania"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3315-3762","authenticated-orcid":false,"given":"Gabriel-Teodor","family":"Pripoae","sequence":"additional","affiliation":[{"name":"Faculty of Mathematics and Computer Science, University of Bucharest, Academiei 14, 010014 Bucharest, Romania"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2115-3113","authenticated-orcid":false,"given":"Vasile","family":"Preda","sequence":"additional","affiliation":[{"name":"Faculty of Mathematics and Computer Science, University of Bucharest, Academiei 14, 010014 Bucharest, Romania"},{"name":"\u201cGheorghe Mihoc-Caius Iacob\u201d Institute of Mathematical Statistics and Applied Mathematics of Romanian Academy, No.13 Calea 13 Septembrie, Sector 5, 050711 Bucharest, Romania"},{"name":"\u201cCostin C. Kiritescu\u201d National Institute of Economic Research of Romanian Academy, No.13 Calea 13 Septembrie, Sector 5, 050711 Bucharest, Romania"}]}],"member":"1968","published-online":{"date-parts":[[2022,1,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"700","DOI":"10.1017\/S0305004100009580","article-title":"Theory of Statistical Estimation","volume":"22","author":"Fisher","year":"1925","journal-title":"Math. Proc. Cambridge Phil. Soc."},{"key":"ref_2","first-page":"81","article-title":"Information and the accuracy attainable in the estimation of statistical parameters","volume":"37","author":"Rao","year":"1945","journal-title":"Bull. Calcutta Math. 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