{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,13]],"date-time":"2026-03-13T19:52:46Z","timestamp":1773431566148,"version":"3.50.1"},"reference-count":46,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2024,2,23]],"date-time":"2024-02-23T00:00:00Z","timestamp":1708646400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>The article extends the theoretical and applicative analysis of Zipf\u2019s law. We are concerned with a set of properties of Zipf\u2019s law that derive directly from the power law expression and from the discrete nature of the objects to which the law is applied, when the objects are words, lemmas, and the like. We also search for variations of Zipf\u2019s law that can help explain the noisy results empirically reported in the literature and the departures of the empirically obtained nonlinear graph from the theoretical linear one, with the variants analyzed differing from Mandelbrot and lognormal distributions. A problem of interest that we deal with is that of mixtures of populations obeying Zipf\u2019s law. The last problem has relevance in the analysis of texts with words with various etymologies. Computational aspects are also addressed.<\/jats:p>","DOI":"10.3390\/axioms13030146","type":"journal-article","created":{"date-parts":[[2024,2,23]],"date-time":"2024-02-23T10:47:30Z","timestamp":1708685250000},"page":"146","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Some Properties of Zipf\u2019s Law and Applications"],"prefix":"10.3390","volume":"13","author":[{"given":"Speranta Cecilia","family":"Bolea","sequence":"first","affiliation":[{"name":"Institute of Computer Science, Romanian Academy Ia\u015fi Branch, 700481 Ia\u015fi, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mironela","family":"Pirnau","sequence":"additional","affiliation":[{"name":"Faculty of Informatics, Titu Maiorescu University, 040441 Bucharest, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Silviu-Ioan","family":"Bejinariu","sequence":"additional","affiliation":[{"name":"Institute of Computer Science, Romanian Academy Ia\u015fi Branch, 700481 Ia\u015fi, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Vasile","family":"Apopei","sequence":"additional","affiliation":[{"name":"Institute of Computer Science, Romanian Academy Ia\u015fi Branch, 700481 Ia\u015fi, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Daniela","family":"Gifu","sequence":"additional","affiliation":[{"name":"Institute of Computer Science, Romanian Academy Ia\u015fi Branch, 700481 Ia\u015fi, Romania"},{"name":"Faculty of Computer Science, \u201cAlexandru Ioan Cuza\u201d University of Ia\u015fi, 700483 Ia\u0219i, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Horia-Nicolai","family":"Teodorescu","sequence":"additional","affiliation":[{"name":"Institute of Computer Science, Romanian Academy Ia\u015fi Branch, 700481 Ia\u015fi, Romania"},{"name":"Department Applied Electronics, Technical University of Ia\u0219i, 700050 Ia\u0219i, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,2,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"739","DOI":"10.1162\/003355399556133","article-title":"Zipf\u2019s Law for Cities: An Explanation","volume":"114","author":"Gabaix","year":"1999","journal-title":"Q. 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