{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:18:00Z","timestamp":1760242680189,"version":"build-2065373602"},"reference-count":48,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2016,3,9]],"date-time":"2016-03-09T00:00:00Z","timestamp":1457481600000},"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>The distribution of word probabilities in the monkey model of Zipf\u2019s law is associated with two universality properties: (1) the exponent in the approximate power law approaches                                        \u22121                                  as the alphabet size increases and the letter probabilities are specified as the spacings from a random division of the unit interval for any distribution with a bounded density function on                                        [0,1]                                 ; and (2), on a logarithmic scale the version of the model with a finite word length cutoff and unequal letter probabilities is approximately normally distributed in the part of the distribution away from the tails. The first property is proved using a remarkably general limit theorem from Shao and Hahn for the logarithm of sample spacings constructed on                                        [0,1]                                  and the second property follows from Anscombe\u2019s central limit theorem for a random number of independent and identically distributed (i.i.d.) random variables. The finite word length model leads to a hybrid Zipf-lognormal mixture distribution closely related to work in other areas.<\/jats:p>","DOI":"10.3390\/e18030089","type":"journal-article","created":{"date-parts":[[2016,3,9]],"date-time":"2016-03-09T10:38:02Z","timestamp":1457519882000},"page":"89","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Two Universality Properties Associated with the Monkey Model of Zipf\u2019s Law"],"prefix":"10.3390","volume":"18","author":[{"given":"Richard","family":"Perline","sequence":"first","affiliation":[{"name":"Independent Researcher, 34\u201350 80th Street, Jackson Heights, New York, NY 11372, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ron","family":"Perline","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Drexel University, Korman Center at 33rd and Market Streets, Philadelphia, PA 19104, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2016,3,9]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Pitici, M. 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