{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:07:09Z","timestamp":1760234829512,"version":"build-2065373602"},"reference-count":25,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2021,7,1]],"date-time":"2021-07-01T00:00:00Z","timestamp":1625097600000},"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>The beta and Kumaraswamy distributions are two of the most widely used distributions for modeling bounded data. When the histogram of a certain dataset exhibits increasing or decreasing behavior, one-parameter distributions such as the power, Marshall\u2013Olkin extended uniform and skew-uniform distributions become viable alternatives. In this article, we propose a new one-parameter distribution for modeling bounded data, the Lambert-uniform distribution. The proposal can be considered as a natural alternative to well known one-parameter distributions in the statistical literature and, in certain scenarios, a viable alternative even for the two-parameter beta and Kumaraswamy distributions. We show that the density function of the proposal tends to positive finite values at the ends of the support, a behavior that favors good performance in certain scenarios. The raw moments are derived from the moment-generating function and used to describe the skewness and kurtosis behavior. The quantile function is expressed in closed form in terms of the Lambert W function, which allows reparameterizing the distribution such that the involved parameter represents the qth quantile. Thus, for the analysis of a bounded range variable, for which a set of covariates is available, we propose a regression model that relates the qth quantile of the response to a linear predictor through a link function. The parameter estimation is carried out using the maximum likelihood method and the behavior of the estimators is evaluated through simulation experiments. Finally, three application examples are considered in order to illustrate the usefulness of the proposal.<\/jats:p>","DOI":"10.3390\/sym13071190","type":"journal-article","created":{"date-parts":[[2021,7,1]],"date-time":"2021-07-01T05:00:10Z","timestamp":1625115610000},"page":"1190","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["An Alternative One-Parameter Distribution for Bounded Data Modeling Generated from the Lambert Transformation"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9847-1497","authenticated-orcid":false,"given":"Yuri A.","family":"Iriarte","sequence":"first","affiliation":[{"name":"Departamento de Matem\u00e1tica, Facultad de Ciencias B\u00e1sicas, Universidad de Antofagasta, Antofagasta 1240000, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8685-9470","authenticated-orcid":false,"given":"M\u00e1rio","family":"de Castro","sequence":"additional","affiliation":[{"name":"Instituto de Ci\u00eancias Matem\u00e1ticas e de Computa\u00e7\u00e3o, Universidade de S\u00e3o Paulo, S\u00e3o Carlos 13560-095, SP, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3726-5507","authenticated-orcid":false,"given":"H\u00e9ctor W.","family":"G\u00f3mez","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1tica, Facultad de Ciencias B\u00e1sicas, Universidad de Antofagasta, Antofagasta 1240000, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,7,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1080\/07350015.1995.10524593","article-title":"The impact of unemployment insurance benefit levels on recipiency","volume":"13","author":"McCall","year":"1995","journal-title":"J. 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