{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:23:47Z","timestamp":1760059427922,"version":"build-2065373602"},"reference-count":25,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2025,6,12]],"date-time":"2025-06-12T00:00:00Z","timestamp":1749686400000},"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>In this paper, we introduce a new distribution for modeling bimodal data supported on non-negative real numbers and particularly suited with an excess of very small values. This family of distributions is derived by multiplying the exponential distribution by a fourth-degree polynomial, resulting in a model that better fits the shape of the second mode of the empirical distribution of the data. We study the general density of this new family of distributions, along with its properties, moments, and skewness and kurtosis coefficients. A simulation study is performed to estimate parameters by the maximum likelihood method. Additionally, we present two applications to real-world datasets, demonstrating that the new distribution provides a better fit than the bimodal exponential distribution.<\/jats:p>","DOI":"10.3390\/axioms14060461","type":"journal-article","created":{"date-parts":[[2025,6,12]],"date-time":"2025-06-12T11:47:07Z","timestamp":1749728827000},"page":"461","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Modified Bimodal Exponential Distribution with Applications"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2921-3056","authenticated-orcid":false,"given":"Jimmy","family":"Reyes","sequence":"first","affiliation":[{"name":"Departamento de Estad\u00edstica y Ciencia de Datos, Facultad de Ciencias B\u00e1sicas, Universidad de Antofagasta, Antofagasta 1240000, Chile"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6952-2075","authenticated-orcid":false,"given":"Barry C.","family":"Arnold","sequence":"additional","affiliation":[{"name":"Department of Statistics, University of California, Riverside, CA 92521, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8092-9666","authenticated-orcid":false,"given":"Yolanda M.","family":"G\u00f3mez","sequence":"additional","affiliation":[{"name":"Departamento de Estad\u00edstica, Facultad de Ciencias, Universidad del B\u00edo-B\u00edo, Concepci\u00f3n 4081112, Chile"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6643-6972","authenticated-orcid":false,"given":"Osvaldo","family":"Venegas","sequence":"additional","affiliation":[{"name":"Departamento de Ciencias Matem\u00e1ticas y F\u00edsicas, Facultad de Ingenier\u00eda, Universidad Cat\u00f3lica de Temuco, Temuco 4780000, Chile"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3726-5507","authenticated-orcid":false,"given":"H\u00e9ctor W.","family":"G\u00f3mez","sequence":"additional","affiliation":[{"name":"Departamento de Estad\u00edstica y Ciencia de Datos, Facultad de Ciencias B\u00e1sicas, Universidad de Antofagasta, Antofagasta 1240000, Chile"}]}],"member":"1968","published-online":{"date-parts":[[2025,6,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1111\/j.1469-1809.1934.tb02105.x","article-title":"The effects of methods of ascertainment upon the estimation of frequencies","volume":"6","author":"Fisher","year":"1934","journal-title":"Ann. 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