{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,20]],"date-time":"2026-01-20T04:54:18Z","timestamp":1768884858463,"version":"3.49.0"},"reference-count":38,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2021,10,30]],"date-time":"2021-10-30T00:00:00Z","timestamp":1635552000000},"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 article, we introduce a new flexible discrete family of distributions, which accommodates wide collection of monotone failure rates. A sub-model of geometric distribution or a discrete generalization of the exponential model is proposed as a special case of the derived family. Besides, we point out a comprehensive record of some of its mathematical properties. Two distinct estimation methods for parameters estimation and two different methods for constructing confidence intervals are explored for the proposed distribution. In addition, three extensive Monte Carlo simulations studies are conducted to assess the advantages between estimation methods. Finally, the utility of the new model is embellished by dint of two real datasets.<\/jats:p>","DOI":"10.3390\/axioms10040287","type":"journal-article","created":{"date-parts":[[2021,11,1]],"date-time":"2021-11-01T11:47:38Z","timestamp":1635767258000},"page":"287","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":19,"title":["On the Discrete Weibull Marshall\u2013Olkin Family of Distributions: Properties, Characterizations, and Applications"],"prefix":"10.3390","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1329-8283","authenticated-orcid":false,"given":"Jiju","family":"Gillariose","sequence":"first","affiliation":[{"name":"Department of Statistics, CHRIST (Deemed to Be University), Bangalore 560029, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8870-9692","authenticated-orcid":false,"given":"Oluwafemi Samson","family":"Balogun","sequence":"additional","affiliation":[{"name":"School of Computing, University of Eastern Finland, 70211 Kuopio,   Finland"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3888-1275","authenticated-orcid":false,"given":"Ehab M.","family":"Almetwally","sequence":"additional","affiliation":[{"name":"Department of Statistics, Delta University of Science and Technology, Belkas 35631, Egypt"}]},{"given":"Rehan Ahmad Khan","family":"Sherwani","sequence":"additional","affiliation":[{"name":"College of Statistical and Actuarial Sciences, University of the Punjab, Lahore 54000, Pakistan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6192-9890","authenticated-orcid":false,"given":"Farrukh","family":"Jamal","sequence":"additional","affiliation":[{"name":"Department of Statistics, The Islamia University of Bahawalpur, Bahawalpur 63100, Pakistan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8304-0005","authenticated-orcid":false,"given":"Joshin","family":"Joseph","sequence":"additional","affiliation":[{"name":"Department of Finance, KMML a Company under Government of Kerala, Sankaramangalam, Kollam 691583, India"}]}],"member":"1968","published-online":{"date-parts":[[2021,10,30]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"641","DOI":"10.1093\/biomet\/84.3.641","article-title":"A new method for adding a parameter to a family of distributions with application to the exponential and Weibull families","volume":"84","author":"Marshall","year":"1997","journal-title":"Biometrica"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"4537","DOI":"10.1080\/03610926.2014.922986","article-title":"On the Marshall-Olkin extended distributions","volume":"45","author":"Castellares","year":"2016","journal-title":"Commun. 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