{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:06:47Z","timestamp":1760148407640,"version":"build-2065373602"},"reference-count":33,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2023,4,28]],"date-time":"2023-04-28T00:00:00Z","timestamp":1682640000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Researchers Supporting Project","award":["RSP2023R488"],"award-info":[{"award-number":["RSP2023R488"]}]},{"name":"King Saud University, Riyadh, Saudi Arabia","award":["RSP2023R488"],"award-info":[{"award-number":["RSP2023R488"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this article, we present a Markov Bernoulli Lomax (MB-L) model, which is obtained by a countable mixture of Markov Bernoulli and Lomax distributions, with decreasing and unimodal hazard rate function (HRF). The new model contains Marshall- Olkin Lomax and Lomax distributions as a special case. The mathematical properties, as behavior of probability density function (PDF), HRF, rth moments, moment generating function (MGF) and minimum (maximum) Markov-Bernoulli Geometric (MBG) stable are studied. Moreover, the estimates of the model parameters by maximum likelihood are obtained. The maximum likelihood estimation (MLE), bias and mean squared error (MSE) of MB-L parameters are inspected by simulation study. Finally, a MB-L distribution was fitted to the randomly censored and COVID-19 (complete) data.<\/jats:p>","DOI":"10.3390\/axioms12050439","type":"journal-article","created":{"date-parts":[[2023,4,28]],"date-time":"2023-04-28T09:54:53Z","timestamp":1682675693000},"page":"439","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["The Markov Bernoulli Lomax with Applications Censored and COVID-19 Drought Mortality Rate Data"],"prefix":"10.3390","volume":"12","author":[{"given":"Bahady I.","family":"Mohammed","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Al-Azhar University, Nasr City 11884, Cairo, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2878-4460","authenticated-orcid":false,"given":"Yusra A.","family":"Tashkandy","sequence":"additional","affiliation":[{"name":"Department of Statistics and Operations Research, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3608-8449","authenticated-orcid":false,"given":"Mohmoud M. Abd","family":"El-Raouf","sequence":"additional","affiliation":[{"name":"Basic and Applied Science Institute, Arab Academy for Science, Technology and Maritime Transport (AASTMT), Alexandria P.O. Box 1029, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3593-6936","authenticated-orcid":false,"given":"Md. Moyazzem","family":"Hossain","sequence":"additional","affiliation":[{"name":"School of Mathematics, Statistics & Physics, Newcastle University, Newcastle upon Tyne NE1 7RU, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3493-033X","authenticated-orcid":false,"given":"Mahmoud E.","family":"Bakr","sequence":"additional","affiliation":[{"name":"Giza Engineering Institute GEI, Basic Sciences Department, Giza 12519, Cairo, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,4,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"487","DOI":"10.18576\/jsap\/060305","article-title":"A New Method for Adding Two Parameters to a Family of Distributions with Application","volume":"6","author":"Gharib","year":"2017","journal-title":"J. Stat. Appl. 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