{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,19]],"date-time":"2026-04-19T10:15:12Z","timestamp":1776593712191,"version":"3.51.2"},"reference-count":34,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2023,2,20]],"date-time":"2023-02-20T00:00:00Z","timestamp":1676851200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004686","name":"The Deputyship for Research &amp; Innovation, Ministry of Education in Saudi Arabia","doi-asserted-by":"publisher","award":["INST 051"],"award-info":[{"award-number":["INST 051"]}],"id":[{"id":"10.13039\/501100004686","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this article, we introduce a new extension of the power Lomax (PLo) model by combining the type II exponentiated half-logistic class of statistical models and the PLo model. The new suggested statistical model called type II exponentiated half-logistic-PLo (TIIEHL-PLo) model. However, the new TIIEHL-PLo model is more flexible and applicable than the PLo model and some extensions of THE PLo model, especially those in environmental and medical fields. Some general statistical properties of the TIIEHL-PLo model are computed. Six different estimation approaches, namely maximum likelihood (ML), least-square (LS), weighted least-squares (WLS), maximum product spacing (MPS), Cram\u00e9r\u2013von Mises (CVM), and Anderson\u2013Darling (AD) estimation approaches, are utilized to estimate the parameters of the TIIEHL-PLo model. The simulation experiment examines the accuracy of the model parameters by employing six different methodologies of estimation. In this study, we analyze three real datasets from the environmental and medical fields to highlight the relevance and adaptability of the proposed approach. The newly suggested model is exceptionally adaptable and outperforms several well-known statistical models.<\/jats:p>","DOI":"10.3390\/axioms12020220","type":"journal-article","created":{"date-parts":[[2023,2,20]],"date-time":"2023-02-20T03:29:06Z","timestamp":1676863746000},"page":"220","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Different Estimation Methods for New Probability Distribution Approach Based on Environmental and Medical Data"],"prefix":"10.3390","volume":"12","author":[{"given":"Eid A. A.","family":"Hassan","sequence":"first","affiliation":[{"name":"Department of Accounting, Applied College, King Faisal University, Al-Ahsa 31982, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1333-3862","authenticated-orcid":false,"given":"Mohammed","family":"Elgarhy","sequence":"additional","affiliation":[{"name":"Mathematics and Computer Science Department, Faculty of Science, Beni-Suef University, Beni-Suef 62521, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Eman A.","family":"Eldessouky","sequence":"additional","affiliation":[{"name":"Department of Quantitative Methods, Applied College, King Faisal University, Al-Ahsa 31982, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9226-3267","authenticated-orcid":false,"given":"Osama H. Mahmoud","family":"Hassan","sequence":"additional","affiliation":[{"name":"Department of Quantitative Methods, School of Business, King Faisal University, Al-Ahsa 31982, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Essam A.","family":"Amin","sequence":"additional","affiliation":[{"name":"Department of Mathematical Statistics, College of Graduate Studies for Statistical Research, Cairo University, Giza 12613, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3888-1275","authenticated-orcid":false,"given":"Ehab M.","family":"Almetwally","sequence":"additional","affiliation":[{"name":"Faculty of Business Administration, Delta University for Science and Technology, Gamasa 11152, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,2,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"847","DOI":"10.1080\/01621459.1954.10501239","article-title":"Business failures: Another example of the analysis of failure data","volume":"49","author":"Lomax","year":"1954","journal-title":"J. Am. Stat. Assoc."},{"key":"ref_2","first-page":"2153","article-title":"Optimum step stress accelerated life testing for Lomax distribution","volume":"5","author":"Hassan","year":"2009","journal-title":"J. Appl. Sci. Res."},{"key":"ref_3","unstructured":"Atkinson, A., and Harrison, A. (1978). Distribution of Personal Wealth in Britain, Cambridge University Press."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"307","DOI":"10.1287\/opre.16.2.307","article-title":"The Pareto distribution as a queue service discipline","volume":"16","author":"Harris","year":"1968","journal-title":"Oper. Res."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"367","DOI":"10.1109\/LCOMM.2014.2385083","article-title":"Performance evaluation of a queue fed by a Poisson Lomax Burst Process","volume":"19","author":"Chen","year":"2015","journal-title":"IEEE Commun. Lett."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1855","DOI":"10.1080\/03610920601126571","article-title":"Marshall Olkin extended Lomax distribution and its application to censored data","volume":"36","author":"Ghitany","year":"2007","journal-title":"Commun. Stat. Theory Methods"},{"key":"ref_7","first-page":"2144","article-title":"On exponentiated Lomax distribution","volume":"3","year":"2012","journal-title":"Int. J. Math. Arch."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"121","DOI":"10.12691\/ajams-1-6-3","article-title":"Transmuted Lomax distribution","volume":"1","author":"Ashour","year":"2013","journal-title":"Am. J. Appl. Math. Stat."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"800","DOI":"10.1080\/02331888.2011.568119","article-title":"An extended Lomax distribution","volume":"47","author":"Lemonte","year":"2013","journal-title":"Statistics"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"225","DOI":"10.15446\/rce.v37n1.44369","article-title":"The Poisson-Lomax distribution","volume":"37","author":"Sagor","year":"2014","journal-title":"Rev. Colomb. Estad."},{"key":"ref_11","first-page":"24","article-title":"Exponential Lomax distribution","volume":"121","author":"Abdo","year":"2015","journal-title":"Int. J. Comput. Appl."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"305","DOI":"10.1080\/00949655.2013.822869","article-title":"The gamma Lomax distribution","volume":"85","author":"Cordeiro","year":"2015","journal-title":"J. Stat. Comput. Simul."},{"key":"ref_13","first-page":"461","article-title":"The Weibull-Lomax distribution: Properties and applications","volume":"44","author":"Tahir","year":"2015","journal-title":"Hacet. J. Math. Stat."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1862","DOI":"10.1186\/s40064-016-3489-2","article-title":"Weighted Lomax distribution","volume":"5","author":"Kilany","year":"2016","journal-title":"SpringerPlus"},{"key":"ref_15","first-page":"6043169","article-title":"A New Generalization of the Lomax Distribution with Increasing, Decreasing and Constant Failure Rate","volume":"2017","author":"Oguntunde","year":"2017","journal-title":"Model. Simul. Eng."},{"key":"ref_16","first-page":"290","article-title":"Statistical Properties and Estimation of Type II Half Logistic Lomax Distribution","volume":"18","author":"Hassan","year":"2020","journal-title":"Thail. Stat."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"61","DOI":"10.2991\/jsta.2016.15.1.6","article-title":"The Gumbel-Lomax distribution: Properties and applications","volume":"15","author":"Tahir","year":"2016","journal-title":"J. Stat. Theory Appl."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1838","DOI":"10.1186\/s40064-016-3464-y","article-title":"The power Lomax distribution with an application to bladder cancer data","volume":"5","author":"Rady","year":"2016","journal-title":"SpringerPlus"},{"key":"ref_19","first-page":"67","article-title":"A transmuted Power Lomax distribution","volume":"20","author":"Moltok","year":"2017","journal-title":"Afr. J. Nat. Sci."},{"key":"ref_20","first-page":"59","article-title":"A new generalization of power Lomax distribution","volume":"7","year":"2018","journal-title":"Int. J. Math. Math. Sci."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"167","DOI":"10.3844\/jmssp.2018.167.174","article-title":"On odds generalized exponential-power Lomax distribution","volume":"14","author":"Assar","year":"2018","journal-title":"J. Math. Stat."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"259","DOI":"10.1007\/s40745-018-0183-y","article-title":"On the inverse power Lomax distribution","volume":"6","author":"Hassan","year":"2019","journal-title":"Ann. Data Sci."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Al-Marzouki, S., Jamal, F., Chesneau, C., and Elgarhy, M. (2020). Type II Topp Leone Power Lomax Distribution with Applications. Mathematics, 8.","DOI":"10.3390\/math8010004"},{"key":"ref_24","first-page":"677","article-title":"Sine Power Lomax Model with Application to Bladder Cancer Data","volume":"12","author":"Algarni","year":"2020","journal-title":"Nanosci. Nanotechnol. Lett."},{"key":"ref_25","first-page":"36","article-title":"Type II exponentiated half logistic generated family of distributions with applications","volume":"13","author":"Elgarhy","year":"2020","journal-title":"Electron. J. Appl. Stat. Anal."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"85","DOI":"10.18576\/msl\/100302","article-title":"Extended odd weibull inverse Nadarajah-Haghighi distribution with application on COVID-19 in Saudi Arabia","volume":"10","author":"Almetwally","year":"2021","journal-title":"Math. Sci. Lett. Int. J."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1399","DOI":"10.1016\/j.jfranklin.2010.06.010","article-title":"The Kumaraswamy Weibull distribution with application to failure data","volume":"347","author":"Cordeiro","year":"2010","journal-title":"J. Frankl. Inst."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"293","DOI":"10.35378\/gujs.741755","article-title":"Marshall olkin alpha power extended Weibull distribution: Different methods of estimation based on type i and type II censoring","volume":"35","author":"Almetwally","year":"2022","journal-title":"Gazi Univ. J. Sci."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"994","DOI":"10.1214\/aos\/1176350046","article-title":"Skewness and asymmetry: Measures and orderings","volume":"14","author":"MacGillivray","year":"1986","journal-title":"Ann. Stat."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"326","DOI":"10.1111\/j.2517-6161.1971.tb00884.x","article-title":"Comments and queries comment on \u201can estimation procedure for mixtures of distributions\u201d by choi and bulgren","volume":"33","author":"Macdonald","year":"1971","journal-title":"J. R. Stat. Soc. Ser. B (Methodol.)"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"271","DOI":"10.1080\/00949658808811068","article-title":"Least-squares estimation of distribution functions in Johnson\u2019s translation system","volume":"29","author":"Swain","year":"1988","journal-title":"J. Stat. Comput. Simul."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Ross, M.S. (2010). Introductory Statistics, Elsevier. [3rd ed.].","DOI":"10.1016\/B978-0-12-374388-6.50002-7"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"6308","DOI":"10.1080\/03610918.2016.1202274","article-title":"The inverse power Lindley distribution","volume":"46","author":"Barco","year":"2017","journal-title":"Commun. Stat.-Simul. Comput."},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Alyami, S.A., Elbatal, I., Alotaibi, N., Almetwally, E.M., Okasha, H.M., and Elgarhy, M. (2022). Topp-Leone Modified Weibull Model: Theory and Applications to Medical and Engineering Data. Appl. Sci., 12.","DOI":"10.3390\/app122010431"}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/12\/2\/220\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T18:36:59Z","timestamp":1760121419000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/12\/2\/220"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,2,20]]},"references-count":34,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2023,2]]}},"alternative-id":["axioms12020220"],"URL":"https:\/\/doi.org\/10.3390\/axioms12020220","relation":{},"ISSN":["2075-1680"],"issn-type":[{"value":"2075-1680","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,2,20]]}}}