{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,3]],"date-time":"2026-06-03T18:03:36Z","timestamp":1780509816115,"version":"3.54.1"},"reference-count":40,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2023,2,23]],"date-time":"2023-02-23T00:00:00Z","timestamp":1677110400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"King Saud University","award":["RSP2023R464"],"award-info":[{"award-number":["RSP2023R464"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The half-logistic modified Kies exponential (HLMKEx) distribution is a novel three-parameter model that is introduced in the current work to expand the modified Kies exponential distribution and improve its flexibility in modeling real-world data. Due to its versatility, the density function of the HLMKEx distribution offers symmetrical, asymmetrical, unimodal, and reversed-J-shaped, as well as increasing, reversed-J shaped, and upside-down hazard rate forms. An infinite linear representation can be used to represent the HLMKEx density. The HLMKEx model\u2019s fundamental mathematical features are obtained, such as the quantile function, moments, incomplete moments, and moments of residuals. Additionally, some measures of uncertainty as well as stochastic ordering are derived. To estimate its parameters, eight estimation methods are used. With the use of detailed simulation data, we compare the performance of each estimating technique and obtain partial and total ranks for the accuracy measures of absolute bias, mean squared error, and mean absolute relative error. The simulation results demonstrate that, in contrast to other competing distributions, the proposed distribution can actually fit the data more accurately. Two actual data sets are investigated in the field of engineering to demonstrate the adaptability and application of the suggested distribution. The findings demonstrate that, in contrast to other competing distributions, the provided distribution can actually fit the data more accurately.<\/jats:p>","DOI":"10.3390\/sym15030586","type":"journal-article","created":{"date-parts":[[2023,2,24]],"date-time":"2023-02-24T03:01:01Z","timestamp":1677207661000},"page":"586","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":30,"title":["Statistical Inference of the Half Logistic Modified Kies Exponential Model with Modeling to Engineering Data"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6656-5344","authenticated-orcid":false,"given":"Safar M.","family":"Alghamdi","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3456-8393","authenticated-orcid":false,"given":"Mansour","family":"Shrahili","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":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4442-8458","authenticated-orcid":false,"given":"Amal S.","family":"Hassan","sequence":"additional","affiliation":[{"name":"Faculty of Graduate Studies for Statistical Research, Cairo University, 5 Dr. Ahmed Zewail Street, Giza 12613, Egypt"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6767-4016","authenticated-orcid":false,"given":"Ahmed M.","family":"Gemeay","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Tanta University, Tanta 31527, Egypt"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ibrahim","family":"Elbatal","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, Faculty of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi Arabia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"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":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,2,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Souza, L., de Oliveira, W.R., de Brito, C.C.R., Chesneau, C., Fernandes, R., and Ferreira, T.A.E. 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