{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:12:29Z","timestamp":1760058749692,"version":"build-2065373602"},"reference-count":29,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2025,4,26]],"date-time":"2025-04-26T00:00:00Z","timestamp":1745625600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Training Program of Innovation and Entrepreneurship for Undergraduates","award":["202510004172","N2023Z020"],"award-info":[{"award-number":["202510004172","N2023Z020"]}]},{"name":"Science and Technology Research and Development Project of China State Railway Group Company, Ltd.","award":["202510004172","N2023Z020"],"award-info":[{"award-number":["202510004172","N2023Z020"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>The Lomax distribution has important applications in survival analysis, reliability engineering, insurance, finance, and other fields. Middle-censoring is an important censoring scheme, and data with middle-censoring will produce censoring in random intervals. This paper studies the parameter estimation of the Lomax distribution based on middle-censored data. The expectation\u2013maximization algorithm is employed to compute the maximum likelihood estimates of the two unknown parameters of the Lomax distribution. After processing the data using the midpoint approach estimation, the parameter estimates are obtained by two computational methods: the Newton\u2013Raphson iteration method and the fixed-point method. Moreover, the calculation methods for the asymptotic confidence intervals of the two parameters are provided, with the confidence interval coverage rate serving as one of the criteria for evaluating the estimation performance. In the Bayesian estimation aspect, the shape parameter is estimated using a Gamma prior distribution, and the Gibbs sampling method is employed for the solution. Finally, both simulation data and real data are used to compare the accuracy of the various estimation methods.<\/jats:p>","DOI":"10.3390\/axioms14050330","type":"journal-article","created":{"date-parts":[[2025,4,28]],"date-time":"2025-04-28T09:39:47Z","timestamp":1745833187000},"page":"330","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Parameter Estimation of the Lomax Lifetime Distribution Based on Middle-Censored Data: Methodology, Applications, and Comparative Analysis"],"prefix":"10.3390","volume":"14","author":[{"given":"Peiyao","family":"Ren","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Beijing Jiaotong University, Beijing 100044, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4318-1780","authenticated-orcid":false,"given":"Wenhao","family":"Gui","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Beijing Jiaotong University, Beijing 100044, China"}]},{"given":"Shan","family":"Liang","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Beijing Jiaotong University, Beijing 100044, China"}]}],"member":"1968","published-online":{"date-parts":[[2025,4,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1038\/242247a0","article-title":"African Infant Precocity and Some Social Influences during the First Year","volume":"242","author":"Leiderman","year":"1973","journal-title":"Nature"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Groeneboom, P., and Wellner, J.A. 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