{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,3]],"date-time":"2026-01-03T14:50:46Z","timestamp":1767451846778,"version":"build-2065373602"},"reference-count":26,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2025,6,13]],"date-time":"2025-06-13T00:00:00Z","timestamp":1749772800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Deanship of Graduate Studies and Scientific Research at Qassim University","award":["QU-APC-2025"],"award-info":[{"award-number":["QU-APC-2025"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>This study introduces a new and flexible class of probability distributions known as the novel alpha-power X (NAP-X) family. A key development within this framework is the novel alpha-power half-logistic (NAP-HL) distribution, which extends the classical half-logistic model through an alpha-power transformation, allowing for greater adaptability to various data shapes. The paper explores several theoretical aspects of the proposed model, including its moments, quantile function and hazard rate. To assess the effectiveness of parameter estimation, a detailed simulation study is conducted using seven estimation techniques: Maximum likelihood estimation (MLE), Cram\u00e9r\u2013von Mises estimation (CVME), maximum product of spacings estimation (MPSE), least squares estimation (LSE), weighted least squares estimation (WLSE), Anderson\u2013Darling estimation (ADE) and a right-tailed version of Anderson\u2013Darling estimation (RTADE). The results offer comparative insights into the performance of each method across different sample sizes. The practical value of the NAP-HL distribution is demonstrated using two real datasets from the metrology and engineering domains. In both cases, the proposed model provides a better fit than the traditional half-logistic and related distributions, as shown by lower values of standard model selection criteria. Graphical tools such as fitted density curves, Q\u2013Q and P\u2013P plots, survival functions and box plots further support the suitability of the model for real-world data analysis.<\/jats:p>","DOI":"10.3390\/e27060632","type":"journal-article","created":{"date-parts":[[2025,6,16]],"date-time":"2025-06-16T10:47:22Z","timestamp":1750070842000},"page":"632","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["A Novel Alpha-Power X Family: A Flexible Framework for Distribution Generation with Focus on the Half-Logistic Model"],"prefix":"10.3390","volume":"27","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3079-5097","authenticated-orcid":false,"given":"A. A.","family":"Bhat\u00a0","sequence":"first","affiliation":[{"name":"Department of Mathematical Sciences, Islamic University of Science and Technology, Awantipora 192122, India"}]},{"ORCID":"https:\/\/orcid.org\/0009-0009-3169-1311","authenticated-orcid":false,"given":"Aadil Ahmad","family":"Mir\u00a0","sequence":"additional","affiliation":[{"name":"Department of Statistics, University of Kashmir, Srinagar 190006, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1809-1396","authenticated-orcid":false,"given":"S. P.","family":"Ahmad\u00a0","sequence":"additional","affiliation":[{"name":"Department of Statistics, University of Kashmir, Srinagar 190006, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1541-6239","authenticated-orcid":false,"given":"Badr S.","family":"Alnssyan\u00a0","sequence":"additional","affiliation":[{"name":"Department of Management Information Systems, College of Business and Economics, Qassim University, Buraydah 51452, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8681-5774","authenticated-orcid":false,"given":"Abdelaziz","family":"Alsubie\u00a0","sequence":"additional","affiliation":[{"name":"Department of Basic Sciences, College of Science and Theoretical Studies, Saudi Electronic University, Riyadh 11673, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9410-9079","authenticated-orcid":false,"given":"Yashpal Singh","family":"Raghav","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science, Jazan University, P.O. Box 2097, Jazan 45142, Saudi Arabia"}]}],"member":"1968","published-online":{"date-parts":[[2025,6,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"299","DOI":"10.1109\/24.229504","article-title":"Exponentiated weibull family for analyzing bathtub failure-rate data","volume":"42","author":"Mudholkar","year":"1993","journal-title":"IEEE Trans. Reliab."},{"key":"ref_2","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":"Biometrika"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"6543","DOI":"10.1080\/03610926.2015.1130839","article-title":"A new method for generating distributions with an application to exponential distribution","volume":"46","author":"Mahdavi","year":"2017","journal-title":"Commun. Stat.-Theory Methods"},{"key":"ref_4","first-page":"1","article-title":"A new family of generalized distributions with an application to weibull distribution","volume":"22","author":"Lone","year":"2024","journal-title":"Thail. Stat."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Shah, Z., Khan, D.M., Khan, I., Ahmad, B., Jeridi, M., and Al-Marzouki, S. (2024). A novel flexible exponent power-x family of distributions with applications to COVID-19 mortality rate in mexico and canada. Sci. Rep., 14.","DOI":"10.1038\/s41598-024-59720-1"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1007\/s40300-013-0007-y","article-title":"A new method for generating families of continuous distributions","volume":"71","author":"Alzaatreh","year":"2013","journal-title":"Metron"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"e29861","DOI":"10.1016\/j.heliyon.2024.e29861","article-title":"A new family of distributions using a trigonometric function: Properties and applications in the healthcare sector","volume":"10","author":"Odhah","year":"2024","journal-title":"Heliyon"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Mir, A.A., Rasool, S.U., Ahmad, S.P., Bhat, A.A., Jawa, T.M., Sayed-Ahmed, N., and Tolba, A.H. (2025). A robust framework for probability distribution generation: Analyzing structural properties and applications in engineering and medicine. Axioms, 14.","DOI":"10.3390\/axioms14040281"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1007\/s40745-018-0169-9","article-title":"The zubair-g family of distributions: Properties and applications","volume":"7","author":"Ahmad","year":"2020","journal-title":"Ann. Data Sci."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Hussein, M., Elsayed, H., and Cordeiro, G.M. (2022). A new family of continuous distributions: Properties and estimation. Symmetry, 14.","DOI":"10.3390\/sym14020276"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"726","DOI":"10.6339\/JDS.201910_17(4).0006","article-title":"The extended alpha power transformed family of distributions: Properties and applications","volume":"17","author":"Ahmad","year":"2019","journal-title":"J. Data Sci."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1016\/j.aej.2024.05.024","article-title":"Alpha\u2013beta-power family of distributions with applications to exponential distribution","volume":"100","author":"Semary","year":"2024","journal-title":"Alex. Eng. J."},{"key":"ref_13","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. Stat. Methodol."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"394","DOI":"10.1111\/j.2517-6161.1983.tb01268.x","article-title":"Estimating parameters in continuous univariate distributions with a shifted origin","volume":"45","author":"Cheng","year":"1983","journal-title":"J. R. Stat. Soc. Ser. (Methodol.)"},{"key":"ref_15","first-page":"93","article-title":"The maximum spacing method. an estimation method related to the maximum likelihood method","volume":"11","author":"Ranneby","year":"1984","journal-title":"Scand. J. Stat."},{"key":"ref_16","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_17","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1214\/aoms\/1177729437","article-title":"Asymptotic theory of certain \u201cgoodness of fit\u201d criteria based on stochastic processes","volume":"23","author":"Anderson","year":"1952","journal-title":"Ann. Math. Stat."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"663","DOI":"10.1080\/01621459.1981.10477701","article-title":"Minimum distance estimators for location and goodness of fit","volume":"76","author":"Boos","year":"1981","journal-title":"J. Am. Stat. Assoc."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Bhat, A.A., Ahmad, S.P., Gemeay, A.M., Muse, A.H., Bakr, M.E., and Balogun, O.S. (2024). A novel extension of half-logistic distribution with statistical inference, estimation and applications. Sci. Rep., 14.","DOI":"10.1038\/s41598-024-53768-9"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"597","DOI":"10.18576\/jsap\/060315","article-title":"Kumaraswamy half-logistic distribution: Properties and applications","volume":"6","author":"Usman","year":"2017","journal-title":"J. Stat. Appl. Probab."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"864396","DOI":"10.1155\/2014\/864396","article-title":"The exponentiated half-logistic family of distributions: Properties and applications","volume":"2014","author":"Cordeiro","year":"2014","journal-title":"J. Probab. Stat."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"407","DOI":"10.17093\/alphanumeric.409992","article-title":"Marshall-olkin half logistic distribution with theory and applications","volume":"6","author":"Yegen","year":"2018","journal-title":"Alphanumeric J."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1080\/00949658508810784","article-title":"Order statistics from the half logistic distribution","volume":"20","author":"Balakrishnan","year":"1985","journal-title":"J. Stat. Comput. Simul."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"2084236","DOI":"10.1155\/2016\/2084236","article-title":"On a power transformation of half-logistic distribution","volume":"2016","author":"Krishnarani","year":"2016","journal-title":"J. Probab. Stat."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"527","DOI":"10.1080\/02331880310001598837","article-title":"Bayesian one-sample prediction of future observations under pareto distribution","volume":"37","author":"Nigm","year":"2003","journal-title":"Statistics"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1007\/s40745-016-0094-8","article-title":"A new extension of weibull distribution with application to lifetime data","volume":"4","author":"Dey","year":"2017","journal-title":"Ann. Data Sci."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/27\/6\/632\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T17:51:50Z","timestamp":1760032310000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/27\/6\/632"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,6,13]]},"references-count":26,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2025,6]]}},"alternative-id":["e27060632"],"URL":"https:\/\/doi.org\/10.3390\/e27060632","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2025,6,13]]}}}