{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:22:05Z","timestamp":1760059325734,"version":"build-2065373602"},"reference-count":41,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2025,6,5]],"date-time":"2025-06-05T00:00:00Z","timestamp":1749081600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004242","name":"Princess Nourah bint Abdulrahman University","doi-asserted-by":"publisher","award":["PNURSP2025R50"],"award-info":[{"award-number":["PNURSP2025R50"]}],"id":[{"id":"10.13039\/501100004242","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>This paper investigates an understudied generalization of the classical exponential, Rayleigh, and Weibull distributions, known as the power generalized Weibull distribution, particularly in the context of censored data. Characterized by one scale parameter and two shape parameters, the proposed model offers enhanced flexibility for modeling diverse lifetime data patterns and hazard rate behaviors. Notably, its hazard rate function can exhibit five distinct shapes, including upside-down bathtub and bathtub shapes. The study focuses on classical and Bayesian estimation frameworks for the model parameters and associated reliability metrics under a unified hybrid censoring scheme. Methodologies include both point estimation (maximum likelihood and posterior mean estimators) and interval estimation (approximate confidence intervals and Bayesian credible intervals). To evaluate the performance of these estimators, a comprehensive simulation study is conducted under varied experimental conditions. Furthermore, two empirical applications on real-world cancer datasets underscore the efficacy of the proposed estimation methods and the practical viability and flexibility of the explored model compared to eleven other existing lifespan models.<\/jats:p>","DOI":"10.3390\/axioms14060442","type":"journal-article","created":{"date-parts":[[2025,6,5]],"date-time":"2025-06-05T08:34:32Z","timestamp":1749112472000},"page":"442","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Statistical Analysis of a Generalized Variant of the Weibull Model Under Unified Hybrid Censoring with Applications to Cancer Data"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6353-2245","authenticated-orcid":false,"given":"Mazen","family":"Nassar","sequence":"first","affiliation":[{"name":"Department of Statistics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia"},{"name":"Department of Statistics, Faculty of Commerce, Zagazig University, Zagazig 44519, Egypt"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9449-7489","authenticated-orcid":false,"given":"Refah","family":"Alotaibi","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9916-259X","authenticated-orcid":false,"given":"Ahmed","family":"Elshahhat","sequence":"additional","affiliation":[{"name":"Faculty of Technology and Development, Zagazig University, Zagazig 44519, Egypt"}]}],"member":"1968","published-online":{"date-parts":[[2025,6,5]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Bagdonavi \u010dius, V., and Nikulin, M. (2001). Accelerated Life Models: Modeling and Statistical Analysis, Chapman and Hall\/CRC.","DOI":"10.1201\/9781420035872"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"308","DOI":"10.1109\/TR.2007.895304","article-title":"A lifetime distribution with an upside-down bathtub-shaped hazard function","volume":"56","author":"Dimitrakopoulou","year":"2007","journal-title":"IEEE Trans. Reliab."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"543","DOI":"10.1080\/02331881003678678","article-title":"An extension of the exponential distribution","volume":"45","author":"Nadarajah","year":"2011","journal-title":"Statistics"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1333","DOI":"10.1007\/s10958-006-0043-8","article-title":"A Chi-Squared Test for the Generalized Power Weibull Family for the Head-and-Neck Cancer Censored Data","volume":"133","author":"Nikulin","year":"2006","journal-title":"J. Math. Sci."},{"key":"ref_5","first-page":"75","article-title":"On the power generalized Weibull family: Model for cancer censored data","volume":"67","author":"Nikulin","year":"2009","journal-title":"Metron"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"61","DOI":"10.47302\/jsr.2017510104","article-title":"Power generalized Weibull distribution based on order statistics","volume":"51","author":"Kumar","year":"2017","journal-title":"J. Stat. Res."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"131","DOI":"10.18576\/jsapl\/050303","article-title":"On progressive-stress accelerated life testing for power generalized Weibull distribution under progressive type-II censoring","volume":"5","year":"2018","journal-title":"J. Stat. Appl. Probab. Lett."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s40819-018-0573-z","article-title":"Bayesian analysis of power generalized Weibull distribution","volume":"4","author":"Pandey","year":"2018","journal-title":"Int. J. Appl. Comput. Math."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"113","DOI":"10.18576\/jsap\/080205","article-title":"Parameter estimation for the power generalized Weibull distribution based on one-and two-stage ranked set sampling designs","volume":"8","author":"Sabry","year":"2019","journal-title":"J. Stat. Appl. Probab."},{"key":"ref_10","first-page":"339","article-title":"Comparison of Estimation Methods of the Power Generalized Weibull Distribution","volume":"82","author":"Dey","year":"2022","journal-title":"Statistica"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"555","DOI":"10.1214\/aoms\/1177728723","article-title":"Truncated life tests in the exponential case","volume":"25","author":"Epstein","year":"1954","journal-title":"Ann. Math. Stat."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"319","DOI":"10.1007\/BF02530502","article-title":"Exact likelihood inference based on Type-I and Type-II hybrid censored samples from the exponential distribution","volume":"55","author":"Childs","year":"2003","journal-title":"Ann. Inst. Stat. Math."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"994","DOI":"10.1002\/nav.20038","article-title":"Exact likelihood inference for the exponential distribution under generalized Type-I and Type-II hybrid censoring","volume":"51","author":"Chandrasekar","year":"2004","journal-title":"Nav. Res. Logist."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"475","DOI":"10.1080\/00949650601158336","article-title":"Exact likelihood inference based on an unified hybrid censored sample from the exponential distribution","volume":"78","author":"Balakrishnan","year":"2008","journal-title":"J. Stat. Comput. Simul."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1080\/00949655.2014.993985","article-title":"Estimation and prediction for a unified hybrid-censored Burr Type XII distribution","volume":"86","author":"Panahi","year":"2016","journal-title":"J. Stat. Comput. Simul."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"59","DOI":"10.17713\/ajs.v50i1.990","article-title":"Estimation of the Rayleigh distribution under unified hybrid censoring","volume":"50","author":"Jeon","year":"2021","journal-title":"Austrian J. Stat."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"3867","DOI":"10.1002\/qre.3180","article-title":"Bayesian and non-Bayesian inference of Weibull lifetime model based on partially observed competing risks data under unified hybrid censoring scheme","volume":"38","author":"Dutta","year":"2022","journal-title":"Qual. Reliab. Eng. Int."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"376","DOI":"10.1080\/00949655.2023.2249165","article-title":"Parametric inferences using dependent competing risks data with partially observed failure causes from MOBK distribution under unified hybrid censoring","volume":"94","author":"Dutta","year":"2024","journal-title":"J. Stat. Comput. Simul."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"045111","DOI":"10.1063\/5.0201467","article-title":"Statistical inference of unified hybrid censoring scheme for generalized inverted exponential distribution with application to COVID-19 data","volume":"14","author":"Hasaballah","year":"2024","journal-title":"AIP Adv."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1007\/s41872-024-00295-1","article-title":"Statistical inference and prediction in unified hybrid censored power Lindley distribution","volume":"14","author":"Shukla","year":"2025","journal-title":"Life Cycle Reliab. Saf. Eng."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1085","DOI":"10.3934\/math.2025052","article-title":"Entropy evaluation in inverse Weibull unified hybrid censored data with application to mechanical components and head-neck cancer patients","volume":"10","author":"Alotaibi","year":"2025","journal-title":"AIMS Math."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"144","DOI":"10.1198\/004017008000000217","article-title":"Bayesian inference and life testing plan for the Weibull distribution in presence of progressive censoring","volume":"50","author":"Kundu","year":"2008","journal-title":"Technometrics"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"443","DOI":"10.1007\/s00180-010-0217-1","article-title":"maxLik: A package for maximum likelihood estimation in R","volume":"26","author":"Henningsen","year":"2011","journal-title":"Comput. Stat."},{"key":"ref_24","first-page":"7","article-title":"CODA: Convergence diagnosis and output analysis for MCMC","volume":"6","author":"Plummer","year":"2006","journal-title":"R News"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Lee, E.T., and Wang, J.W. (2003). Statistical Methods for Survival Data Analysis, Wiley. [3rd ed.].","DOI":"10.1002\/0471458546"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"24109","DOI":"10.3934\/math.20241172","article-title":"Analysis of Weibull progressively first-failure censored data with beta-binomial removals","volume":"9","author":"Alotaibi","year":"2024","journal-title":"AIMS Math."},{"key":"ref_27","first-page":"100961","article-title":"A new extended Pham distribution for modelling cancer data","volume":"17","author":"Alotaibi","year":"2024","journal-title":"J. Radiat. Res. Appl. Sci."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"34","DOI":"10.1016\/j.ress.2013.07.007","article-title":"Estimation and application for a new extended Weibull distribution","volume":"121","author":"Peng","year":"2014","journal-title":"Reliab. Eng. Syst. Saf."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"3486","DOI":"10.1080\/03610926.2013.851221","article-title":"The Harris extended exponential distribution","volume":"44","author":"Pinho","year":"2015","journal-title":"Commun. Stat.-Theory Methods"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1305","DOI":"10.3923\/jas.2015.1305.1311","article-title":"The Weibull-exponential distribution: Its properties and applications","volume":"15","author":"Oguntunde","year":"2015","journal-title":"J. Appl. Sci."},{"key":"ref_31","unstructured":"Marshall, A.W., and Olkin, I. (2007). Life Distributions, Springer."},{"key":"ref_32","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_33","doi-asserted-by":"crossref","first-page":"315","DOI":"10.1080\/00949650108812098","article-title":"Generalized exponential distribution: Different method of estimations","volume":"69","author":"Gupta","year":"2001","journal-title":"J. Stat. Comput. Simul."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"637","DOI":"10.1137\/0116052","article-title":"A probabilistic interpretation of Miner\u2019s rule","volume":"16","author":"Birnbaum","year":"1968","journal-title":"SIAM J. Appl. Math."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"293","DOI":"10.1115\/1.4010337","article-title":"A statistical distribution function of wide applicability","volume":"18","author":"Weibull","year":"1951","journal-title":"J. Appl. Mech."},{"key":"ref_36","unstructured":"Johnson, N., Kotz, S., and Balakrishnan, N. (1994). Continuous Univariate Distributions, John Wiley & Sons. [2nd ed.]."},{"key":"ref_37","first-page":"1","article-title":"A vtub-shaped hazard rate function with applications to system safety","volume":"3","author":"Pham","year":"2002","journal-title":"Int. J. Reliab. Appl."},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Marinho, P.R.D., Silva, R.B., Bourguignon, M., Cordeiro, G.M., and Nadarajah, S. (2019). AdequacyModel: An R package for probability distributions and general purpose optimization. PLoS ONE, 14.","DOI":"10.1371\/journal.pone.0221487"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"414","DOI":"10.1080\/01621459.1988.10478612","article-title":"Logistic regression, survival analysis, and the Kaplan-Meier curve","volume":"83","author":"Efron","year":"1988","journal-title":"J. Am. Stat. Assoc."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"675","DOI":"10.18187\/pjsor.v18i3.3766","article-title":"Bayesian Life Analysis of Generalized Chen\u2019s Population Under Progressive Censoring","volume":"18","author":"Elshahhat","year":"2022","journal-title":"Pak. J. Stat. Oper. Res."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"1077","DOI":"10.1080\/00949655.2022.2127149","article-title":"Analysis of adaptive Type-II progressively hybrid censoring with binomial removals","volume":"93","author":"Elshahhat","year":"2023","journal-title":"J. Stat. Comput. Simul."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/14\/6\/442\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T17:47:01Z","timestamp":1760032021000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/14\/6\/442"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,6,5]]},"references-count":41,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2025,6]]}},"alternative-id":["axioms14060442"],"URL":"https:\/\/doi.org\/10.3390\/axioms14060442","relation":{},"ISSN":["2075-1680"],"issn-type":[{"type":"electronic","value":"2075-1680"}],"subject":[],"published":{"date-parts":[[2025,6,5]]}}}