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Imran M, Alsadat N, Tahir MH, Jamal F, Elgarhy M, Ahmad H, Johannssen A. The development of an extended Weibull model with applications to medicine, industry and actuarial sciences. Sci Rep 2024; 14:12338. [PMID: 38811667 PMCID: PMC11190291 DOI: 10.1038/s41598-024-61308-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/16/2023] [Accepted: 05/03/2024] [Indexed: 05/31/2024] Open
Abstract
This paper delves into the theoretical and practical exploration of the complementary Bell Weibull (CBellW) model, which serves as an analogous counterpart to the complementary Poisson Weibull model. The study encompasses a comprehensive examination of various statistical properties of the CBellW model. Real data applications are carried out in three different fields, namely the medical, industrial and actuarial fields, to show the practical versatility of the CBellW model. For the medical data segment, the study utilizes four data sets, including information on daily confirmed COVID-19 cases and cancer data. Additionally, a Group Acceptance Sampling Plan (GASP) is designed by using the median as quality parameter. Furthermore, some actuarial risk measures for the CBellW model are obtained along with a numerical illustration of the Value at Risk and the Expected Shortfall. The research is substantiated by a comprehensive numerical analysis, model comparisons, and graphical illustrations that complement the theoretical foundation.
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Affiliation(s)
- Muhammad Imran
- Department of Statistics, The Islamia University of Bahawalpur, Bahawalpur, 63100, Pakistan
| | - Najwan Alsadat
- Department of Quantitative Analysis, College of Business Administration, King Saud University, P.O. Box 71115, 11587, Riyadh, Saudi Arabia
| | - M H Tahir
- Department of Statistics, The Islamia University of Bahawalpur, Bahawalpur, 63100, Pakistan
| | - Farrukh Jamal
- Department of Statistics, The Islamia University of Bahawalpur, Bahawalpur, 63100, Pakistan
| | - Mohammed Elgarhy
- Department of Basic Sciences, Higher Institute for Administrative Sciences, Belbeis, Al-Sharqia, Egypt
- Mathematics and Computer Science Department, Faculty of Science, Beni-Suef University, Beni-Suef, 62521, Egypt
| | - Hijaz Ahmad
- Near East University, Operational Research Center in Healthcare, TRNC Mersin 10, Nicosia, 99138, Turkey
- Center for Applied Mathematics and Bioinformatics, Gulf University for Science and Technology, Mishref, Kuwait
- Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon
| | - Arne Johannssen
- Faculty of Business Administration, University of Hamburg, 20146, Hamburg, Germany.
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Peña-Ramírez FA, Guerra RR, Mafalda CP. The unit ratio-extended Weibull family and the dropout rate in Brazilian undergraduate courses. PLoS One 2023; 18:e0290885. [PMID: 37972044 PMCID: PMC10653530 DOI: 10.1371/journal.pone.0290885] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/19/2023] [Accepted: 08/11/2023] [Indexed: 11/19/2023] Open
Abstract
We propose a new family of distributions, so-called the unit ratio-extended Weibull family ([Formula: see text]). It is derived from ratio transformation in an extended Weibull random variable. The use of this transformation is a novelty of the work since it has been less explored than the exponential and has not yet been studied within the extended Weibull class. Moreover, we offer a valuable alternative to model double-bounded variables on the unit interval. Five [Formula: see text] special models are studied in detail, namely the: i) unit ratio-Gompertz; ii) unit ratio-Burr XII; iii) unit ratio-Lomax; v) unit ratio-Rayleigh, and vi) unit ratio-Weibull distributions. We propose a quantile-parameterization for the new family. The maximum likelihood estimators (MLEs) are presented. A Monte Carlo study is performed to evaluate the behavior of the MLEs of unit ratio-Gompertz and unit ratio-Rayleigh distributions. This last model has closed-form and approximately unbiased MLE for small sample sizes. Further, the [Formula: see text] submodels are adjusted to the dropout rate in Brazilian undergraduate courses. We focus on the areas of civil engineering, economics, computer sciences, and control engineering. The applications show that the new family is suitable for modeling educational data and may provide effective alternatives compared to other usual unit models, such as the Beta, Kumaraswamy, and unit gamma distributions. They can also outperform some recent contributions in the unit distribution literature. Thus, the [Formula: see text] family can provide competitive alternatives when those models are unsuitable.
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Affiliation(s)
| | - Renata R. Guerra
- Departamento de Estatística, Universidade Federal de Santa Maria, Santa Maria, RS, Brazil
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