A Weighted Cosine-G Family of Distributions: Properties and Illustration Using Time-to-Event Data
Modeling and predicting time-to-event phenomena in engineering, sports, and medical sectors are very crucial. Numerous models have been proposed for modeling such types of data sets. These models are introduced by adding one or more parameters to the traditional distributions. The addition of new pa...
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MDPI AG
2023-08-01
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| Online Access: | https://www.mdpi.com/2075-1680/12/9/849 |
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| author | Omalsad Hamood Odhah Huda M. Alshanbari Zubair Ahmad Gadde Srinivasa Rao |
| author_facet | Omalsad Hamood Odhah Huda M. Alshanbari Zubair Ahmad Gadde Srinivasa Rao |
| author_sort | Omalsad Hamood Odhah |
| collection | DOAJ |
| description | Modeling and predicting time-to-event phenomena in engineering, sports, and medical sectors are very crucial. Numerous models have been proposed for modeling such types of data sets. These models are introduced by adding one or more parameters to the traditional distributions. The addition of new parameters to the traditional distributions leads to serious issues, such as estimation consequences and re-parametrization problems. To avoid such problems, this paper introduces a new method for generating new probability distributions without any additional parameters. The proposed method may be called a weighted cosine-<i>G</i> family of distributions. Different distributional properties of the weighted cosine-<i>G</i> family, along with the maximum likelihood estimators, are obtained. A special model of the weighted cosine-<i>G</i> family, by utilizing the Weibull model, is considered. The special model of the weighted cosine-<i>G</i> family may be called a weighted cosine-Weibull distribution. A simulation study of the weighted cosine-Weibull model is conducted to evaluate the performances of its estimators. Finally, the applications of the weighted cosine-Weibull distribution are shown by considering three data sets related to the time-to-event phenomena. |
| first_indexed | 2024-03-10T23:02:15Z |
| format | Article |
| id | doaj.art-3c79d2bd88824131be7e85b0c7968dda |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-10T23:02:15Z |
| publishDate | 2023-08-01 |
| publisher | MDPI AG |
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| spelling | doaj.art-3c79d2bd88824131be7e85b0c7968dda2023-11-19T09:32:35ZengMDPI AGAxioms2075-16802023-08-0112984910.3390/axioms12090849A Weighted Cosine-G Family of Distributions: Properties and Illustration Using Time-to-Event DataOmalsad Hamood Odhah0Huda M. Alshanbari1Zubair Ahmad2Gadde Srinivasa Rao3Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi ArabiaDepartment of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi ArabiaDepartment of Statistics, Quaid-i-Azam University, Islamabad 44000, PakistanDepartment of Mathematics and Statistics, University of Dodoma, Dodoma P.O. Box 259, TanzaniaModeling and predicting time-to-event phenomena in engineering, sports, and medical sectors are very crucial. Numerous models have been proposed for modeling such types of data sets. These models are introduced by adding one or more parameters to the traditional distributions. The addition of new parameters to the traditional distributions leads to serious issues, such as estimation consequences and re-parametrization problems. To avoid such problems, this paper introduces a new method for generating new probability distributions without any additional parameters. The proposed method may be called a weighted cosine-<i>G</i> family of distributions. Different distributional properties of the weighted cosine-<i>G</i> family, along with the maximum likelihood estimators, are obtained. A special model of the weighted cosine-<i>G</i> family, by utilizing the Weibull model, is considered. The special model of the weighted cosine-<i>G</i> family may be called a weighted cosine-Weibull distribution. A simulation study of the weighted cosine-Weibull model is conducted to evaluate the performances of its estimators. Finally, the applications of the weighted cosine-Weibull distribution are shown by considering three data sets related to the time-to-event phenomena.https://www.mdpi.com/2075-1680/12/9/849cosine functiontrigonometric functionWeibull distributiondistributional propertiessimulationtime-to-event data |
| spellingShingle | Omalsad Hamood Odhah Huda M. Alshanbari Zubair Ahmad Gadde Srinivasa Rao A Weighted Cosine-G Family of Distributions: Properties and Illustration Using Time-to-Event Data Axioms cosine function trigonometric function Weibull distribution distributional properties simulation time-to-event data |
| title | A Weighted Cosine-G Family of Distributions: Properties and Illustration Using Time-to-Event Data |
| title_full | A Weighted Cosine-G Family of Distributions: Properties and Illustration Using Time-to-Event Data |
| title_fullStr | A Weighted Cosine-G Family of Distributions: Properties and Illustration Using Time-to-Event Data |
| title_full_unstemmed | A Weighted Cosine-G Family of Distributions: Properties and Illustration Using Time-to-Event Data |
| title_short | A Weighted Cosine-G Family of Distributions: Properties and Illustration Using Time-to-Event Data |
| title_sort | weighted cosine g family of distributions properties and illustration using time to event data |
| topic | cosine function trigonometric function Weibull distribution distributional properties simulation time-to-event data |
| url | https://www.mdpi.com/2075-1680/12/9/849 |
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