A flexible Weibull geometric distribution with characterizations and its parameter estimation
Abstract The current paper introduces a new version of the Weibull-geometric distribution, which offers a more flexible model for lifetime data. The statistical properties of the proposed distribution—such as the probability density function, reliability and failure rate functions, quantiles, and mo...
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| Format: | Article |
| Language: | English |
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Nature Portfolio
2025-07-01
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| Series: | Scientific Reports |
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| Online Access: | https://doi.org/10.1038/s41598-025-12378-9 |
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| author | Ahmadreza Zanboori Ehsan Zanboori Hamid Parvin Mohammadreza Mahmoudi |
| author_facet | Ahmadreza Zanboori Ehsan Zanboori Hamid Parvin Mohammadreza Mahmoudi |
| author_sort | Ahmadreza Zanboori |
| collection | DOAJ |
| description | Abstract The current paper introduces a new version of the Weibull-geometric distribution, which offers a more flexible model for lifetime data. The statistical properties of the proposed distribution—such as the probability density function, reliability and failure rate functions, quantiles, and moments—are discussed. The EM algorithm is used to compute the asymptotic variances and covariances of the parameters. Point estimators of the unknown parameters, under various symmetric and asymmetric loss functions, are obtained using the Bayesian framework and the Markov Chain Monte Carlo (MCMC) technique. Furthermore, using the importance sampling procedure, the highest posterior density (HPD) credible intervals for the parameters are derived. Maximum likelihood and Bayesian estimators are also employed to compute the shrinkage preliminary test estimators. Consequently, a simulation study is conducted to evaluate the performance of all proposed estimation methods. Finally, a real data set is analyzed to demonstrate the effectiveness and flexibility of the new distribution. |
| format | Article |
| id | doaj-art-1f7c56d7fa934eef99504ff8c4c62a81 |
| institution | Kabale University |
| issn | 2045-2322 |
| language | English |
| publishDate | 2025-07-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | Scientific Reports |
| spelling | doaj-art-1f7c56d7fa934eef99504ff8c4c62a812025-08-20T03:42:35ZengNature PortfolioScientific Reports2045-23222025-07-0115111610.1038/s41598-025-12378-9A flexible Weibull geometric distribution with characterizations and its parameter estimationAhmadreza Zanboori0Ehsan Zanboori1Hamid Parvin2Mohammadreza Mahmoudi3Department of Statistics, Marvdasht Branch, Islamic Azad UniversityDepartment of Mathematics, NM.C, Islamic Azad UniversityDepartment of Computer Engineering, Nourabad Mamasani Branch, Islamic Azad universityDepartment of Statistics, Faculty of Science, Fasa UniversityAbstract The current paper introduces a new version of the Weibull-geometric distribution, which offers a more flexible model for lifetime data. The statistical properties of the proposed distribution—such as the probability density function, reliability and failure rate functions, quantiles, and moments—are discussed. The EM algorithm is used to compute the asymptotic variances and covariances of the parameters. Point estimators of the unknown parameters, under various symmetric and asymmetric loss functions, are obtained using the Bayesian framework and the Markov Chain Monte Carlo (MCMC) technique. Furthermore, using the importance sampling procedure, the highest posterior density (HPD) credible intervals for the parameters are derived. Maximum likelihood and Bayesian estimators are also employed to compute the shrinkage preliminary test estimators. Consequently, a simulation study is conducted to evaluate the performance of all proposed estimation methods. Finally, a real data set is analyzed to demonstrate the effectiveness and flexibility of the new distribution.https://doi.org/10.1038/s41598-025-12378-9Bayesian estimation, EM algorithmFailure rate functionShrinkage preliminary test estimatorsAsymptotic normalityNew Weibull-geometric distribution |
| spellingShingle | Ahmadreza Zanboori Ehsan Zanboori Hamid Parvin Mohammadreza Mahmoudi A flexible Weibull geometric distribution with characterizations and its parameter estimation Scientific Reports Bayesian estimation, EM algorithm Failure rate function Shrinkage preliminary test estimators Asymptotic normality New Weibull-geometric distribution |
| title | A flexible Weibull geometric distribution with characterizations and its parameter estimation |
| title_full | A flexible Weibull geometric distribution with characterizations and its parameter estimation |
| title_fullStr | A flexible Weibull geometric distribution with characterizations and its parameter estimation |
| title_full_unstemmed | A flexible Weibull geometric distribution with characterizations and its parameter estimation |
| title_short | A flexible Weibull geometric distribution with characterizations and its parameter estimation |
| title_sort | flexible weibull geometric distribution with characterizations and its parameter estimation |
| topic | Bayesian estimation, EM algorithm Failure rate function Shrinkage preliminary test estimators Asymptotic normality New Weibull-geometric distribution |
| url | https://doi.org/10.1038/s41598-025-12378-9 |
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