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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Main Authors: Ahmadreza Zanboori, Ehsan Zanboori, Hamid Parvin, Mohammadreza Mahmoudi
Format: Article
Language:English
Published: Nature Portfolio 2025-07-01
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.
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institution Kabale University
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publishDate 2025-07-01
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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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