Estimating the Lifetime Parameters of the Odd-Generalized-Exponential–Inverse-Weibull Distribution Using Progressive First-Failure Censoring: A Methodology with an Application
This paper investigates statistical methods for estimating unknown lifetime parameters using a progressive first-failure censoring dataset. The failure mode’s lifetime distribution is modeled by the odd-generalized-exponential–inverse-Weibull distribution. Maximum-likelihood estimators for the model...
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2024-11-01
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| author | Mahmoud M. Ramadan Rashad M. EL-Sagheer Amel Abd-El-Monem |
| author_facet | Mahmoud M. Ramadan Rashad M. EL-Sagheer Amel Abd-El-Monem |
| author_sort | Mahmoud M. Ramadan |
| collection | DOAJ |
| description | This paper investigates statistical methods for estimating unknown lifetime parameters using a progressive first-failure censoring dataset. The failure mode’s lifetime distribution is modeled by the odd-generalized-exponential–inverse-Weibull distribution. Maximum-likelihood estimators for the model parameters, including the survival, hazard, and inverse hazard rate functions, are obtained, though they lack closed-form expressions. The Newton–Raphson method is used to compute these estimations. Confidence intervals for the parameters are approximated via the normal distribution of the maximum-likelihood estimation. The Fisher information matrix is derived using the missing information principle, and the delta method is applied to approximate the confidence intervals for the survival, hazard rate, and inverse hazard rate functions. Bayes estimators were calculated with the squared error, linear exponential, and general entropy loss functions, utilizing independent gamma distributions for informative priors. Markov-chain Monte Carlo sampling provides the highest-posterior-density credible intervals and Bayesian point estimates for the parameters and reliability characteristics. This study evaluates these methods through Monte Carlo simulations, comparing Bayes and maximum-likelihood estimates based on mean squared errors for point estimates, average interval widths, and coverage probabilities for interval estimators. A real dataset is also analyzed to illustrate the proposed methods. |
| format | Article |
| id | doaj-art-6b8f81152bb546ffbf0f92e31ac8fa2c |
| institution | Kabale University |
| issn | 2075-1680 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | MDPI AG |
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| series | Axioms |
| spelling | doaj-art-6b8f81152bb546ffbf0f92e31ac8fa2c2024-12-27T14:10:19ZengMDPI AGAxioms2075-16802024-11-01131282210.3390/axioms13120822Estimating the Lifetime Parameters of the Odd-Generalized-Exponential–Inverse-Weibull Distribution Using Progressive First-Failure Censoring: A Methodology with an ApplicationMahmoud M. Ramadan0Rashad M. EL-Sagheer1Amel Abd-El-Monem2Department of Mathematics, Faculty of Education, Ain Shams University, Roxy 11341, Cairo, EgyptMathematics Department, Faculty of Science, Al-Azhar University, Naser City 11884, Cairo, EgyptDepartment of Mathematics, Faculty of Education, Ain Shams University, Roxy 11341, Cairo, EgyptThis paper investigates statistical methods for estimating unknown lifetime parameters using a progressive first-failure censoring dataset. The failure mode’s lifetime distribution is modeled by the odd-generalized-exponential–inverse-Weibull distribution. Maximum-likelihood estimators for the model parameters, including the survival, hazard, and inverse hazard rate functions, are obtained, though they lack closed-form expressions. The Newton–Raphson method is used to compute these estimations. Confidence intervals for the parameters are approximated via the normal distribution of the maximum-likelihood estimation. The Fisher information matrix is derived using the missing information principle, and the delta method is applied to approximate the confidence intervals for the survival, hazard rate, and inverse hazard rate functions. Bayes estimators were calculated with the squared error, linear exponential, and general entropy loss functions, utilizing independent gamma distributions for informative priors. Markov-chain Monte Carlo sampling provides the highest-posterior-density credible intervals and Bayesian point estimates for the parameters and reliability characteristics. This study evaluates these methods through Monte Carlo simulations, comparing Bayes and maximum-likelihood estimates based on mean squared errors for point estimates, average interval widths, and coverage probabilities for interval estimators. A real dataset is also analyzed to illustrate the proposed methods.https://www.mdpi.com/2075-1680/13/12/822odds-generalized-exponential–inverse-Weibull distributionprogressive first-failure censoringBayesian and non-Bayesian approachesMCMC techniqueGibbs sampler within Metropolis–Hasting algorithm |
| spellingShingle | Mahmoud M. Ramadan Rashad M. EL-Sagheer Amel Abd-El-Monem Estimating the Lifetime Parameters of the Odd-Generalized-Exponential–Inverse-Weibull Distribution Using Progressive First-Failure Censoring: A Methodology with an Application Axioms odds-generalized-exponential–inverse-Weibull distribution progressive first-failure censoring Bayesian and non-Bayesian approaches MCMC technique Gibbs sampler within Metropolis–Hasting algorithm |
| title | Estimating the Lifetime Parameters of the Odd-Generalized-Exponential–Inverse-Weibull Distribution Using Progressive First-Failure Censoring: A Methodology with an Application |
| title_full | Estimating the Lifetime Parameters of the Odd-Generalized-Exponential–Inverse-Weibull Distribution Using Progressive First-Failure Censoring: A Methodology with an Application |
| title_fullStr | Estimating the Lifetime Parameters of the Odd-Generalized-Exponential–Inverse-Weibull Distribution Using Progressive First-Failure Censoring: A Methodology with an Application |
| title_full_unstemmed | Estimating the Lifetime Parameters of the Odd-Generalized-Exponential–Inverse-Weibull Distribution Using Progressive First-Failure Censoring: A Methodology with an Application |
| title_short | Estimating the Lifetime Parameters of the Odd-Generalized-Exponential–Inverse-Weibull Distribution Using Progressive First-Failure Censoring: A Methodology with an Application |
| title_sort | estimating the lifetime parameters of the odd generalized exponential inverse weibull distribution using progressive first failure censoring a methodology with an application |
| topic | odds-generalized-exponential–inverse-Weibull distribution progressive first-failure censoring Bayesian and non-Bayesian approaches MCMC technique Gibbs sampler within Metropolis–Hasting algorithm |
| url | https://www.mdpi.com/2075-1680/13/12/822 |
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