Numerical Inference on the Inverse Weibull Model Parameters Based on Dual Generalized Hybrid Progressive Censoring Data

Mohamed Maswadah; Alia A. Alkhathami

doi:doi:10.11648/j.ijsda.20251102.12

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Numerical Inference on the Inverse Weibull Model Parameters Based on Dual Generalized Hybrid Progressive Censoring Data

Mohamed Maswadah^*

, Alia A. Alkhathami

Published in International Journal of Statistical Distributions and Applications (Volume 11, Issue 2)

Received: 23 January 2025 Accepted: 10 February 2025 Published: 9 May 2025

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Abstract

In parameter estimation techniques, several methods exist for estimating the distribution parameters in life data analysis. However, some of them are less efficient than Bayes’ method, despite its subjectivity to prior information other than data that can mislead subsequent inferences. Thus, the main objective of this study is to present optimal numerical iteration techniques, such as the Picard and the Runge-Kutta methods, which are more efficient than Bayes’ method. The proposed methods have been applied to the inverse Weibull distribution parameters and compared to the Bayes’ method based on the informative gamma prior and the non-parametric kernel and characteristic priors, via an extensive Monte Carlo simulation study through the absolute average bias and the mean squared errors for the parameter estimators. The simulation results indicated that the Picard and Runge-Kutta methods provide better estimates and outperform the Bayes’ method based on the dual generalized progressive hybrid censoring data. Finally, it has been shown that the inverse Weibull distribution gives a good fit to new areas of dataset applications, such as flood data and reactor pump data. We have analyzed and illustrated the proposed methods using these datasets to confirm the simulation results.

Published in	International Journal of Statistical Distributions and Applications (Volume 11, Issue 2)
DOI	10.11648/j.ijsda.20251102.12
Page(s)	28-44
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2025. Published by Science Publishing Group

Keywords

Bayesian Estimation, Characteristic Prior, Informative Prior, Kernel Prior, Picard’s Method, Runge- Kutta Method

References

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APA Style

Maswadah, M., Alkhathami, A. A. (2025). Numerical Inference on the Inverse Weibull Model Parameters Based on Dual Generalized Hybrid Progressive Censoring Data. International Journal of Statistical Distributions and Applications, 11(2), 28-44. https://doi.org/10.11648/j.ijsda.20251102.12

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ACS Style

Maswadah, M.; Alkhathami, A. A. Numerical Inference on the Inverse Weibull Model Parameters Based on Dual Generalized Hybrid Progressive Censoring Data. Int. J. Stat. Distrib. Appl. 2025, 11(2), 28-44. doi: 10.11648/j.ijsda.20251102.12

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AMA Style

Maswadah M, Alkhathami AA. Numerical Inference on the Inverse Weibull Model Parameters Based on Dual Generalized Hybrid Progressive Censoring Data. Int J Stat Distrib Appl. 2025;11(2):28-44. doi: 10.11648/j.ijsda.20251102.12

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@article{10.11648/j.ijsda.20251102.12,
  author = {Mohamed Maswadah and Alia A. Alkhathami},
  title = {Numerical Inference on the Inverse Weibull Model Parameters Based on Dual Generalized Hybrid Progressive Censoring Data
},
  journal = {International Journal of Statistical Distributions and Applications},
  volume = {11},
  number = {2},
  pages = {28-44},
  doi = {10.11648/j.ijsda.20251102.12},
  url = {https://doi.org/10.11648/j.ijsda.20251102.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijsda.20251102.12},
  abstract = {In parameter estimation techniques, several methods exist for estimating the distribution parameters in life data analysis. However, some of them are less efficient than Bayes’ method, despite its subjectivity to prior information other than data that can mislead subsequent inferences. Thus, the main objective of this study is to present optimal numerical iteration techniques, such as the Picard and the Runge-Kutta methods, which are more efficient than Bayes’ method. The proposed methods have been applied to the inverse Weibull distribution parameters and compared to the Bayes’ method based on the informative gamma prior and the non-parametric kernel and characteristic priors, via an extensive Monte Carlo simulation study through the absolute average bias and the mean squared errors for the parameter estimators. The simulation results indicated that the Picard and Runge-Kutta methods provide better estimates and outperform the Bayes’ method based on the dual generalized progressive hybrid censoring data. Finally, it has been shown that the inverse Weibull distribution gives a good fit to new areas of dataset applications, such as flood data and reactor pump data. We have analyzed and illustrated the proposed methods using these datasets to confirm the simulation results.
},
 year = {2025}
}

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TY  - JOUR
T1  - Numerical Inference on the Inverse Weibull Model Parameters Based on Dual Generalized Hybrid Progressive Censoring Data

AU  - Mohamed Maswadah
AU  - Alia A. Alkhathami
Y1  - 2025/05/09
PY  - 2025
N1  - https://doi.org/10.11648/j.ijsda.20251102.12
DO  - 10.11648/j.ijsda.20251102.12
T2  - International Journal of Statistical Distributions and Applications
JF  - International Journal of Statistical Distributions and Applications
JO  - International Journal of Statistical Distributions and Applications
SP  - 28
EP  - 44
PB  - Science Publishing Group
SN  - 2472-3509
UR  - https://doi.org/10.11648/j.ijsda.20251102.12
AB  - In parameter estimation techniques, several methods exist for estimating the distribution parameters in life data analysis. However, some of them are less efficient than Bayes’ method, despite its subjectivity to prior information other than data that can mislead subsequent inferences. Thus, the main objective of this study is to present optimal numerical iteration techniques, such as the Picard and the Runge-Kutta methods, which are more efficient than Bayes’ method. The proposed methods have been applied to the inverse Weibull distribution parameters and compared to the Bayes’ method based on the informative gamma prior and the non-parametric kernel and characteristic priors, via an extensive Monte Carlo simulation study through the absolute average bias and the mean squared errors for the parameter estimators. The simulation results indicated that the Picard and Runge-Kutta methods provide better estimates and outperform the Bayes’ method based on the dual generalized progressive hybrid censoring data. Finally, it has been shown that the inverse Weibull distribution gives a good fit to new areas of dataset applications, such as flood data and reactor pump data. We have analyzed and illustrated the proposed methods using these datasets to confirm the simulation results.

VL  - 11
IS  - 2
ER  -

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Author Information

Mohamed Maswadah

Department of Mathematics, Faculty of Science, Aswan University, Aswan, Egypt

Contact Email

http://orcid.org/0000-0002-2296-931X
Alia A. Alkhathami

Department of Basic Science, College of Science and Theoretical Studies, Saudi Electronic University, Riyadh, Kingdom of Saudi Arabia

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APA Style

Maswadah, M., Alkhathami, A. A. (2025). Numerical Inference on the Inverse Weibull Model Parameters Based on Dual Generalized Hybrid Progressive Censoring Data. International Journal of Statistical Distributions and Applications, 11(2), 28-44. https://doi.org/10.11648/j.ijsda.20251102.12

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ACS Style

Maswadah, M.; Alkhathami, A. A. Numerical Inference on the Inverse Weibull Model Parameters Based on Dual Generalized Hybrid Progressive Censoring Data. Int. J. Stat. Distrib. Appl. 2025, 11(2), 28-44. doi: 10.11648/j.ijsda.20251102.12

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AMA Style

Maswadah M, Alkhathami AA. Numerical Inference on the Inverse Weibull Model Parameters Based on Dual Generalized Hybrid Progressive Censoring Data. Int J Stat Distrib Appl. 2025;11(2):28-44. doi: 10.11648/j.ijsda.20251102.12

Copy | Download

@article{10.11648/j.ijsda.20251102.12,
  author = {Mohamed Maswadah and Alia A. Alkhathami},
  title = {Numerical Inference on the Inverse Weibull Model Parameters Based on Dual Generalized Hybrid Progressive Censoring Data
},
  journal = {International Journal of Statistical Distributions and Applications},
  volume = {11},
  number = {2},
  pages = {28-44},
  doi = {10.11648/j.ijsda.20251102.12},
  url = {https://doi.org/10.11648/j.ijsda.20251102.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijsda.20251102.12},
  abstract = {In parameter estimation techniques, several methods exist for estimating the distribution parameters in life data analysis. However, some of them are less efficient than Bayes’ method, despite its subjectivity to prior information other than data that can mislead subsequent inferences. Thus, the main objective of this study is to present optimal numerical iteration techniques, such as the Picard and the Runge-Kutta methods, which are more efficient than Bayes’ method. The proposed methods have been applied to the inverse Weibull distribution parameters and compared to the Bayes’ method based on the informative gamma prior and the non-parametric kernel and characteristic priors, via an extensive Monte Carlo simulation study through the absolute average bias and the mean squared errors for the parameter estimators. The simulation results indicated that the Picard and Runge-Kutta methods provide better estimates and outperform the Bayes’ method based on the dual generalized progressive hybrid censoring data. Finally, it has been shown that the inverse Weibull distribution gives a good fit to new areas of dataset applications, such as flood data and reactor pump data. We have analyzed and illustrated the proposed methods using these datasets to confirm the simulation results.
},
 year = {2025}
}

Copy | Download

TY  - JOUR
T1  - Numerical Inference on the Inverse Weibull Model Parameters Based on Dual Generalized Hybrid Progressive Censoring Data

AU  - Mohamed Maswadah
AU  - Alia A. Alkhathami
Y1  - 2025/05/09
PY  - 2025
N1  - https://doi.org/10.11648/j.ijsda.20251102.12
DO  - 10.11648/j.ijsda.20251102.12
T2  - International Journal of Statistical Distributions and Applications
JF  - International Journal of Statistical Distributions and Applications
JO  - International Journal of Statistical Distributions and Applications
SP  - 28
EP  - 44
PB  - Science Publishing Group
SN  - 2472-3509
UR  - https://doi.org/10.11648/j.ijsda.20251102.12
AB  - In parameter estimation techniques, several methods exist for estimating the distribution parameters in life data analysis. However, some of them are less efficient than Bayes’ method, despite its subjectivity to prior information other than data that can mislead subsequent inferences. Thus, the main objective of this study is to present optimal numerical iteration techniques, such as the Picard and the Runge-Kutta methods, which are more efficient than Bayes’ method. The proposed methods have been applied to the inverse Weibull distribution parameters and compared to the Bayes’ method based on the informative gamma prior and the non-parametric kernel and characteristic priors, via an extensive Monte Carlo simulation study through the absolute average bias and the mean squared errors for the parameter estimators. The simulation results indicated that the Picard and Runge-Kutta methods provide better estimates and outperform the Bayes’ method based on the dual generalized progressive hybrid censoring data. Finally, it has been shown that the inverse Weibull distribution gives a good fit to new areas of dataset applications, such as flood data and reactor pump data. We have analyzed and illustrated the proposed methods using these datasets to confirm the simulation results.

VL  - 11
IS  - 2
ER  -

Copy | Download