Bayesian and non-Bayesian estimation of some entropy measures for a Weibull distribution

Amal S. Hassan; Najwan Alsadat; Oluwafemi Samson Balogun; Baria A. Helmy; Amal S. Hassan; Najwan Alsadat; Oluwafemi Samson Balogun; Baria A. Helmy

doi:10.3934/math.20241563

AIMS Mathematics

2024, Volume 9, Issue 11: 32646-32673. doi: 10.3934/math.20241563

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Research article

Bayesian and non-Bayesian estimation of some entropy measures for a Weibull distribution

1.
Department of Mathematical Statistics, Cairo University, Faculty of Graduate Studies for Statistical Research, Giza 12613, Egypt
2.
Department of Quantitative Analysis, College of Business Administration, King Saud University, P.O. Box 71115, Riyadh 11587, Saudi Arabia
3.
Department of Computing, University of Eastern Finland, FI-70211, Finland
4.
Department of Mathematics, Al-Azhar University (Girls Branch), Faculty of Science, Cairo 11651, Egypt

Received: 13 August 2024 Revised: 02 November 2024 Accepted: 07 November 2024 Published: 19 November 2024
MSC : 62F15, 62F30, 94A17

Entropy measures have been employed in various applications as a helpful indicator of information content. This study considered the estimation of Shannon entropy, $ \zeta $-entropy, Arimoto entropy, and Havrda and Charvat entropy measures for the Weibull distribution. The classical and Bayesian estimators for the suggested entropy measures were derived using generalized Type Ⅱ hybrid censoring data. Based on symmetric and asymmetric loss functions, Bayesian estimators of entropy measurements were developed. Asymptotic confidence intervals with the help of the delta method and the highest posterior density intervals of entropy measures were constructed. The effectiveness of the point and interval estimators was evaluated through a Monte Carlo simulation study and an application with actual data sets. Overall, the study's results indicate that with longer termination times, both maximum likelihood and Bayesian entropy estimates were effective. Furthermore, Bayesian entropy estimates using the linear exponential loss function tended to outperform those using other loss functions in the majority of scenarios. In conclusion, the analysis results from real-world examples aligned with the simulated data. Drawing insights from the analysis of glass fiber, we can assert that this research holds practical applications in reliability engineering and financial analysis.
- Weibull distribution,
- $ \zeta $-entropy,
- Havrda and Charvat's entropy,
- Bayesian estimation
Citation: Amal S. Hassan, Najwan Alsadat, Oluwafemi Samson Balogun, Baria A. Helmy. Bayesian and non-Bayesian estimation of some entropy measures for a Weibull distribution[J]. AIMS Mathematics, 2024, 9(11): 32646-32673. doi: 10.3934/math.20241563

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Abstract

Entropy measures have been employed in various applications as a helpful indicator of information content. This study considered the estimation of Shannon entropy, $ \zeta $-entropy, Arimoto entropy, and Havrda and Charvat entropy measures for the Weibull distribution. The classical and Bayesian estimators for the suggested entropy measures were derived using generalized Type Ⅱ hybrid censoring data. Based on symmetric and asymmetric loss functions, Bayesian estimators of entropy measurements were developed. Asymptotic confidence intervals with the help of the delta method and the highest posterior density intervals of entropy measures were constructed. The effectiveness of the point and interval estimators was evaluated through a Monte Carlo simulation study and an application with actual data sets. Overall, the study's results indicate that with longer termination times, both maximum likelihood and Bayesian entropy estimates were effective. Furthermore, Bayesian entropy estimates using the linear exponential loss function tended to outperform those using other loss functions in the majority of scenarios. In conclusion, the analysis results from real-world examples aligned with the simulated data. Drawing insights from the analysis of glass fiber, we can assert that this research holds practical applications in reliability engineering and financial analysis.

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