Entropy evaluation in inverse Weibull unified hybrid censored data with application to mechanical components and head-neck cancer patients

Refah Alotaibi; Mazen Nassar; Zareen A. Khan; Wejdan Ali Alajlan; Ahmed Elshahhat; Refah Alotaibi; Mazen Nassar; Zareen A. Khan; Wejdan Ali Alajlan; Ahmed Elshahhat

doi:10.3934/math.2025052

AIMS Mathematics

2025, Volume 10, Issue 1: 1085-1115. doi: 10.3934/math.2025052

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Entropy evaluation in inverse Weibull unified hybrid censored data with application to mechanical components and head-neck cancer patients

1.
Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
2.
Department of Statistics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
3.
Faculty of Technology and Development, Zagazig University, Zagazig 44519, Egypt

Received: 12 September 2024 Revised: 25 December 2024 Accepted: 08 January 2025 Published: 20 January 2025
MSC : 62F10, 62F15, 62N01, 62N02, 62N05

Entropy is a scientific term that finds applications in various domains, such as the laws of thermodynamics, where it was initially discovered, as well as statistical physics and information theory. We used unified hybrid censored data to investigate some inverse Weibull distribution entropy metrics. Entropy is defined using three measures: Rényi, Shannon, and Tsallis entropy. The classical estimates of the entropy measures were developed using the unified hybrid censored data, which included both point and approximation confidence intervals. The Bayesian method utilized the Markov Chain Monte Carlo sampling technique to develop Bayesian estimations. This was done by employing two loss functions, namely squared error and general entropy loss functions. Additionally, we delved into the investigation of Bayes credible intervals. Monte Carlo simulations were applied to explain how the estimates functioned at different sample sizes and censoring strategies via some accuracy criteria. Several observations were made in light of the simulation results. To provide a clear explanation of the offered methodologies, two applications using mechanical and cancer data sets were investigated.
- entropy,
- inverse Weibull,
- censored data,
- likelihood estimation,
- Bayesian estimation,
- MCMC process,
- Monte Carlo simulation
Citation: Refah Alotaibi, Mazen Nassar, Zareen A. Khan, Wejdan Ali Alajlan, Ahmed Elshahhat. Entropy evaluation in inverse Weibull unified hybrid censored data with application to mechanical components and head-neck cancer patients[J]. AIMS Mathematics, 2025, 10(1): 1085-1115. doi: 10.3934/math.2025052

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Abstract

Entropy is a scientific term that finds applications in various domains, such as the laws of thermodynamics, where it was initially discovered, as well as statistical physics and information theory. We used unified hybrid censored data to investigate some inverse Weibull distribution entropy metrics. Entropy is defined using three measures: Rényi, Shannon, and Tsallis entropy. The classical estimates of the entropy measures were developed using the unified hybrid censored data, which included both point and approximation confidence intervals. The Bayesian method utilized the Markov Chain Monte Carlo sampling technique to develop Bayesian estimations. This was done by employing two loss functions, namely squared error and general entropy loss functions. Additionally, we delved into the investigation of Bayes credible intervals. Monte Carlo simulations were applied to explain how the estimates functioned at different sample sizes and censoring strategies via some accuracy criteria. Several observations were made in light of the simulation results. To provide a clear explanation of the offered methodologies, two applications using mechanical and cancer data sets were investigated.

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