Theoretical framework and inference for fitting extreme data through the modified Weibull distribution in a...

Area of Science:

• Biomedical Engineering
• Statistical Modeling
• Reliability Engineering

Background:

• Biomedical physical data is vital for understanding human health, disease mechanisms, and developing medical treatments.
• Accurate estimation of parameters and reliability measures is crucial for analyzing censored progressive biomedical data.
• The modified Weibull distribution is a key model for reliability analysis in biomedical contexts.

Purpose of the Study:

• To address challenges in estimating unknown parameters and reliability measures for the modified Weibull distribution with censored progressive biomedical data.
• To propose and compare classical and Bayesian estimation techniques for survival and failure rate functions.
• To evaluate the performance of different estimation strategies using simulation and identify optimal control strategies.

Main Methods:

• Application of classical and Bayesian estimation techniques for parameter and reliability function estimation.
• Utilization of asymmetric and symmetric loss functions for Bayesian estimates.
• Employing the Markov chain Monte Carlo (MCMC) method for Bayesian estimates and highest posterior density credible intervals.
• Conducting a simulation study to compare the performance of various estimation procedures.
• Utilizing optimization criteria to determine effective progressive control strategies.

Main Results:

• Bayesian estimation methods demonstrated superior performance compared to other techniques.
• Bayesian estimates achieved minimal root mean square errors (RMSE) and narrower interval lengths.
• The proposed methods were validated through a medical application, showcasing their effectiveness.

Conclusions:

• Bayesian estimation offers a more accurate and reliable approach for analyzing censored progressive biomedical data using the modified Weibull distribution.
• The study provides valuable insights into parameter estimation and reliability assessment in biomedical research.
• The findings contribute to enhancing the quality of healthcare decisions and improving individual well-being through advanced statistical analysis.