Statistical Inference for the Entropy of the Transmuted Weibull Distribution Under Progressive Type-II Censored...

Area of Science:

• Statistics
• Reliability Engineering
• Information Theory

Background:

• The Transmuted Weibull Distribution enhances flexibility for lifetime data modeling.
• Progressively Type-II censored samples are common in reliability and survival analysis.
• Shannon entropy quantifies uncertainty in probability distributions.

Purpose of the Study:

• To derive and estimate Shannon entropy for the Transmuted Weibull Distribution.
• To compare frequentist (Maximum Likelihood Estimation) and Bayesian inference methods.
• To evaluate performance using progressively Type-II censored data.

Main Methods:

• Derivation of a closed-form expression for Shannon entropy.
• Numerical estimation via Newton-Raphson algorithm (MLE).
• Asymptotic and Bootstrap confidence intervals (frequentist).
• Markov Chain Monte Carlo (MCMC) methods for Bayesian inference.
• Comparison using Monte Carlo simulations.

Main Results:

• Bayesian estimators show better performance (lower bias, MSE) than MLE.
• Bayesian methods are more effective with small sample sizes and heavy censoring.
• Highest posterior density credible intervals provide accurate coverage and shorter lengths.

Conclusions:

• The proposed Bayesian approach is robust and practical for Shannon entropy estimation.
• The Transmuted Weibull Distribution is a flexible model for complex lifetime data.
• The study demonstrates the utility of advanced statistical inference in real-world applications.