Objective Bayesian Estimation for the Differential Entropy Measure Under Generalized Half-Normal Distribution.

Area of Science:

• Statistics
• Mechanical Engineering
• Reliability Engineering

Background:

• Information entropy is vital for assessing fatigue damage.
• The generalized half-normal distribution is linked to fatigue progression.
• Objective inference of differential entropy is needed for accurate fatigue analysis.

Purpose of the Study:

• To develop and evaluate Bayesian methods for estimating the differential entropy of the generalized half-normal distribution.
• To compare Bayesian estimates with maximum likelihood estimators for differential entropy.
• To explore the application of non-informative priors in fatigue damage assessment.

Main Methods:

• Bayesian inference using Metropolis-Hastings samplers.
• Derivation of maximum likelihood estimators and asymptotic confidence intervals.
• Simulation studies and real-data analysis for performance evaluation.

Main Results:

• Bayesian estimates and credible intervals were computed using various non-informative priors.
• The proposed Bayesian methods were evaluated against maximum likelihood estimators.
• Performance of statistical inference methods was assessed through simulations and real data.

Conclusions:

• The study provides a robust framework for differential entropy estimation in generalized half-normal distributions.
• Bayesian approaches offer valuable insights for fatigue damage assessment.
• The findings contribute to the objective inference of entropy measures in reliability engineering.