Statistical inference for Gompertz distribution under adaptive type-II progressive hybrid censoring

Area of Science:

• Reliability Engineering
• Statistical Inference
• Probability Distributions

Background:

• The Gompertz distribution is crucial in reliability engineering for modeling lifetime data.
• Adaptive Type-II hybrid progressive censoring schemes offer efficient data collection strategies.

Purpose of the Study:

• To investigate statistical inference methods for the Gompertz distribution under adaptive Type-II hybrid progressive censoring.
• To compare frequentist and Bayesian approaches for parameter estimation and confidence interval construction.

Main Methods:

• Frequentist inference: Maximum Likelihood Estimation (MLE) and Bootstrap methods (Bootstrap-p, Bootstrap-t).
• Bayesian inference: Markov Chain Monte Carlo (MCMC) simulations using squared error and LINEX loss functions.
• Numerical simulations and a real-life example for performance assessment.

Main Results:

• Point and interval estimations derived using MLE and Bootstrap methods.
• Bayes estimates obtained via MCMC, with analysis of credible interval performance.
• Comparative analysis highlighting the strengths of different inferential approaches.

Conclusions:

• The Bayesian approach, particularly MCMC, generally outperforms other methods for Gompertz distribution inference under the studied censoring scheme.
• Both frequentist and Bayesian methods offer valuable insights, with specific advantages depending on the application.
• The study provides a comprehensive framework for analyzing lifetime data using the Gompertz distribution with advanced censoring techniques.