Bayesian and non-Bayesian inference under adaptive type-II progressive censored sample with exponentiated power...

Area of Science:

• Statistics
• Probability Theory
• Reliability Engineering

Background:

• The exponentiated power Lindley distribution is a flexible model for analyzing lifetime data.
• Adaptive progressive type-II censoring is an efficient sampling technique for reliability studies.
• Accurate parameter estimation is crucial for understanding and predicting the behavior of statistical distributions.

Purpose of the Study:

• To perform statistical inference for the unknown parameters of the three-parameter exponentiated power Lindley distribution.
• To investigate parameter estimation under adaptive progressive type-II censored samples.
• To compare the performance of Maximum Likelihood Estimation (MLE) and Bayesian estimation methods.

Main Methods:

• Approximate Maximum Likelihood Estimators (MLEs) were derived using the Newton-Raphson method.
• Bayesian estimation was performed using the Markov Chain Monte Carlo (MCMC) method.
• Squared error and Linear Exponential (LINEX) loss functions were considered for Bayesian estimation.

Main Results:

• Asymptotic confidence intervals and Bayesian credible intervals were computed for the parameters.
• Simulation analysis demonstrated the performance of MLE and Bayesian methods.
• An optimal criterion was developed for censoring schemes, minimizing bias and mean square error.

Conclusions:

• The study provides a comprehensive framework for parameter estimation of the exponentiated power Lindley distribution under censoring.
• Bayesian estimation methods, particularly under LINEX loss, showed competitive performance compared to MLE.
• The proposed methods were illustrated using a real-world data example, confirming the model's goodness of fit.