Statistical inference with joint progressive censoring for two populations using power Rayleigh lifetime distribution

Area of Science:

• Statistics
• Probability Theory
• Reliability Engineering

Background:

• The power Rayleigh distribution is a flexible model used in various statistical applications.
• Censoring techniques are crucial for analyzing incomplete data in reliability and survival analysis.
• Joint progressive type-II censoring offers an efficient data collection strategy.

Purpose of the Study:

• To derive point and interval estimations for the power Rayleigh distribution under joint progressive type-II censoring.
• To compare the performance of maximum likelihood and Bayesian estimation methods.
• To assess the utility of Markov chain Monte Carlo (MCMC) for Bayesian inference.

Main Methods:

• Joint progressive type-II censoring was applied to the power Rayleigh distribution.
• Maximum Likelihood Estimation (MLE) and Bayesian estimation techniques were utilized.
• Markov Chain Monte Carlo (MCMC) methods, specifically Metropolis-Hastings with Gibbs sampling, were implemented for Bayesian inference.
• Confidence intervals and approximate credible intervals were computed.

Main Results:

• Point and interval estimators for the power Rayleigh distribution parameters were successfully derived.
• The study demonstrated the application of both frequentist (MLE) and Bayesian approaches.
• MCMC methods provided reliable Bayesian estimates for different loss functions.
• A real data set analysis validated the proposed estimation techniques.

Conclusions:

• The study provides a comprehensive framework for estimating parameters of the power Rayleigh distribution using advanced censoring and estimation techniques.
• Both MLE and Bayesian methods, supported by MCMC, are effective for this distribution under the specified censoring scheme.
• The findings contribute to the statistical analysis of lifetime data, particularly in scenarios with progressive censoring.