Estimation for two Gompertz populations under a balanced joint progressive Type-II censoring scheme

Area of Science:

• Statistics
• Reliability Engineering
• Survival Analysis

Background:

• Comparative lifetime experiments are crucial for product development and reliability assessment.
• Gompertz distribution is frequently used to model lifetime data.
• Joint progressive Type-II censoring offers efficient data collection in lifetime studies.

Purpose of the Study:

• To develop statistical methods for comparing the lifetimes of two Gompertz populations under balanced joint progressive Type-II censoring.
• To derive and validate maximum likelihood and Bayesian estimates for unknown parameters.
• To investigate statistical inferences with order restriction and analyze real-world data.

Main Methods:

• Maximum Likelihood Estimation (MLE) with Expectation-Maximization (EM) and Stochastic EM algorithms.
• Bootstrap methods (bootstrap-p, bootstrap-t) for confidence interval construction.
• Bayesian inference using Metropolis-Hastings algorithm with specified priors and loss functions.
• Order-restricted statistical inference.

Main Results:

• Existence and computation methods for MLEs are established.
• Effective Bayesian estimation and credible intervals are provided.
• Simulation studies demonstrate the performance of proposed methods.
• Application to white organic light-emitting diodes and jute fiber breaking strengths.

Conclusions:

• The proposed methods provide robust statistical inferences for comparative lifetime experiments.
• The study offers practical tools for analyzing reliability data in various fields.
• The Gompertz distribution under joint progressive censoring is a viable model for lifetime analysis.