E-Bayesian Estimation Using Spacing Function for Inverse Lindley Adaptive Type-I Progressively Censored Samples:...

Area of Science:

• Statistics
• Probability Theory
• Reliability Engineering

Background:

• Classical statistical methods often rely on likelihood functions.
• The inverse Lindley distribution is valuable for modeling various phenomena.
• Progressive censoring is a common technique in reliability studies.

Purpose of the Study:

• To introduce Bayesian and E-Bayesian estimation methods utilizing the spacing function (SF) for the inverse Lindley distribution.
• To compare these novel methods with classical approaches using progressively censored samples.
• To evaluate the performance and practicality of the proposed estimation techniques.

Main Methods:

• Bayesian and E-Bayesian estimation using spacing functions.
• Classical estimation using likelihood and product of spacing methods.
• Adaptive Type-I progressively censored sampling.
• Monte Carlo simulations for performance assessment.

Main Results:

• The study derives posterior distributions using both likelihood and SFs for Bayesian analysis.
• Approximate confidence intervals and Bayes/E-Bayes credible intervals are computed.
• Monte Carlo experiments demonstrate the performance of the estimators under various scenarios.

Conclusions:

• The proposed Bayesian and E-Bayesian methods using SFs are practical and effective for inverse Lindley distribution estimation.
• The study validates the superiority of the new approaches through simulations and real-world data analysis.
• These methods offer valuable tools for reliability analysis in engineering and physics.