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This study introduces novel Bayesian and E-Bayesian estimation methods using the spacing function for the inverse Lindley distribution. These new techniques offer practical advantages for parameter and reliability estimation in engineering and physics applications.

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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.