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Bayesian and Non-Bayesian Reliability Estimation of Stress-Strength Model for Power-Modified Lindley Distribution.

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A new power-modified Lindley (PML) distribution is introduced for statistical modeling. This flexible distribution and its properties are analyzed, showing promise for real-world data applications and reliability analysis.

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Area of Science:

  • Statistics
  • Probability Theory
  • Reliability Engineering

Background:

  • Continuous probability distributions are fundamental in statistical modeling.
  • Existing distributions may not always capture the complexity of real-world data.
  • Reliability analysis is crucial for system performance and safety.

Purpose of the Study:

  • To propose and analyze a new two-parameter continuous distribution called the power-modified Lindley (PML) distribution.
  • To investigate the structural properties and estimation methods for the PML distribution.
  • To apply the PML distribution to reliability engineering and stress-strength modeling.

Main Methods:

  • Derivation of key statistical properties: moments, moment-generating function, conditional moments, mean deviations, mean residual lifetime, and mean past lifetime.
  • Development of maximum-likelihood estimation (MLE) for parameters and asymptotic standard errors.
  • Application of Bayesian estimation with gamma priors, utilizing Markov Chain Monte Carlo (MCMC) via the Metropolis-Hastings algorithm for stress-strength parameters.
  • Construction of confidence intervals for model parameters and stress-strength reliability using both likelihood and Bayesian approaches.

Main Results:

  • The structural properties of the PML distribution were mathematically derived.
  • Maximum-likelihood and Bayesian estimation methods were successfully developed and applied.
  • The performance of the PML distribution was demonstrated through real data applications, highlighting its flexibility.
  • Confidence intervals for parameters and stress-strength reliability were obtained.

Conclusions:

  • The proposed power-modified Lindley (PML) distribution offers a flexible and valuable addition to the family of continuous distributions.
  • The developed estimation techniques (MLE and Bayesian) are effective for parameter estimation and reliability assessment.
  • The PML distribution shows significant potential for modeling complex real-world data, particularly in reliability and stress-strength scenarios.