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Bayesian and non-Bayesian inference under adaptive type-II progressive censored sample with exponentiated power

Hanan Haj Ahmad1, Mukhtar M Salah2, M S Eliwa3

  • 1Department of Basic Science, Preparatory Year Deanship, King Faisal University, Hofuf, Al-Ahsa, Saudi Arabia.

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Summary

This study introduces statistical inference for the exponentiated power Lindley distribution using adaptive progressive type-II censored samples. It compares maximum likelihood estimation (MLE) and Bayesian methods, finding Bayesian approaches offer robust parameter estimation.

Keywords:
Bayesian estimationExponentiated power LindleyMarkov chain Monte Carloadaptive progressive type-II censoringmaximum likelihood estimatorsimulation

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Area of Science:

  • Statistics
  • Probability Theory
  • Reliability Engineering

Background:

  • The exponentiated power Lindley distribution is a flexible model for analyzing lifetime data.
  • Adaptive progressive type-II censoring is an efficient sampling technique for reliability studies.
  • Accurate parameter estimation is crucial for understanding and predicting the behavior of statistical distributions.

Purpose of the Study:

  • To perform statistical inference for the unknown parameters of the three-parameter exponentiated power Lindley distribution.
  • To investigate parameter estimation under adaptive progressive type-II censored samples.
  • To compare the performance of Maximum Likelihood Estimation (MLE) and Bayesian estimation methods.

Main Methods:

  • Approximate Maximum Likelihood Estimators (MLEs) were derived using the Newton-Raphson method.
  • Bayesian estimation was performed using the Markov Chain Monte Carlo (MCMC) method.
  • Squared error and Linear Exponential (LINEX) loss functions were considered for Bayesian estimation.

Main Results:

  • Asymptotic confidence intervals and Bayesian credible intervals were computed for the parameters.
  • Simulation analysis demonstrated the performance of MLE and Bayesian methods.
  • An optimal criterion was developed for censoring schemes, minimizing bias and mean square error.

Conclusions:

  • The study provides a comprehensive framework for parameter estimation of the exponentiated power Lindley distribution under censoring.
  • Bayesian estimation methods, particularly under LINEX loss, showed competitive performance compared to MLE.
  • The proposed methods were illustrated using a real-world data example, confirming the model's goodness of fit.