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E-Bayesian Estimation of Chen Distribution Based on Type-I Censoring Scheme.

Ali Algarni1, Abdullah M Almarashi1, Hassan Okasha1

  • 1Department of Statistics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudia Arabia.

Entropy (Basel, Switzerland)
|December 8, 2020
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Summary

This study introduces E-Bayesian estimators for the Chen distribution under type-I censoring. These new estimators, based on a balanced squared error loss function, offer improved efficiency for reliability and hazard rate analysis.

Keywords:
Bayes estimationChen distributionE-Bayes estimationbalanced loss functiontype-I censoring scheme

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Area of Science:

  • Statistics
  • Probability Theory
  • Reliability Engineering

Background:

  • The Chen distribution is a flexible model used in various applications.
  • Type-I censoring is a common data collection scheme in reliability studies.
  • Estimating distribution parameters under censoring is crucial for accurate analysis.

Purpose of the Study:

  • To develop and investigate E-Bayesian estimators for the scale parameter, reliability, and hazard rate functions of the Chen distribution.
  • To apply these estimators under a type-I censoring scheme.
  • To compare the performance of the proposed estimators against existing methods.

Main Methods:

  • E-Bayesian estimation framework utilizing a balanced squared error loss function.
  • Employing a gamma distribution as a conjugate prior for the scale parameter.
  • Derivation of estimators using three distinct hyper-parameter distributions.
  • A simulation study to assess estimator efficiency via minimum mean squared errors.
  • Analysis of a real-world dataset to demonstrate practical utility.

Main Results:

  • The study successfully derived novel E-Bayesian estimators for key Chen distribution functions.
  • Simulation results indicated the comparative efficiencies of the proposed estimators.
  • The real data analysis confirmed the applicability and potential advantages of the E-Bayesian approach.

Conclusions:

  • The proposed E-Bayesian estimators provide a valuable tool for analyzing Chen distribution data, particularly under type-I censoring.
  • The balanced squared error loss function and specific prior choices influence estimator performance.
  • The developed methods offer a practical approach for reliability and hazard rate estimation in engineering and statistical applications.