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Bayesian inference: Weibull Poisson model for censored data using the expectation-maximization algorithm and its

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Summary

This study estimates parameters for the Weibull Poisson Model using progressive type-II censoring with binomial removals. The expectation-maximization algorithm and Bayes estimators were employed, demonstrating the model

Keywords:
Bayes predictionGELFPT-II CBRsexpectation–maximization algorithmexpected experiment timelikelihood ratio test

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Area of Science:

  • Statistics
  • Reliability Engineering
  • Survival Analysis

Background:

  • Parameter estimation is crucial for reliability analysis.
  • Progressive type-II censoring with binomial removals (PT-II CBRs) is an efficient data collection scheme.
  • The Weibull Poisson Model is widely used in reliability and survival analysis.

Purpose of the Study:

  • To estimate parameters of the Weibull Poisson Model under PT-II CBRs.
  • To compare the performance of Maximum Likelihood Estimators (MLEs) and Bayes estimators.
  • To illustrate the model's applicability using real-world bladder cancer data.

Main Methods:

  • Utilized the expectation-maximization algorithm for MLEs.
  • Derived MLEs and Bayes estimators under various loss functions (symmetric and asymmetric).
  • Employed simulation studies to evaluate the risks of different estimators.

Main Results:

  • The expectation-maximization algorithm provided efficient MLEs.
  • Bayes estimators showed competitive performance under different loss functions.
  • The proposed methodology and model were validated using a bladder cancer dataset.

Conclusions:

  • The study successfully estimated parameters for the Weibull Poisson Model under PT-II CBRs.
  • The comparison of estimators provides valuable insights for practical applications.
  • The real data analysis confirms the model's suitability and the proposed methods' effectiveness.