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Bayesian and Non-Bayesian Inference for Weibull Inverted Exponential Model under Progressive First-Failure Censoring Data

Author

Listed:
  • Abdullah Fathi

    (Mathematics Department, Faculty of Science, South Valley University, Qena 83523, Egypt)

  • Al-Wageh A. Farghal

    (Mathematics Department, Faculty of Science, Sohag University, Sohag 82524, Egypt)

  • Ahmed A. Soliman

    (Mathematics Department, Faculty of Science, Sohag University, Sohag 82524, Egypt)

Abstract

In this article, the estimation of the parameters and the reliability and hazard functions for Weibull inverted exponential (WIE) distribution is considered based on progressive first-failure censoring (PFFC) data. For non-Bayesian inference, maximum likelihood (ML) estimators are acquired; meanwhile, their existence is verified. Via asymptotic normality of ML estimators and delta method, the corresponding confidence intervals (CIs) of the parameters and the reliability and hazard functions are constructed. For Bayesian inference, Lindley’s approximation and Markov chain Monte Carlo (MCMC) techniques are proposed to obain the Bayes estimators and the corresponding credible intervals (CRIs). To this end, both symmetric and asymmetric loss functions are used. A large number of Monte Carlo simulations are implemented to evaluate the efficiency of the developed methods. Eventually, a numerical example is analyzed for illustrative purposes.

Suggested Citation

  • Abdullah Fathi & Al-Wageh A. Farghal & Ahmed A. Soliman, 2022. "Bayesian and Non-Bayesian Inference for Weibull Inverted Exponential Model under Progressive First-Failure Censoring Data," Mathematics, MDPI, vol. 10(10), pages 1-19, May.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:10:p:1648-:d:813833
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    References listed on IDEAS

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