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

Abdullah Fathi, Al-Wageh A. Farghal and Ahmed A. Soliman
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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

Mathematics, 2022, vol. 10, issue 10, 1-19

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.

Keywords: Weibull-inverted exponential distribution; progressive first-failure censoring; maximum likelihood inference; Lindley’s approximation; MCMC technique (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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