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Algorithms 2017, 10(2), 71; doi:10.3390/a10020071

Bayesian and Classical Estimation of Stress-Strength Reliability for Inverse Weibull Lifetime Models

Department of Mathematics, Beijing Jiaotong University, Beijing 100044, China
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Received: 25 May 2017 / Revised: 8 June 2017 / Accepted: 16 June 2017 / Published: 21 June 2017
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Abstract

In this paper, we consider the problem of estimating stress-strength reliability for inverse Weibull lifetime models having the same shape parameters but different scale parameters. We obtain the maximum likelihood estimator and its asymptotic distribution. Since the classical estimator doesn’t hold explicit forms, we propose an approximate maximum likelihood estimator. The asymptotic confidence interval and two bootstrap intervals are obtained. Using the Gibbs sampling technique, Bayesian estimator and the corresponding credible interval are obtained. The Metropolis-Hastings algorithm is used to generate random variates. Monte Carlo simulations are conducted to compare the proposed methods. Analysis of a real dataset is performed. View Full-Text
Keywords: maximum likelihood estimator; approximate maximum likelihood estimator; bootstrap confidence intervals; Bayes estimator; Metropolis–Hastings algorithm; inverse Weibull distribution maximum likelihood estimator; approximate maximum likelihood estimator; bootstrap confidence intervals; Bayes estimator; Metropolis–Hastings algorithm; inverse Weibull distribution
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Bi, Q.; Gui, W. Bayesian and Classical Estimation of Stress-Strength Reliability for Inverse Weibull Lifetime Models. Algorithms 2017, 10, 71.

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