Modified Weibull model: A Bayes study using MCMC approach based on progressive censoring data

Soliman, Ahmed A.; Abdellah, Ahmed H.; Abou-Elheggag, N. A.; Ahmed, Essam A.

doi:10.1016/j.ress.2011.12.013

Cited by 58 publications

(21 citation statements)

References 28 publications

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“…Second: Extreme case can occur when T = 0, which results in the conventional Type-II censoring scheme R 1 = R 2 = ⋅⋅⋅ = R m−1 = 0 and R m = n − m. Many papers dealing with adaptive progressive Type-II censoring have been appeared. Among them, Soliman et al (2011;2012) have used a Bayes study using MCMC approach based on progressive censoring data. (For more details about MCMC; see, for example, Robert and Casella (2005) and Recently, Rezaei et al (2010).…”

Section: The Model Descriptionmentioning

confidence: 99%

Estimation for Unknown Parameters of the Burr Type-XII Distribution Based on an Adaptive Progressive Type-II Censoring Scheme

Amein¹

2016

Journal of Mathematics and Statistics

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In this study, the Maximum Likelihood Estimation (MLE) and Bayes estimation are exploited to make interval estimation based on adaptive progressive Type-II censoring for the Burr Type-XII distribution. Explicit form for the parameters of Bayes estimator doesn't exist, so, Markov Chain Monte Carlo (MCMC) method is used as approximation to find posterior mean under squared error loss function. Real data set are presented to illustrate the methods of inference.

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Section: The Model Descriptionmentioning

confidence: 99%

Estimation for Unknown Parameters of the Burr Type-XII Distribution Based on an Adaptive Progressive Type-II Censoring Scheme

Amein¹

2016

Journal of Mathematics and Statistics

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“…A complete introduction and review of importance sampling as well as MCMC methods including Gibbs sampling and Metropolis-Hastings (MH) and related algorithms can be found in Chen and Shao (1999); Kundu and Howlader (2010); Soliman et al (2011a) and Soliman et al (2012).…”

Section: Mcmc For Prediction Problems Under Progressively Type-ii Cenmentioning

confidence: 99%

Bayesian Two-sample Prediction with Progressively Censored Data for Generalized Exponential Distribution Under Symmetric and Asymmetric Loss Functions

Ghafouri¹,

Rad²,

Doostparast³

2016

JSRI

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Abstract. Statistical prediction analysis plays an important role in a wide range of fields. Examples include engineering systems, design of experiments, etc. In this paper, based on progressively Type-II right censored data, Bayesian two-sample point and interval predictors are developed under both informative and non-informative priors. By assuming a generalized exponential model, prediction bounds as well as Bayes point predictors are obtained under the squared error loss (SEL) and the Linear-Exponential (LINEX) loss functions for the order statistic in a future progressively Type-II censored sample with an arbitrary progressive censoring scheme. The derived results may be used for prediction of total time on test in lifetime experiments. In addition to numerical method, Gibbs sampling procedure (as Markov Chain Monte Carlo method) are used to assess approximate prediction bounds and Bayes point predictors under the SEL and LINEX loss functions. The performance of the proposed prediction procedures are also demonstrated via a Monte Carlo simulation study and an illustrative example, for each method.

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“…In fact, Metropolis algorithm is an alternative to Gibbs sampler that does not require availability of full conditionals see Hastings [14] and Soliman et al [15].…”

Section: Metropolis-hastings Algorithmmentioning

confidence: 99%

Comparison of the Bayesian Methods on Interval-Censored Data for Weibull Distribution

Ahmed¹

2014

OJS

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This study considers the estimation of Maximum Likelihood Estimator and the Bayesian Estimator of the Weibull distribution with interval-censored data. The Bayesian estimation can't be used to solve the parameters analytically and therefore Markov Chain Monte Carlo is used, where the full conditional distribution for the scale and shape parameters are obtained via Metropolis-Hastings algorithm. Also Lindley's approximation is used. The two methods are compared to maximum likelihood counterparts and the comparisons are made with respect to the mean square error (MSE) to determine the best for estimating of the scale and shape parameters.

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Modified Weibull model: A Bayes study using MCMC approach based on progressive censoring data

Cited by 58 publications

References 28 publications

Estimation for Unknown Parameters of the Burr Type-XII Distribution Based on an Adaptive Progressive Type-II Censoring Scheme

Estimation for Unknown Parameters of the Burr Type-XII Distribution Based on an Adaptive Progressive Type-II Censoring Scheme

Bayesian Two-sample Prediction with Progressively Censored Data for Generalized Exponential Distribution Under Symmetric and Asymmetric Loss Functions

Comparison of the Bayesian Methods on Interval-Censored Data for Weibull Distribution

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