scholarly journals Bayesian Estimation and Prediction for Flexible Weibull Model under Type-II Censoring Scheme

2013 ◽  
Vol 2013 ◽  
pp. 1-16 ◽  
Author(s):  
Sanjay Kumar Singh ◽  
Umesh Singh ◽  
Vikas Kumar Sharma
Keyword(s):  
Monte Carlo ◽  
Weibull Distribution ◽  
Bayesian Estimation ◽  
Model Parameters ◽  
Type Ii ◽  
Data Set ◽  
Monte Carlo Simulation Study ◽  
Type Ii Censoring ◽  
Highest Posterior Density ◽  
Censoring Scheme

We have developed the Bayesian estimation procedure for flexible Weibull distribution under Type-II censoring scheme assuming Jeffrey's scale invariant (noninformative) and Gamma (informative) priors for the model parameters. The interval estimation for the model parameters has been performed through normal approximation, bootstrap, and highest posterior density (HPD) procedures. Further, we have also derived the predictive posteriors and the corresponding predictive survival functions for the future observations based on Type-II censored data from the flexible Weibull distribution. Since the predictive posteriors are not in the closed form, we proposed to use the Monte Carlo Markov chain (MCMC) methods to approximate the posteriors of interest. The performance of the Bayes estimators has also been compared with the classical estimators of the model parameters through the Monte Carlo simulation study. A real data set representing the time between failures of secondary reactor pumps has been analysed for illustration purpose.

scholarly journals Competing Risks Model with Partially Step-Stress Accelerate Life Tests in Analyses Lifetime Chen Data under Type-II Censoring Scheme

Open Physics ◽  
2019 ◽  
Vol 17 (1) ◽  
pp. 192-199 ◽  
Author(s):  
Hanaa H. Abu-Zinadah ◽  
Neveen Sayed-Ahmed
Keyword(s):  
Risk Factors ◽  
Risk Model ◽  
Asymptotic Distributions ◽  
Likelihood Method ◽  
Model Parameters ◽  
Type Ii ◽  
Monte Carlo Simulation Study ◽  
Type Ii Censoring ◽  
Life Tests ◽  
Censoring Scheme

Abstract The experiment design may need a stress level higher than use condition which is called accelerate life tests (ALTs). One of the most ALTs appears in different applications in the life testes experiment is partially step stress ALTs. Also, the experiment items is failure with several fatal risk factors, the only one is caused to failure which called competing risk model. In this paper, the partially step-stress ALTs based on Type-II censoring scheme is adopted under the different risk factors belong to Chen lifetime distributions. Under this assumption, we will estimate the model parameters of the different causes with the maximum likelihood method. The two, asymptotic distributions and the parametric bootstrap will be used to build each confidence interval of the model parameters. The precision results will be assessed through Monte Carlo simulation study.

Bayesian estimation of $$R=P[Y

2019 ◽  
Vol 10 (5) ◽  
pp. 905-917 ◽  
Author(s):  
Abhimanyu Singh Yadav ◽  
S. K. Singh ◽  
Umesh Singh
Keyword(s):  
Bayesian Estimation ◽  
Type Ii ◽  
Type Ii Censoring ◽  
Lomax Distribution ◽  
Progressive Type ◽  
Inverse Lomax Distribution ◽  
Censoring Scheme ◽  
Progressive Type Ii Censoring

scholarly journals Bayesian Estimation of the Exponential Parameter under a Multiply Type-II Censoring Scheme

2016 ◽  
Vol 36 (3) ◽  
Author(s):  
Umesh Singh ◽  
Anil Kumar
Keyword(s):  
Monte Carlo ◽  
Loss Function ◽  
Scale Parameter ◽  
Type Ii ◽  
Bayes Estimators ◽  
Conjugate Prior ◽  
Exponential Parameter ◽  
Type Ii Censoring ◽  
Error Loss ◽  
Censoring Scheme

This paper provides the estimation of the scale parameter of the exponential distribution under multiply type-II censoring. Using generalized non-informative prior and natural conjugate prior, Bayes estimator and approximate Bayes estimators of the scale parameter have been obtained under square error loss function. The proposed Bayes estimators and approximate Bayes estimators are compared with the estimators proposed by Singh et al. (2005) and Balasubramanian and Balakrishnan (1992) on the basis of theirsimulated risks under square error loss function of 1000 randomly generated Monte Carlo samples.

scholarly journals Estimation procedures on Type-II censored data from a scaled Muth distribution

2021 ◽  
pp. 148-158
Author(s):  
Hayrinisa Demirci BIÇER
Keyword(s):  
Censored Data ◽  
Mean Squared Error ◽  
Real Life ◽  
Model Parameters ◽  
Type Ii ◽  
Monte Carlo Simulation Study ◽  
Anal Ysis ◽  
Squared Error ◽  
Type Ii Censored Data ◽  
Censoring Scheme

In the present paper, we consider the estimation problem for the scaled Muth distribution under Type-II censoring scheme. In order to estimate the model parameters α and β, the maximum likelihood, the least-squares, and the maximum spacing estimators are derived. To show estimation efficiencies of the estimators obtained with this paper, we present an exten- sive Monte-Carlo simulation study in which the estimators are compared according to bias and mean squared error criteria. Furthermore, we evaluate the applicability of the scaled Muth distribution by taking into account both full and Type-II censored data situations by an anal- ysis conducted on a real-life dataset.

scholarly journals Bayesian Estimation for Inverse Weibull Distribution Under Progressive Type-II Censored Data With Beta-Binomial Removals

2018 ◽  
Vol 47 (1) ◽  
pp. 77-94
Author(s):  
Pradeep Kumar Vishwakarma ◽  
Arun Kaushik ◽  
Aakriti Pandey ◽  
Umesh Singh ◽  
Sanjay Kumar Singh
Keyword(s):  
Weibull Distribution ◽  
Real Data ◽  
Estimation Procedure ◽  
Type Ii ◽  
Unknown Parameters ◽  
Data Set ◽  
Progressive Type ◽  
Inverse Weibull Distribution ◽  
Type Ii Censored Data ◽  
Censoring Scheme

This paper deals with the estimation procedure for inverse Weibull distribution under progressive type-II censored samples when removals follow Beta-binomial probability law. To estimate the unknown parameters, the maximum likelihood and Bayes estimators are obtained under progressive censoring scheme mentioned above. Bayes estimates are obtained using Markov chain Monte Carlo (MCMC) technique considering square error loss function and compared with the corresponding MLE's. Further, the expected total time on test is obtained under considered censoring scheme.  Finally, a real data set has been analysed to check the validity of the study.

scholarly journals Accelerated competing risks model from Gompertz lifetime distributions with type-II censoring scheme

2020 ◽  
Vol 24 (Suppl. 1) ◽  
pp. 165-175
Author(s):  
Abdullah Almarashi ◽  
Gamal Abd-Elmougod
Keyword(s):  
Accelerated Life Test ◽  
Likelihood Method ◽  
Model Parameters ◽  
Test Model ◽  
Time To Failure ◽  
Type Ii ◽  
Type Ii Censoring ◽  
Accelerated Life ◽  
Interval Estimators ◽  
Censoring Scheme

Time to failure under normal stress conditions may take a long period of time and statistical inferences under this condition is more serious. Then, the experiment is loaded under stress higher than normal one which is defined as accelerated life tests. This problem in this paper is discussed in the form of partially step-stress accelerated life test model when the lifetime of the product has Gompertz lifetime distribution and unites are fails under the two independent risks. The maximum likelihood method under type-II censoring scheme is used to formulate the point and asymptotic confidence interval estimators of model parameters. The two boot?strap methods are also used to formulate the point and approximate interval estimators. The numerical results are adopted in the form of Monte Carlo studying to illustrate, assess and compare all of the theoretical results. Finally, results are discussed in points to clarify results validity.

scholarly journals Statistical Inferences of Type-II Progressively Hybrid Censored Fuzzy Data with Rayleigh Distribution

2018 ◽  
Vol 47 (3) ◽  
pp. 40-62 ◽  
Author(s):  
Ankita Chaturvedi ◽  
Sanjay Kumar Singh ◽  
Umesh Singh
Keyword(s):  
Real Data ◽  
Rayleigh Distribution ◽  
Model Parameters ◽  
Type Ii ◽  
Posterior Density ◽  
Numerical Illustration ◽  
Data Set ◽  
Bayesian Procedures ◽  
Credible Intervals ◽  
Highest Posterior Density

This article presents the procedures for the estimation of the parameter of Rayleighdistribution based on Type-II progressive hybrid censored fuzzy lifetime data. Classicalas well as the Bayesian procedures for the estimation of unknown model parameters has been developed. The estimators obtained here are Maximum likelihood (ML) estimator, Method of moments (MM) estimator, Computational approach (CA) estimator and Bayes estimator. Highest posterior density (HPD) credible intervals of the unknown parameter are obtained by using Markov Chain Monte Carlo (MCMC) technique. For numerical illustration, a real data set has been considered.

scholarly journals Statistical Inference for Weibull Distribution Based on a Modified Progressive Type-II Censoring Scheme

2014 ◽  
Vol 5 (4) ◽  
pp. 95
Author(s):  
Ismail Kinaci ◽  
Yunus Akdogan ◽  
Coskun Kus ◽  
H. K. T. Ng
Keyword(s):  
Weibull Distribution ◽  
Statistical Inference ◽  
Type Ii ◽  
Type Ii Censoring ◽  
Progressive Type ◽  
Censoring Scheme ◽  
Progressive Type Ii Censoring
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