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 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 Bayesian Estimation of Parameters of Weibull Distribution Using Linex Error Loss Function

2020 ◽  
Vol 9 (2) ◽  
pp. 38
Author(s):  
Josphat. K. Kinyanjui ◽  
Betty. C. Korir
Keyword(s):  
Weibull Distribution ◽  
Loss Function ◽  
Scale Parameter ◽  
Risk Function ◽  
Bayes Estimators ◽  
Squared Error Loss Function ◽  
Squared Error Loss ◽  
Error Loss ◽  
Squared Error ◽  
Linex Loss

This paper develops a Bayesian analysis of the scale parameter in the Weibull distribution with a scale parameter  θ  and shape parameter  β (known). For the prior distribution of the parameter involved, inverted Gamma distribution has been examined. Bayes estimates of the scale parameter, θ  , relative to LINEX loss function are obtained. Comparisons in terms of risk functions of those under LINEX loss and squared error loss functions with their respective alternate estimators, viz: Uniformly Minimum Variance Unbiased Estimator (U.M.V.U.E) and Bayes estimators relative to squared error loss function are made. It is found that Bayes estimators relative to squared error loss function dominate the alternative estimators in terms of risk function.

scholarly journals Exact Likelihood Inference for an Exponential Parameter under Generalized Adaptive Progressive Hybrid Censoring

Symmetry ◽  
2020 ◽  
Vol 12 (7) ◽  
pp. 1149 ◽  
Author(s):  
Hyojin Lee ◽  
Kyeongjun Lee
Keyword(s):  
Scale Parameter ◽  
Moment Generating Function ◽  
Likelihood Inference ◽  
Exponential Parameter ◽  
Hybrid Censoring ◽  
Lower Confidence ◽  
Lower Confidence Bound ◽  
New Type ◽  
The Moment ◽  
Censoring Scheme

In this paper, we propose a new type censoring scheme named a generalized adaptive progressive hybrid censoring scheme (GenAdPrHyCS). In this new type censoring scheme, the experiment is assured to stop at a pre-assigned time. This censoring scheme is designed to correct the drawbacks in the AdPrHyCS. Furthermore, we discuss inference for one parameter exponential distribution (ExD) under GenAdPrHyCS. We derive the moment generating function of the maximum likelihood estimator (MLE) of scale parameter of ExD and the resulting lower confidence bound under GenAdPrHyCS.

scholarly journals Different Approaches to Estimation of the Gompertz Distribution under the Progressive Type-II Censoring Scheme

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Kyeongjun Lee ◽  
Jung-In Seo
Keyword(s):  
Nuisance Parameter ◽  
Estimation Method ◽  
Real Data ◽  
Type Ii ◽  
Gompertz Distribution ◽  
Type Ii Censoring ◽  
Scale Parameters ◽  
Progressive Type ◽  
Censoring Scheme ◽  
Progressive Type Ii Censoring

This paper provides an estimation method for an unknown parameter by extending weighted least-squared and pivot-based methods to the Gompertz distribution with the shape and scale parameters under the progressive Type-II censoring scheme, which induces a consistent estimator and an unbiased estimator of the scale parameter. In addition, a way to deal with a nuisance parameter is provided in the pivot-based approach. For evaluation and comparison, the Monte Carlo simulations are conducted, and real data are analyzed.

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