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Estimation Based on Progressive First-Failure Censored Sampling with Binomial Removals
Faculty of Science, Islamic University, Madinah, Saudi Arabia
Mathematics Department, Sohag University, Sohag, Egypt
Mathematics Department, Sohag University, Sohag, Egypt
Mathematics Department, Faculty of Science, Al-Azhar University, Nasr-City, Cairo, Egypt
- 1 Faculty of Science, Islamic University, Madinah, Saudi Arabia
- 2 Mathematics Department, Sohag University, Sohag, Egypt
- 3 Mathematics Department, Sohag University, Sohag, Egypt
- 4 Mathematics Department, Faculty of Science, Al-Azhar University, Nasr-City, Cairo, Egypt
Intelligent Information Management·Volume 05 (2013)·Pages 117–125·Published 2 July 2013·DOI10.4236/iim.2013.54012
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Abstract
In this paper, the inference for the Burr - X model under progressively first-failure censoring scheme is discussed. Based on this new censoring were the number of units removed at each failure time has a discrete binomial distribution. The maximum likelihood, Bootstrap and Bayes estimates for the Burr-X distribution are obtained. The Bayes estimators are obtained using both the symmetric and asymmetric loss functions. Approximate confidence interval and highest poste rior density interval (HPDI) are discussed. A numerical example is provided to illustrate the proposed estimation meth ods developed here. The maximum likelihood and the different Bayes estimates are compared via a Monte Carlo s imu lation study.
KeywordsBurr-X DistributionProgressive First-Failure CensoredBayesian and Non-Bayesian EstimationsLoss FunctionBootstrapRandom Removals
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