Estimation Based on Progressive First-Failure Censored Sampling with Binomial Removals

Ahmed A. Soliman, Ahmed H. Abd Ellah, Nasser A. Abou-Elheggag, Rashad M. El-Sagheer

Faculty of Science, Islamic University, Madinah, Saudi Arabia.
Mathematics Department, Faculty of Science, Al-Azhar University, Nasr-City, Cairo, Egypt.
Mathematics Department, Sohag University, Sohag, Egypt.

DOI: 10.4236/iim.2013.54012                

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 posterior density interval (HPDI) are discussed. A numerical example is provided to illustrate the proposed estimation methods developed here. The maximum likelihood and the different Bayes estimates are compared via a Monte Carlo simulation study.

Keywords

Burr-X Distribution; Progressive First-Failure Censored; Bayesian and Non-Bayesian Estimations; Loss Function; Bootstrap; Random Removals

Conflicts of Interest

The authors declare no conflicts of interest.

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