Bayesian and Frequentist Prediction Using Progressive Type-II Censored 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, Cairo, Egypt.
Mathematics Department, Faculty of Science, Sohag University, Sohag, Egypt.

DOI: 10.4236/iim.2013.55017                

Abstract

In this article, we study the problem of predicting future records and order statistics (two-sample prediction) based on progressive type-II censored with random removals, where the number of units removed at each failure time has a discrete binomial distribution. We use the Bayes procedure to derive both point and interval bounds prediction. Bayesian point prediction under symmetric and symmetric loss functions is discussed. The maximum likelihood (ML) prediction intervals using “plug-in” procedure for future records and order statistics are derived. An example is discussed to illustrate the application of the results under this censoring scheme.

Keywords

Bayesian Prediction; Burr-X Model; Progressive Censoring; Random Removals

Conflicts of Interest

The authors declare no conflicts of interest.

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