On Bayes predictor of times to failure of Type-II progressively censored sample

Abstract

The purpose of this paper is Bayesian prediction, robust Bayesian prediction and two-sided predictive interval for both one-sample and two-sample prediction problems. In one-sample prediction problem, we discuss the prediction of the life-lengths (j=1, 2, … , ri; i=1, 2, … , m) of all censored units in all m stages of censoring, where denotes the jth-order statistics out of ri removed units at stage i. While in two-sample prediction problem, we discuss the prediction of the life-lengths (T1, … , Ts) which is a second independent ordered sample of size s of future observation from the same population of Y, where Y is the progressively Type-II right-censored order statistics. Finally, we conduct a simulation study, and consider an illustrative example for our proposed predictors.