Bayesin estimation and prediction whit multiply type-II censored sample of sequential order statistics from one-and-two-parameter exponential distribution

In this article introduce the sequential order statistics. Therefore based on multiply Type-II censored sample of sequential order statistics, Bayesian estimators are derived for the parameters of one- and two- parameter exponential distributions under the assumption that the prior distribution is given by an inverse gamma distribution and the Bayes estimator with respect to squared error loss is calculated. Moreover, prediction of future failure time is considered. Finally in example Bayesian estimator and non-bayesian estimatores, namely the Best Linear Unbiased Estimator (BLUE) and Approximate Maximum Likelihood Estimator (AMLE) are derived.