Bayesian and non-Bayesian two-sample prediction for the Fréchet distribution under progressive type II censoring

In many domains, including medical and technical sciences, prediction based on censored data is a very significant issue. On the other hand, the Fréchet distribution is a continuous model, which has wide applicability in extreme value theory, based on a progressively type-II right censoring scheme. Based on two-sample prediction, Bayesian and non-Bayesian predictions are discussed in this study for the Fréchet distribution. For obtaining prediction bounds as well as Bayes predictive estimations under a squared error loss function for the sth-order statistic in a future random sample drawn independently of the parent population, with an arbitrary progressive censoring scheme, a general form for the lifetime model as the Fréchet model is taken into consideration. As an example, a simulation study was done as examples to demonstrate how the operations are carried out. Moreover, two sets of real data are applied.