Prediction of the remaining testing time for the generalized Pareto progressive censoring samples with applications to extreme hydrology events

The prediction of the unobserved units is typically based on the derivations of the predictive distributions of the individual observations. This technique is of little interest when one wishes to predict a function of missing or unobserved data such as the remaining testing time. In this article, based on a progressive type-II censored sample from the generalized Pareto (GP) distribution, we consider the problem of predicting times to failure of units in multiple stages. Importance sampling is used to estimate the model parameters, and Gibbs and Metropolis samplers are used to predict the testing times of the removed unfailed units. Data analyses involving the water-level exceedances by the River Nidd in North Yorkshire, England, have been performed and predictions of the total remaining level exceedances are discussed.