Prediction Intervals of the Record-Values Process

Abstract

In this paper, exact prediction intervals of the record-values process are constructed. The record-values process model, may be considered as the collection of record-values with integer or non-integer indices. It includes both usual k-th record-values and fractional k-th record-values models. For constructing the prediction intervals, two predictive pivotal quantities are developed. The distributions of the predictive pivotal quantities are derived and it is revealed that the distribution functions of the predictive pivotal quantities are similar for the upper and lower fractional record-values. More results are obtained for the exponential upper record-values process, including two point predictors and their exact mean square errors. Some efficient algorithms are given and Monte Carlo simulation studies are conducted for comparing pivotal quantities. Finally, three real data sets are analyzed.