One- and two-sided prediction intervals for future Pareto record values with applications

Abstract Based on upper record values in a series of observations over time from a Pareto distribution, an exact and several approximate one-sided and two-sided prediction intervals for the next record value (or for another future record value) to appear are studied and compared by means of an extensive simulation study. The performances of the prediction intervals are evaluated and recommendations are proposed for what method should be used in a given situation with respect to the form of the prediction interval on the one hand and to the tail behaviour on the other. The proposed methods are applied to insurance, environmental and sports data, where the respectively fitted Pareto distributions show a different tail behaviour. As a result, it is seen that although the number of observed record values in the presented real data applications is rather small, as it is usually the case, the selected prediction intervals are of practical use.