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

Journal of Statistical Theory and Applications, vol. 24, pp. 489–514

Abstract

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.

Authors 3

1. Anja Bettina Schmiedt corresponding

   OTH Regensburg

   Affiliation as printed

   Department of Computer Science and Mathematics, Regensburg University of Applied Sciences, Regensburg, 93053, Germany

2. Christina Empacher Aachen Institute of Statistics

   RWTH Aachen University

   Affiliation as printed

   Institute of Statistics, RWTH Aachen University, Aachen, 52056, Germany

3. Udo Kamps Aachen Institute of Statistics

   RWTH Aachen University

   Affiliation as printed

   Institute of Statistics, RWTH Aachen University, Aachen, 52056, Germany