@article{SchmiedtEmpacherKamps, author = {Schmiedt, Anja B. and Empacher, Christina and Kamps, Udo}, title = {One- and two-sided prediction intervals for future Pareto record values with applications}, series = {Journal of Statistical Theory and Applications}, journal = {Journal of Statistical Theory and Applications}, publisher = {Springer}, issn = {2214-1766}, doi = {10.1007/s44199-025-00119-w}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:898-opus4-81605}, pages = {26}, 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.}, language = {en} } @article{EmpacherKampsSchmiedt, author = {Empacher, Christina and Kamps, Udo and Schmiedt, Anja Bettina}, title = {Prediction intervals for future Pareto record claims}, series = {European Actuarial Journal}, volume = {15}, journal = {European Actuarial Journal}, number = {1}, publisher = {Springer}, issn = {2190-9733}, doi = {10.1007/s13385-024-00397-1}, pages = {163 -- 197}, abstract = {Stochastic models and methods for quantifying extreme events are of interest in numerous disciplines. Within this paper, statistical prediction of extreme claims or losses in insurance industry is considered based on upper record values, which describe successively largest observations in a sequence of data over time. The problem of predicting a future record value (here in particular, a future record claim) based on a sequence of previously observed record values (here, past record claims) is addressed by means of prediction intervals. For an underlying Pareto distribution, respective exact and approximate intervals from the literature are summarized and modified and new ones are developed. In a simulation study, these prediction intervals are evaluated and compared regarding coverage frequency and length. The impact of the number of observed record values as well as the choice of the Pareto distribution is discussed. In the case of a small number of record values, the use of k-th record values is considered as an option for statistical analyses to predict, e.g., second largest record claims. Selected prediction methods are applied to several real data sets, which turn out to perform well and to be able to capture the magnitude of future record claims, even for fairly small numbers of record observations. For comparison, generalized Pareto distributions are fitted to real data sets and a corresponding point predictor as well as a respective upper prediction interval for the next record to appear are derived and evaluated.}, language = {en} }