Extreme value prediction: an application to sport records

Extreme value theory studies the extreme deviations from the central portion of a probability distribution. Results in this field have considerable importance in assessing the risk that characterises rare events, such as collapse of the stock market, or earthquakes of exceptional intensity, or floods. In the last years, application of extreme value theory for prediction of sport records have received increased interest by the scientific community. In this work we face the problem of constructing prediction limits for series of extreme values coming from sport data. We propose the use of a calibration procedure applied to the generalised extreme value distribution, in order to obtain a proper predictive distribution for future records. The calibrated procedure is applied to series of real data related to sport records. In particular, we consider sequences of annual maxima for different athletic events. Using the proposed calibrated predictive distribution, we show how to correctly predict the probability of future records and we discuss the existence and interpretation of ultimate records.