Forecast verification for extreme value distributions with an application to probabilistic peak wind prediction

Predictions of the uncertainty associated with extreme events are a vital component of any prediction system for such events. Consequently, the prediction system ought to be probabilistic in nature, with the predictions taking the form of probability distributions. This paper concerns probabilistic prediction systems where the data are assumed to follow either a generalized extreme value (GEV) distribution or a generalized Pareto distribution. In this setting, the properties of proper scoring rules that facilitate the assessment of the prediction uncertainty are investigated, and closed form expressions for the continuous ranked probability score (CRPS) are provided. In an application to peak wind prediction, the predictive performance of a GEV model under maximum likelihood estimation, optimum score estimation with the CRPS, and a Bayesian framework are compared. The Bayesian inference yields the highest overall prediction skill and is shown to be a valuable tool for covariate selection, while the predictions obtained under optimum CRPS estimation are the sharpest and give the best performance for high thresholds and quantiles.