Some Practical Aspects of Extreme Value Analyses

As stated in Chaps. 1 and 5, extreme value statistics, even in applications, is generally based on asymptotic results. This is done either by assuming that the epochal extremes, for example, yearly extreme wind speeds at a given location, are distributed according to the generalized (asymptotic) extreme value distribution with unknown parameters to be estimated on the basis of the observed data, cf. Chap. 2, or by assuming that the exceedances above high thresholds follow a generalized (asymptotic) Pareto distribution with parameters that are estimated from the data, cf. Chap. 3. With the ACER method now available, the performance of these three methods on simulated or measured data may be compared. Note that all calculations of the empirical ACER functions in this chapter were performed using the ACER program package for Matlab (Karpa (2012) ACER User Guide and Program. NTNU: Freely available at the internet address: https://folk.ntnu.no/arvidn/ACER ). This package also allows for optimized fitting of parametric functions for prediction of long return period extreme values for the case of asymptotic Gumbel distributions, cf. Sect. 5.5, which totally dominates engineering applications.