Flexible extreme value inference

We introduce flexible small sample modeling for extremes by introducing the new numerical characteristics of heavy tail. We illustrate in this article advantages of such flexibility. In this article, we show that we can obtain asymptotic normality of generalized Hill estimators by application of Karamata's representation for regularly varying tails. Second order regularity conditions however better relates to Edgeworth types of normal approximations albeit requiring larger data samples. Finally both expansions are prone for bootstrap and other subsampling techniques. All existing results indicate that proper representation of tail behavior play a special and somewhat intriguing role in that context. The application of this new methodology is simple and flexible, handsome for real data sets. Alternative and powerful versions of the Hill plot are also introduced and illustrated on real data of snow extremes from Slovakia. We also demonstrate the importance of box-plot based techniques for small samples.