From generalized Pareto to extreme values law: Scaling properties and derived features

Given the fact that, assuming a generalized Pareto distribution for a process, it is possible to derive an asymptotic generalized extreme values law for the corresponding maxima, in this paper we consider the theoretical relations linking the parameters of such distributions. In addition, temporal scaling properties are shown to hold for both laws when considering proper power-law forms for both the position and the scale parameters; also shown is the relation between the scaling exponents of the distributions of interest, how the scaling properties of one distribution yield those of the other, and how the scaling features may be used to estimate the parameters of the distributions at different temporal scales. Finally, an application to rainfall is given.