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

Given the fact that, assuming a generalized Pareto distribution for a proce ss, it is possible to derive an asymptotic generalized extreme values law f or the corresponding maxima, in this paper we consider the theoretical rela tions linking the parameters of such distributions. In addition, temporal s caling properties are shown to hold for both laws when considering proper p ower-law forms for both the position and the scale parameters; also shown i s the relation between the scaling exponents of the distributions of intere st, 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 th e distributions at different temporal scales. Finally, an application to ra infall is given.