G. Salvadori et C. De Michele, From generalized Pareto to extreme values law: Scaling properties and derived features, J GEO RES-A, 106(D20), 2001, pp. 24063-24070
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.