Open AccessFrom generalized Pareto to extreme values law: Scaling properties and derived features
Author(s) -
Salvadori Gianfausto,
De Michele Carlo
Publication year - 2001
Publication title -
journal of geophysical research: atmospheres
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.67
H-Index - 298
eISSN - 2156-2202
pISSN - 0148-0227
DOI - 10.1029/2001jd900091
Subject(s) - scaling , pareto distribution , statistical physics , maxima , generalized pareto distribution , power law , extreme value theory , pareto principle , mathematics , distribution (mathematics) , scale (ratio) , position (finance) , scaling law , heavy tailed distribution , law , mathematical analysis , physics , mathematical optimization , statistics , geometry , quantum mechanics , art , finance , performance art , political science , economics , art history
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.