HR: 1340h
AN: H53F-0548    [Abstracts]
TI: Multivariate probability distributions using copulas: Theoretical aspects and applications to hydrology
AU: * De Michele, C
EM: carlo.demichele@polimi.it
AF: DIIAR-Politecnico di Milano, 32, P.zza L. da Vinci, Milano, I-20132 Italy
AU: Salvadori, G
EM: gianfausto.salvadori@unile.it
AF: Dipartimento di Matematica, Universita` di Lecce, Prov. Lecce-Arnesano, Lecce, I-73100 Italy
AB: In many hydrological problems several are the (random) variables that play a significant role in the modelization of the phenomenon under investigation,and such variates are generally not independent. Therefore, it is often of fundamental importance to be able to relate the marginal distributions of different variables in order to obtain a joint law describing the main features of the observed hydrological events. Traditionally, the multivariate probability distributions used in hydrology have Normal or Lognormal marginals or Exponential ones. In general, the development of multivariate probability models (and, in particular, of multivariate Extreme Value distributions) has been limited by mathematical difficulties in generating consistent joint laws with ad hoc marginals. Recent advances in applied mathematics have shown that Copulas may represent an useful tool for investigating the statistical behaviour of dependent variables and build multivariate probability distributions. Copulas are operators on the family of (one-dimensional) probability distributions which generate multivariate laws with specified properties. In fact, given two (continuous) random variables X and Y, with marginal distributions FX and FY, there exists a correspondence between their joint law FXY and a proper 2-Copula C, Sklar's Theorem. The properties of FXY can be discussed in terms of the structure of C. Copulas can produce a real advancement in the subsurface stochastic modeling. We shall outline the general mathematical framework of Copulas, discussing their usefulness in hydrological problems.
DE: 1869 Stochastic hydrology
DE: 1899 General or miscellaneous
DE: 3265 Stochastic processes (3235, 4468, 4475, 7857)
SC: Hydrology [H]
MN: Fall Meeting 2005