Extreme value statistics with applications in hydrology and financial engineering

This work concentrates on features of Extreme Value statistics and bivariate distribution modeling using copulas that are widely applicable to important problems in hydrology and financial engineering. The three-parameter Generalized Extreme Value (GEV) distribution universally applied for modeling extreme processes is employed throughout for data analyses. New MIXed methods for GEV parameter estimation based on constraining the maximum likelihood estimators with different statistics are introduced. It is shown that these methods have good asymptotic behavior and produce better parameter estimates for small samples than do existing maximum likelihood and L-moments methods. The benefits of incorporating additional information into the maximum likelihood parameter estimation methods, such as the value of the second largest flood peak in a given year, are also developed. Annual flood peak data for a sample of 104 drainage basins in the central Appalachians region is analyzed, and the dependence of the estimated GEV distribution parameters on basin morphological properties is addressed.; Based on recent advances in the modeling of bivariate distributions with copulas, a library EVANESCE (Extreme Value ANalysis Employing Statistical Copula Estimation) is developed for the statistical software S-Plus, and the implemented methods are demonstrated on examples in financial engineering. The sensitivity of copula parameter estimates to precision in the description of marginal distributions is studied, and it is concluded that the copula parameter estimates are robust. The possibility of modeling the joint distribution of flood peaks and flood volumes using copulas is explored in both Annual Maximum Series and Partial Duration Series (PDS) frameworks. A particularly useful copula family for modeling this distribution in the PDS framework is identified, and the use of the new approach is illustrated with examples.; Finally, the scaling behavior of flood peak distributions is examined using a statistical model of the spatio-temporal distribution of rainfall coupled to a hydrological model describing the transformation of rainfall to discharge within a drainage network (the Network Model). It is shown that the scaling behavior of the first two moments and coefficients of variations of the distribution of annual flood peaks can be reproduced using such simulations.