| This thesis mainly investigates the estimation and goodness-of-fit tests of the Generalized Extreme Value distribution. We start with finding the maximum likelihood estimates by numerically optimizing the log likelihood function and demonstrate that our estimation procedure offers a high order of accuracy. Based on the asymptotic distribution, we calculate the percentage points of the empirical distribution function based test statistics and their P-values. Combining and modifying two existing procedures, we provide an R program that is able to directly model a data set by a generalized extreme value distribution and assess the goodness-of-fit of the model in terms of P-values. Several numerical examples in hydrology and meteorology are presented to illustrate the usefulness of our program. |
