Goodness-of-fit tests for the generalized Pareto distribution

Tests of fit are given for the generalized Pareto distribution (GPD) based on Cramer-von Mises statistics. Examples are given to illustrate the estimation techniques and the goodness-of-fit procedures. The tests are applied to the exceedances over given thresholds for 238 river flows in Canada, in general, the GPD provides an adequate fit. The tests are useful in deciding the threshold in such applications; this method is investigated and also the closeness of the GPD to some other distributions that might be used for long-tailed data.