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 estima tion techniques and the goodness-of-fit procedures. The tests are applied t o the exceedances over given thresholds for 238 river flows in Canada, in g eneral, the GPD provides an adequate fit. The tests are useful in deciding the threshold in such applications; this method is investigated and also th e closeness of the GPD to some other distributions that might be used for l ong-tailed data.