Generalised smooth tests for the generalised Pareto distribution

The generalised Pareto distribution (GPD) is often used to model extreme values. New smooth tests of goodness of fit are proposed for this distribution. Typical problems with the GPD are that not all moments exist and not all classical estimation procedures work well over the whole parameter space. The generalised smooth test has good powers within a subset of the parameter space for which other tests may not be defined or appropriate, and, conversely, the Anderson-Darling test performs well when the test proposed here does not.