A Computational Approach to Confidence Intervals and Testing for Generalized Pareto Index Using the Greenwood Statistic

* The generalized Pareto distributions (GPDs) play an important role in the statistics of extremes. We point various problems with the likelihood-based inference for the index parameter [alpha] of the GPDs, and develop alternative testing strategies, which do not require parameter estimation. Our test statistic is the Greenwood statistic, which probability distribution is stochastically increasing with respect to [alpha] within the GPDs. We compare the performance of our test to a test with maximum-to-sum ratio test statistic [R.sub.n]New results on the properties of the [R.sub.n] are also presented, as well as recommendations for calculating the p-values and illustrative data examples. Keywords: * coefficient of variation; extremes; generalized Pareto distribution; heavy tailed distribution; power law; peak-over-threshold.