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

Abstract

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 α 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 α within the GPDs. We compare the performance of our test to a test with maximum-to-sum ratio test statistic Rn. New results on the properties of the Rn 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