A Computational Approach to Confidence Intervals and Testing for Generalized Pareto Index Using the Greenwood Statistic
Accepted - January 2022
Keywords:coefficient of variation, extremes, generalized Pareto distribution, heavy tailed distribution, power law, Peak-over-threshold
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.
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