Confidence Intervals for Exceedance Probabilities with Application Tto Extreme Ship Motions

Abstract

Statistical inference of a probability of exceeding a large critical value is studied in the peaks-over-threshold (POT) approach. The focus is on assessing the performance of the various confidence intervals for the exceedance probability, both for the generalized Pareto distribution used above a selected threshold and in the POT setting for general distributions. The developed confidence intervals perform well in an application to extreme ship motion data. Finally, several approaches to uncertainty reduction are also considered.

Keywords

• exceedance probability
• quantiles
• confidence intervals
• peaks over threshold
• generalized Pareto distribution
• threshold selection