Abstract
Extreme value estimation, such as maximum wave height estimation, is critical for robust and cost efficient design of ocean structure. Some previous methods are incapable of quantifying the confidence interval when taking variance of shape parameter into account. We propose a new method based on likelihood. The utilization of group likelihood, profile likelihood and deviation method permits the use of likelihood inference for extreme value estimation, even when the distribution is non-regular. We conducted a Monte Carlo experiment to show the performance of this new method for 3 parameter Weibull distribution. We also revealed the problems with Goda's estimation method. Our robust results suggest the use of likelihood inference to quantify the statistical uncertainty and the asymmetric distribution of confidence intervals, which have been overlooked in previous studies.
