Extreme Value Analysis of Statistically Independent Stochastic Variables

• Published in: Han-guk haeyang gonghak hoeji (Online) Vol. 33; no. 3; pp. 222 - 228
• Main Authors: Choi, Yongho, Yeon, Seong Mo, Kim, Hyunjoe, Lee, Dongyeon
• Format: Journal Article
• Language: Korean
• Published: 2019
• Subjects: GPD (generalized Pareto distribution); EVA (extreme value analysis); EVT (extreme value theory); PACF (partial autocorrelation function); IID (independent and identically distributed); Weibull; GEV (generalized extreme value); Block maxima; POT (peaks-over-threshold)
• ISSN: 1225-0767; 2287-6715

An extreme value analysis (EVA) is essential to obtain a design value for highly nonlinear variables such as long-term environmental data for wind and waves, and slamming or sloshing impact pressures. According to the extreme value theory (EVT), the extreme value distribution is derived by multiplying the initial cumulative distribution functions for independent and identically distributed (IID) random variables. However, in the position mooring of DNVGL, the sampled global maxima of the mooring line tension are assumed to be IID stochastic variables without checking their independence. The ITTC Recommended Procedures and Guidelines for Sloshing Model Tests never deal with the independence of the sampling data. Hence, a design value estimated without the IID check would be under- or over-estimated because of considering observations far away from a Weibull or generalized Pareto distribution (GPD) as outliers. In this study, the IID sampling data are first checked in an EVA. With no IID random variables, an automatic resampling scheme is recommended using the block maxima approach for a generalized extreme value (GEV) distribution and peaks-over-threshold (POT) approach for a GPD. A partial autocorrelation function (PACF) is used to check the IID variables. In this study, only one 5 h sample of sloshing test results was used for a feasibility study of the resampling IID variables approach. Based on this study, the resampling IID variables may reduce the number of outliers, and the statistically more appropriate design value could be achieved with independent samples.