Principles of Extreme Value Statistics

This paper presents the theoreti-cal background of recent techniques to predict extreme loads (and responses) pertinent to ship (or marine system) operation in a seaway. The magnitude of extTeme values, in general, can be estimated through different approaches, each based on a different principle This paper outlines the three different approaches for predicting extreme values vihicb provide information useful for design consideration of a marine system. These are, (1) The initial probability distribution is known; for example, prediction of extreme responses of a marine system in a seaway in the short-term based on the linear superposition principle. In this case, the extreme values can be sinmlv evaluated b“ analytical formul~t;on thr&h rifiplica– tion of order statistics to the initial probability distrih”tion. (2) The initial Drobabilitv distribution is unknow; but obse;ved (or computed) data are available; for example, prediction of the extreme sea state (significant wane height) or prediction of the extreme responses of a marine system in the long-term, etc. Estimation of tbe extreme values is carried out by approximate methods through tbe use of the observed (or computed) data. (3) The initial probability distribution is unknown but observed data of the maxima only are available; for example, prediction of lifetime extreme responses of a marine system from daily observed tna.xim”mvalues,etc. 1 “ this case, the extreme values are obtained from tbe asvmvtotic extreme value distributions &~eloped in order statistics. The difference in these three prediction approaches are clearly explained, and practical examples to evalwite the extreme values following each method are presented