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The statistical estimation of extreme waves MacKenzie, Neil Grant

Abstract

This thesis contains a review of existing statistical techniques for the prediction of extreme waves for coastal and offshore installation design. A description of the four most widely used probability distributions is given, together with a detailed discussion of the methods commonly used for the estimation of their parameters. Although several of these techniques have been in use for several years, it has never been satisfactorily shown which are capable of yielding the most reliable predictions. The main purpose of this thesis is to suggest a practical method of solving this problem and achieving the best estimate. The basic theory for the prediction of extreme values was described in detail by Gumbel (1958) who concentrated largely on the double exponential distribution which is named after him. An order to evaluate the quality of fit between this law and the data, Gumbel derived expressions which enabled one to plot confidence intervals to enclose the data. The method described in this thesis in partly an extension of Gumbel's work, and similar confidence interval methods are given for the remaining distributions, thus permitting direct comparisons to be drawn between their performances. The outcome of this is that the most reliable model of the data may be chosen, and hence the best prediction made. The method also contains a curvature test which has been devised to facilitate computation and lead more directly to the end result. The particular form of the wave data, which is quite different from wind records, is also taken into consideration and a working definition of the sample tail is suggested.

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