Extreme values — an improved method of fitting

Abstract

The Fisher—Tippet Type 1 (FT1) probability distribution has been widely used for plotting extreme values and making long-term predictions from individual sets of data. Commonly some 20–40 annual maximum values may be available whereas an estimate of the 50- or 100-year return period value is actually required. This paper examines the implications of current procedures for fitting wind data to the FT1 distribution. Using a Monte Carlo simulation technique it is shown that, for a set of data generated from the FT1 distribution, a “better” regression model (in the sense that all values, including outliers, are better accounted for) is obtained by selectively ignoring upper percentiles of the data than by including all of the data. The optimum regression model ignores ~10% of the highest values. For the purposes of this paper a new method of determining the “betterness” of a regression model is developed. The variation in the results obtained by using different regression models suggests that the accuracy to which estimates are currently quoted, namely at least two significant figures, should be revised. It is concluded that the true significance of the results would be better expressed by classifying the data recording stations into groups,characterised by a group mean. It remains then to determine the range for each group.