Gumbel re-visited - A new look at extreme value statistics applied to wind speeds

Abstract

This paper re-examines the traditional Gumbel extreme value method for analysing annual maximum windspeeds or similar data, with a view to improving the process. The advantages of transforming the data before applying an extreme value analysis are explained, and it is noted that the traditional Gumbel plot should really have its axes interchanged. An improved set of plotting positions based on the mean values of the order statistics are derived, together with a means of obtaining the standard deviation of each position. This enables a fitting procedure using weighted least squares to be adopted, which gives results similar to the traditional Lieblein BLUE process, but with the advantages that it does not require tabulated coefficients, is available for any number of data up to at least 50, and provides a quantitative measure of goodness of fit. A computer program which automatically implements the method is provided.