Generalized Extreme Value Distribution

The generalized extreme-value (GEV) distribution was introduced by Jenkinson (1955, 1969) and recommended by Natural Environment Research Council (1975) of Great Britain. The GEV distribution is the most widely accepted distribution for describing flood frequency data from the United Kingdom (Sinclair and Ahmad, 1988) and has also become popular elsewhere (Otten and van Montfort, 1980; Prescott and Walden, 1980, 1983; Turkman, 1985; Hosking et al., 1985; Arne11 et al., 1986). Sinclair and Ahmad (1988) introduced location-invariance in the context of using plotting positions in estimating parameters of the GEV distribution by the method of probability-weighted moments. They emphasized that this was an important factor in the selection of an appropriate plotting position, for otherwise the estimate of the shape parameter might not be independent of location. Tawn (1988) presented a method of filtering the original time series containing dependent data to obtain independent extremes. He then used the limiting joint generalized extreme value distribution for the r largest order statistics.