The last 15 years have seen the development of a new body of theory and of a new generation of statistical estimation procedures applicable to extreme data. Essentially these approaches emphasize the primacy of the information concerning the largest of the extremes (the tails), as opposed to information inherent in the bulk of the extreme data (tile body of the distribution). One potentially attractive feature of some of these approaches is that, in principle, they make it possible to ascertain whether the distribution thai best fits a given set of extreme data has a finite tail. Whether extreme ~ind speed distributions have finite tails is a matter of great interest in structural engineering since the answer to this question may affect significantly the estimation of safety factors for wind-sensitive structures. Failure probability estimates based on the assumption that wind speeds are described by the Gumbel distribution (which has infinite upper tail) were shown to be unrealistically high (Ellingwood et a1,1980; Simiu, Shaver, and Filliben, 1981). This may be the case because the probability of occurrence of very high speeds, rather than being finite as in the Gumbel model, is in fact zero, since it is obvious on physical grounds that extratropical wind speeds must be bounded. It is natural to ask whether modern statistical methods can estimate those bounds from available sets of extreme wind speed data, and if so, what is the minimum size of the data sample that would allow the estimates to be made with acceptable confidence. Tile present work is motivated by these questions. It is part of a long<erm project aimed at evaluating various estimation methods Z a the theory of extremes. We examine two such methods here: (1) a condi t iona l mean exeeedanee ( C M E ) slope estimation method (Davisson-Smith,1990); and (2) the P iekands method (Pickands,1975). Both are based on the Generalized Pareto Distribution (GPD) model for excesses over a threshold. The GPD was shown to arise as a limiting distribution for excesses over thresholds if and only if the parent distribution tends asymptotically to one of the extreme value
Read full abstract