Fig. 1.

A comparison of right tails for the three domains of attraction under the generalized Pareto distribution (GPD). The shape parameter k determines the domain, and the scale parameter τ = 1 for all examples. (a) The right tails for distributions in the Gumbel domain correspond to the GPD with k = 0 (i.e., the exponential distribution). Distributions in the Fréchet domain (k > 0) have tails that are heavier than exponential. (b) Distributions in the Weibull domain have right-truncated tails and correspond to the GPD with k < 0. Truncation points are denoted by vertical gray lines