The maximum of n iid random variables converges (after normalization) to one of three extreme value distributions. The Gumbel attracts thin-tailed distributions; Fréchet attracts power laws; Weibull attracts bounded ones.
GEV: F(x) = exp(−[1+ξ(x−μ)/σ]^(−1/ξ)) | ξ=0: Gumbel | ξ>0: Fréchet | ξ<0: Weibull