On the max-domain of attraction of distributions with log-concave densities

We show that both parametric distribution functions appearing in extreme value theory have log-concave densities if the extreme value index γ∈[−1,0]γ∈[−1,0] and that all distribution functions FF with log-concave density belong to the max-domain of attraction of the generalized extreme value distribution with γ∈[−1,0]γ∈[−1,0].