Restricted domains of attraction of exp(-e-x)

For independent and identically distributed random variables the domain of attraction of exp(-e-x) for the maximum is investigated under the restriction that the population distribution has a density. Necessary and sufficient conditions are established in term of the expected residual life and hazard rate. Furthermore, it is shown that, for ultimately concave distributions with increasing hazard rate, the von Mises condition is both necessary and sufficient for a population distribution to be in the domain of attraction of exp(-e-x).