  The Weibull--like distributions form a large class of probability
distributions that belong to the domain of attraction for the maxima of the
Gumbel law. Besides the Weibull distribution, it includes important
distributions as the Gamma laws and, in particular, the $\chi^2$ distributions.
In order to have explicit expressions of the norming constants for the maxima
it is necessary to solve asymptotically a nonlinear equation; however, for some
members of that family, numerical and simulation studies show that the
constants that are usual suggested are inaccurate for moderate or even large
sample sizes. In this paper we propose other norming constants computed with
the asymptotics of the Lambert W function that significantly improve the
accuracy of the approximation to the Gumbel law. These results are applied to
the computation of the constants for the maxima of Gamma random variables that
appear in some applied problems.
