  Profile likelihood intervals of large quantiles in Extreme Value
distributions provide a good way to estimate these parameters of interest since
they take into account the asymmetry of the likelihood surface in the case of
small and moderate sample sizes; however they are seldom used in practice. In
contrast, maximum likelihood asymptotic (mla) intervals are commonly used
without respect to sample size. It is shown here that profile likelihood
intervals actually are a good alternative for the estimation of quantiles for
sample sizes $25 \leq n\leq 100$ of block maxima, since they presented adequate
coverage frequencies in contrast to the poor coverage frequencies of mla
intervals for these sample sizes, which also tended to underestimate the
quantile and therefore might be a dangerous statistical practice.
  In addition, maximum likelihood estimation can present problems when Weibull
models are considered for moderate or small sample sizes due to singularities
of the corresponding density function when the shape parameter is smaller than
one. These estimation problems can be traced to the commonly used continuous
approximation to the likelihood function and could be avoided by using the
exact or correct likelihood function, at least for the settings considered
here. A rainfall data example is presented to exemplify the suggested
inferential procedure based on the analyses of profile likelihoods.
