  In this paper, we consider the problem of estimating an extreme quantile of a
Weibull tail-distribution. The new extreme quantile estimator has a reduced
bias compared to the more classical ones proposed in the literature. It is
based on an exponential regression model that was introduced in Diebolt et al.
(2008). The asymptotic normality of the extreme quantile estimator is
established. We also introduce an adaptive selection procedure to determine the
number of upper order statistics to be used. A simulation study as well as an
application to a real data set are provided in order to prove the efficiency of
the above mentioned methods.
