  Usual estimation methods for the parameters of extreme values distribution
employ only a few values, wasting a lot of information. More precisely, in the
case of the Gumbel distribution, only the block maxima values are used. In this
work, we propose a method to seize all the available information in order to
increase the accuracy of the estimations. This intent can be achieved by taking
advantage of the existing relationship between the parameters of the baseline
distribution, which generates data from the full sample space, and the ones for
the limit Gumbel distribution. In this way, an informative prior distribution
can be obtained. Different statistical tests are used to compare the behaviour
of our method with the standard one, showing that the proposed method performs
well when dealing with very shortened available data. The empirical
effectiveness of the approach is demonstrated through a simulation study and a
case study. Reduction in the credible interval width and enhancement in
parameter location show that the results with improved prior adapt to very
shortened data better than standard method does.
