Resumen
We consider an i.i.d. sample, from an underlying distribution function with unknown shape, location and scale parameters, belonging to some max-domain of attraction. We study the performance of a test statistic which is merely a ratio between the maximum and the mean of the sample of the excesses above some random threshold. This scale/location invariant ratio turns out to be very useful in the construction of an asymptotically size a test for the null hypothesis that the distribution comes from the Gumbel domain of attraction. The test is based on the kn largest observations, where kn is any intermediate sequence of positive integers. Both power of the test and type I error probability are studied for finite sample sizes by simulation.