Some Remarks on Estimating the Parameters of a Bivariate Extreme Value Distribution

In this paper we consider the bivariate extreme value Gumbel distribution and, in order to check against anomalies in the data, we compare the estimates obtained by the method of the moments and by the maximum likelihood principle with the ones achieved applying the minimum integrated square error criterion. We measure the difference among the estimates of the parameters resorting to a similarity index between densities, following from the Cauchy-Schwarz inequality, and a Monte Carlo significance test of statistical hypothesis is introduced to verify the similarity between the estimates. Theory is outlined and a numerical example is provided to show the approach we propose.