Graphical approximation of Best Linear Unbiased Estimators for Extreme Value Distribution Parameters

Graphical estimation methods play a central role in today’s software because may allow for a more straightforward analysis of the data and interpretation of results also by non-statisticians. In this paper, the best unbiased graphical estimators of distribution parameters, which have recently appeared in the literature for location-scale distributions, are conveniently approximated for the special case of the extreme value distributions for minima and maxima. The mean square deviation and bias of the resulting parameter estimators are compared to concurrent ones through proper pivotal indices via Monte Carlo simulation. The proposed approximation involves and is shown to produce also adequate results for the first two moments of order statistics from the standard extreme value distributions.