Best unbiased graphical estimators of location-scale distribution parameters: application to the Pozzuoli’s bradyseism earthquake data

Graphical techniques are recommended for critical applications because they allow for visual analysis and helpful understanding of the results, also for non-statisticians. However, “graphical” estimation methods are often criticized because they are less efficient with respect to “analytical” methods. This paper proposes a new general graphical method that leads to the best linear unbiased estimators of location-scale distribution parameters. Therefore, the reputation of graphical methods is raised and their strategic use is encouraged. An applicative example analyzes the earthquake magnitudes registered during the serious 1983–1984 bradyseismic crisis in Campi Flegrei, Italy. This graphical analysis will certainly work as a strategic reference picture to which the data, arising from the further bradyseismic crises expected in the next future, can be compared.