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Graphical techniques are recommended for critical applications in order toshare information with non-statisticians, since they allow for a visualanalysis and helpful understanding of the results. However, graphicalestimation methods are often underestimated because of their minor efficiencywith respect to the analytical ones. Therefore, finding unbiased plottingpositions can contribute to rise their reputation and to encourage theirstrategic use. This paper proposes a new general plotting position formulawhich can be as close as needed to the exact unbiased plotting positions. Theability of the new solution in estimating quantiles for both symmetrical andskewed location-scale distributions is shown via Monte Carlo simulation. Anapplicative example shows how the proposed formula enables to perform, withknown accuracy, the graphical analysis of critical data, such as the earthquakemagnitudes registered during the serious 1983-1984 bradyseismic crisis in CampiFlegrei (Italy). Moreover, the proposed formula gives a unified look atexisting plotting positions and a definitive insight into plotting positioncontroversies recently renewed in the literature.

Plotting positions close to the exact unbiased solution: application to the Pozzuoli's bradeysism earthquake data