Discussion on “Plotting positions for fitting distributions and extreme value analysis”

Plotting positions are used in the extreme value analysis for many engineering applications. The authors of the discussed paper concluded based on their simulations that distribution dependent plotting position formulae provide a better fit to the underlying cumulative distribution than the distribution free Weibull formula. We show here by Monte Carlo simulations following the theory of probability that the opposite is true, and outline that the criteria used in the comparisons made by the authors of discussed paper are inappropriate. Accordingly, the Weibull formula should be used as the unique plotting position.