these proposed measures suggest a much better fit of the heavier-tailed distributions.
Moreover, for the Pareto distribution, while the statistics that focus on the center of the data (Kolmogorov-Smirnov, Kuiper, Cram´er-von Mises) do not show a good fit, the ADup and AD2
up statistics indicate that the fit in the upper tail is very good. It should be noted that the Pareto and Weibull distributions very often suggest a superior fit in the upper tail to the Lognormal distribution. Yet is it the Lognormal distribution that was suggested in 2001 by the Basel Committee, BIS (2001).