In certain cases the distribution of the normalized maximumof a sample can be better approximated by a sequence ofdifferent extreme value distributions than by the final one. Weshow that these cases are rather restricted and that the possibleimprovement is not spectacular.

In certain cases partial sums of i.i.d. random variables with finite variance are better approximated by asequence of stable distributions with indices alpha n - 2 than by a normal distribution. We discusswhen this happens and how much the convergence rate can be improved by using penultimate...

An abundance of high quality data sets requiring heavy tailed models necessitates reliablemethods of estimating the shape parameter governing the degree of tail heaviness.The Hill estimator is a popular method for doing this but its practical use isencumbered by several difficulties. We show...