The theory of stable probability distributions and their domains of attraction is derived in a direct way(avoiding the usual route via infinitely divisible distributions) using Fourier transforms. Regularly varyingfunctions play an important role in the exposition.

The theory of stable probability distributions and their domains of attraction is derived in a direct way (avoiding the usual route via infinitely divisible distributions) using Fourier transforms. Regularly varying functions play an important role in the exposition.

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.

Estimators of the extreme-value index are based on a set of upper order statistics. We present an adaptivemethod to choose the number of order statistics involved in an optimal way, balancing variance and biascomponents. Recently this has been achieved for the similar but somewhat less involved...

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...

Suppose are independent subexponential random variables with partial sums. We show that if the pairwise sums of the ’s are subexponential, then is subexponential and . The result is applied to give conditions under which as , where are constants such that is a.s. convergent. Asymptotic tail...

The stability of the financial system at higher loss levels is either characterized by asymptotic dependence or asymptotic independence. If asymptotically independent, the dependency, when present, eventually dies out completely at the more extreme quantiles, as in case of the multivariate...

The stability of the financial system at higher loss levels is either characterized by asymptotic dependence or asymptotic independence. If asymptotically independent, the dependency, when present, eventually dies out completely at the more extreme quantiles, as in case of the multivariate...