We prove that the probability distribution of Hill's estimator can be betterapproximated by a series of appropriate gamma distributions than by the limitingnormal distribution.

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...

The paper characterizes first and second order tail behavior ofconvolutions of i.i.d. heavy tailed random variables with supporton the real line. The result is applied to the problem of riskdiversification in portfolio analysis and to the estimation of theparameter in a MA(1) model.