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.

In this paper, we introduce a flexible and widely applicable nonparametric entropy-based testing procedure that can be used to assess the validity of simple hypotheses about a specific parametric population distribution. The testing methodology relies on the characteristic function of the...