Limit laws for the diameter of a set of random points from a distribution supported by a smoothly bounded set

In this thesis we study the asymptotic behavior of the maximum interpoint distance of random points in a d-dimensional set with a unique diameter and a smooth boundary at the poles. The main result covers the case of uniformly distributed points within a d-dimensional ellipsoid with a unique major axis. Moreover, several generalizations of the main result are established, for example a limit law for the maximum interpoint distance of random points from a Pearson type II distribution.