• 1 Utrecht Mathematical Institute
• 2 Faculty of Cybernetics [Kyiv]
• 3 Mathematisches Seminar [Kiel]

Sampling from a random discrete distribution induced by a 'stick-breaking' process is considered. Under a moment condition, it is shown that the asymptotics of the sequence of occupancy numbers, and of the small-parts counts (singletons, doubletons, etc) can be read off from a limiting model involving a unit Poisson point process and a self-similar renewal process on the half-line.