Abstract -For a probability distribution P on an at most countable alphabet A, this article gives finite sample bounds for the expected occupancy counts EK n,r and probabilities EM n,r . Both upper and lower bounds are given in terms of the counting function ν of P . Special attention is given to the case where ν is bounded by a regularly varying function. In this case, it is shown that our general results lead to an optimal-rate control of the expected occupancy counts and probabilities with explicit constants. Our results are also put in perspective with Turing's formula and recent concentration bounds to deduce bounds in probability. At the end of the paper, we discuss an extension of the occupancy problem to arbitrary distributions in a metric space.
Non-asymptotic results are given in REF .
Finite sample properties of the mean occupancy counts and probabilities
arXiv: Statistics Theory
Mathematics