Multidimensional occupancy problems with Poisson randomization

AbstractIn this paper the concept of Poisson randomization is studied as given in [1, 2] and analogous formulae for the generalized process are derived. The generalization regards occupancy problems where different ball types are considered such that each type has an associated probability distribution of urn occupancy. Theorems are given for formulae to calculate probabilities of events and the distribution and moments of waiting time random variables. Finally, the theory is illustrated with examples