The sequential occupancy problem through group throwing of indistinguishable balls (Q539526)

The authors generalize a classical occupancy problem to the case where instead of throwing one ball at a time, a fixed size group of indistiguishable balls are distributed sequentially into cells. Statistics of the Bose-Einstein model are studied whenever each trial is classified according to its jump size (i.e., to the number of newly occupied cells). The authors obtain the exact distribution of the number of occupied cells after \(k\) trials and the distribution of the waiting time until \(n\) cells are occupied. Recursive probability generating functions are also used to obtain a decomposition of the waiting time variable in terms of a series of random variables \(Y_j\), where \(Y_j\) is equal to the number of trials after which exactly \(j\) cells will have been occupied for the first time.