Some Asymptotic Results for Occupancy Problems

Holst, Lars

Ann. Probab., Tome 5 (1977) no. 6, p. 1028-1035 / Harvested from Project Euclid

Résumé

Suppose $n$ balls are placed into $N$ cells with arbitrary probabilities. Limit distributions for the number of empty cells are considered when $N \rightarrow \infty$ and $n \rightarrow \infty$ in such a way that $n/N \rightarrow \infty$. Limit distributions for the number of balls to achieve exactly $b$ empty cells are obtained for $N \rightarrow \infty$ with $b$ fixed and for $b \rightarrow \infty$ with $b/N \rightarrow 0$.

Détail

Publié le : 1977-12-14
Classification:  Occupancy problems,  coupon collectors problem,  limit theorems,  60F05,  60C05