TY  - JOUR
ID  - myais1454
UR  - http://math.usm.my/bulletin/pdf/v30n2/v30n2p4.pdf
IS  - 2
A1  - Boonta, S.,  
A1  - Neammanee, K.,  
Y1  - 2007///
N2  - Let $N(n)$ be a Poisson random variable with Parameter $n$. An infinite urn model is defined as follows: $N(n)$ balls are independently placed in an infinite set of urns and each ball has probability $p_k > 0$ of being assigned to the $k$-th urn. We assume that $p_k \geq p_{k+1}$ for all $k$ and $\sum_{k=1}^{\infty} p_k = 1$. Let $ U_n $, be the number of occupied urns after $N(n)$ balls have been thrown. Dutko showed in 1989 that under the condition $\lim_{n\rightarrow \infty} Var(U_{n}) = \infty$ we have $\frac{U_n - E(U_{n})}{\sqrt{Var(U_{n})}} \rightarrow^d \mathcal{N} (0,1)$ as $n \rightarrow \infty$ where $\mathcal{N} (0,1)$ is the standard random variable. However, Dutko did not give a bound of his approximation. So in this paper, we give uniform and non-uniform bounds of the approximation.


2000 Mathematics Subject Classification: 60F05, 60G50
PB  - Penerbit Universiti Sains Malaysia
JF  - Bulletin of the Malaysian Mathematical Sciences Society
VL  - 30
KW  - Infinite urn model
KW  -  Central limit theorem
KW  -  Uniform and non-uniform bounds
SN  - 0126-6705
TI  - Bounds on Random Infinite Urn Model
SP  - 121
AV  - none
EP  - 128
ER  -