@article{myais1454,
          volume = {30},
          number = {2},
           month = {["lib/utils:month\verb1_11454" not defined]},
          author = {  Boonta, S. and   Neammanee, K.},
           title = {Bounds on Random Infinite Urn Model},
       publisher = {Penerbit Universiti Sains Malaysia},
            year = {2007},
         journal = {Bulletin of the Malaysian Mathematical Sciences Society},
           pages = {121--128},
        keywords = {Infinite urn model, Central limit theorem, Uniform and non-uniform bounds},
             url = {http://myais.fsktm.um.edu.my/1454/},
        abstract = {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}
}