Malaysian Abstracting and Indexing SystemBounds on Random Infinite Urn Model Boonta, S.author Neammanee, K.authorLet $N(n)$ 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, 60G50Q Science, Computer Science2007Penerbit Universiti Sains MalaysiaJournal

For work being deposited by its own author: In self-archiving this collection of files and associated bibliographic metadata, I grant Malaysian Abstracting and Indexing System the right to store them and to make them permanently available publicly for free on-line. I declare that this material is my own intellectual property and I understand that Malaysian Abstracting and Indexing System does not assume any responsibility if there is any breach of copyright in distributing these files or metadata. (All authors are urged to prominently assert their copyright on the title page of their work.)

For work being deposited by someone other than its author: I hereby declare that the collection of files and associated bibliographic metadata that I am archiving at Malaysian Abstracting and Indexing System) is in the public domain. If this is not the case, I accept full responsibility for any breach of copyright that distributing these files or metadata may entail.

Clicking on the deposit button indicates your agreement to these terms.