A Berry-Esseen bound for the uniform multinomial occupancy model

Details A Berry-Esseen bound for the uniform multinomial occupancy model A Berry-Esseen bound for the uniform multinomial occupancy model

2012-02-04

arxiv.org/abs/1202.0909v1

Mathematics

Probability

32 pages

Scientific paper

The inductive size bias coupling technique and Stein's method yield a Berry-Esseen theorem for the number of urns having occupancy $d \ge 2$ when $n$ balls are uniformly distributed over $m$ urns. In particular, there exists a constant $C$ depending only on $d$ such that $$ \sup_{z \in \mathbb{R}}|P(W_{n,m} \le z) -P(Z \le z)| \le C \frac{\sigma_{n,m}}{1+(\frac{n}{m})^3} \quad {for all $n \ge d$ and $m \ge 2$,} $$ where $W_{n,m}$ and $\sigma_{n,m}^2$ are the standardized count and variance, respectively, of the number of urns with $d$ balls, and $Z$ is a standard normal random variable. Asymptotically, the bound is optimal up to constants if $n$ and $m$ tend to infinity together in a way such that $n/m$ stays bounded.

Affiliated with

Also associated with

No associations

Rating

A Berry-Esseen bound for the uniform multinomial occupancy model does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A Berry-Esseen bound for the uniform multinomial occupancy model, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A Berry-Esseen bound for the uniform multinomial occupancy model will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-330570