Clubbed Binomial Approximation for the Lightbulb Process
Probability
2011-11-18 v1
Abstract
In the so called lightbulb process, on days r=1,..,n, out of n lightbulbs, all initially off, exactly r bulbs selected uniformly and independent of the past have their status changed from off to on, or vice versa. With W_n the number of bulbs on at the terminal time n and C_n a suitable clubbed binomial distribution, d_{TV}(W_n,C_n) \le 2.7314 \sqrt{n} e^{-(n+1)/3} for all n \ge 1. The result is shown using Stein's method.
Cite
@article{arxiv.1111.3984,
title = {Clubbed Binomial Approximation for the Lightbulb Process},
author = {Larry Goldstein and Aihua Xia},
journal= {arXiv preprint arXiv:1111.3984},
year = {2011}
}
Comments
9 pages