The Borel Distribution: Approximation and Concentration
Probability
2021-07-27 v3
Abstract
We develop the tools necessary to use Stein's method for approximation by a Borel distribution, which we illustrate by considering the approximation of the number of customers served in the busy period of an M/G/1 queue. We further derive concentration inequalities for the Borel distribution. Both these sets of results are based on a representation for the size-biased version of a Borel random variable.
Cite
@article{arxiv.1912.03219,
title = {The Borel Distribution: Approximation and Concentration},
author = {Fraser Daly and Seva Shneer},
journal= {arXiv preprint arXiv:1912.03219},
year = {2021}
}
Comments
10 pages; substantially rewritten from earlier versions