Improved Lower Bounds on the Total Variation Distance for the Poisson Approximation
Information Theory
2013-07-17 v4 math.IT
Abstract
New lower bounds on the total variation distance between the distribution of a sum of independent Bernoulli random variables and the Poisson random variable (with the same mean) are derived via the Chen-Stein method. The new bounds rely on a non-trivial modification of the analysis by Barbour and Hall (1984) which surprisingly gives a significant improvement. A use of the new lower bounds is addressed.
Keywords
Cite
@article{arxiv.1301.7504,
title = {Improved Lower Bounds on the Total Variation Distance for the Poisson Approximation},
author = {Igal Sason},
journal= {arXiv preprint arXiv:1301.7504},
year = {2013}
}
Comments
To appear in the Statistics and Probability Letters, final version: July 16, 2013. This work was presented in part at the 2013 Information Theory and Applications (ITA) Workshop in San-Diego, February 2013