Improved Lower Bounds on the Total Variation Distance for the Poisson Approximation

Understand

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.