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.
- Chen-Stein method
- Poisson approximation
- Total variation distance
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Statistics, Probability and Uncertainty