Improved lower bounds on the total variation distance and relative entropy for the Poisson approximation

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. Corresponding lower bounds on the relative entropy are derived, based on the lower bounds on the total variation distance and an existing distribution-dependent refinement of Pinsker's inequality. Two uses of these bounds are finally outlined. The full version for this shortened paper is available at http://arxiv.org/abs/1206.6811.