Bounds for the total variation distance between the Binomial and the Poisson distribution in case of medium-sized success probabilities

In applied probability, the distribution of a sum of n independent Bernoulli random variables with success probabilities p1, p2, ... , pn is often approximated by a Poisson distribution with parameter λ = p1 + p2 + ... + pn. Popular bounds for the approximation error are excellent for small values, but less efficient for moderate values of p1, p2, ... , pn. Upper bounds for the total variation distance are established, improving conventional estimates if the success probabilities are of medium size. The results may be applied directly, e.g. to approximation problems in risk theory.