The total variation distance between the binomial and Poisson distributions (Q1114994)

The exact total variation distances are obtained between a binomial distribution with parameters n and p and Poisson distributions with means np and -n log(1-p), for small values of p. It is shown that the latter distance is smaller for \(0<p<c_ n\) and larger for \(c_ n<p<a'_{n0}\), where as \(n\to \infty\), \(nc_ n\to 1.596..\). and \(na'_{n0}\to 3.414..\).