A note on the upper bound for the distance in total variation between the binomal and the Poisson distribution

Abstract  The total variation distance between the binomial B ( n, p ) distribution and the Poisson P ( np ) distribution is smaller than 2 ^1/2 p (1- p )^-1/2 according to V ERVAAT 4], 5]. We shall sharpen this inequality by using a result due to K EMPERMAN 1], C SISZÁR 2] and K ULLBACK 3].