Accuracy of approximation for discrete distributions

The paper is a contribution to the problem of estimating the deviation of two discrete probability distributions in terms of the supremum distance between their generating functions over the interval [ 0,1 ]. deviation can be measured by the difference of the k th terms or by total variation distance. our new bounds have better order of magnitude than those proved previously,and they are even sharp in certain cases. © 2016 tamás f. móri.