Some Moment Relations for the Hipp Approximation

In the present note we consider the Hipp approximation to the convolution of a finite number of probability distributions on the non-negative integers It is shown that the moment up to and including order "r" of the "rth" order approximation are equal to the corresponding moments of the exact distribution. We also give a relation between the exact and approximated (r + l) th order moments and indicate how similar relations can be obtained for higher order moments.