Recursions for distribution functions and stop-loss transforms

For any functions on the non-negative integers, we can evaluate the cumulative function given by (s) = sx=o(x) from the values of by the recursion (s) = (s - 1) + (s). Analogously we can use this procedure t times to evaluate the t-th order cumulative function t when itself satisfies a certain sort of recursion. We shall also derive recursions for the tth order tails t where (s) = x=s+1(x). The recursions can be applied for exact and approximate evaluation of distribution functions and stop-loss transforms of probability distributions. The class of recursions for includes the classes discussed by Sundt (1992), incorporating the class studied by Panjer (1981). We discuss in particular convolutions and compound functions.status: publishe