THE EXACT AND ASYMPTOTIC DISTRIBUTIONS OF CRAMER-VON MISES STATISTICS

It is shown that an asymptotically precise one-term correction to the asymptotic distribution function of the classical Cramer-von Mises sta tistic approximates the exact distribution function remarkably closely for sample sizes as small as 7 or even smaller. This correction can b e quickly evaluated, and hence it is suitable for the computation of p ractically exact p-values when testing simple goodness of fit. Similar findings hold for Watson's rotationally invariant modification, where a sample size of 4 appears to suffice.