Cramér–von Mises criterion

Summary

The Cramér–von Mises criterion measures how far an empirical distribution function is from a hypothesised cumulative distribution function by an integrated squared difference. It gives a goodness-of-fit hypothesis test that, like the Kolmogorov–Smirnov test, has the same null law for every continuous hypothesised distribution. Where the Kolmogorov–Smirnov statistic looks at the single largest gap, this criterion adds up the squared gaps over the whole line. A two-sample version compares two empirical distribution functions.