Cramér–von Mises criterion ($n\int (F_n-F_0{)}^{2}d{F}_0$)

This goodness-of-fit criterion integrates the squared difference between the empirical distribution function and a specified continuous null distribution. Under a fully specified null, the probability integral transform makes its law distribution-free; its limiting law is ${\int }_0^1{B}^0(u{)}^{2}du$ for a Brownian bridge. Parameter fitting changes that calibration.