<P> Under null hypothesis that the sample comes from the hypothesized distribution F (x), </P> <Dl> <Dd> n D n → n → ∞ sup t B (F (t)) (\ displaystyle (\ sqrt (n)) D_ (n) (\ xrightarrow (n \ to \ infty)) \ sup _ (t) B (F (t))) </Dd> </Dl> <Dd> n D n → n → ∞ sup t B (F (t)) (\ displaystyle (\ sqrt (n)) D_ (n) (\ xrightarrow (n \ to \ infty)) \ sup _ (t) B (F (t))) </Dd> <P> in distribution, where B (t) is the Brownian bridge . </P>

Test if two samples are from the same distribution