Dvoretzky–Kiefer–Wolfowitz inequality

In the theory of probability and statistics, the Dvoretzky–Kiefer–Wolfowitz inequality (DKW inequality) provides a bound on the worst case distance of an empirically determined distribution function from its associated population distribution function. It is named after Aryeh Dvoretzky, Jack Kiefer, and Jacob Wolfowitz, who in 1956 proved the inequality P ( sup x ∈ R | F n ( x ) − F ( x ) | > ε ) ≤ C e − 2 n ε 2 for every ε > 0.

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