The variation distance of two distributions X{\displaystyle X} and Y{\displaystyle Y} over a finite domain D{\displaystyle D}, (often referred to as statistical difference or statistical distance in cryptography) is defined as
Δ(X,Y)=12∑α∈D|Pr[X=α]−Pr[Y=α]|{\displaystyle \Delta (X,Y)={\frac {1}{2}}\sum _{\alpha \in D}|\Pr[X=\alpha ]-\Pr[Y=\alpha ]|}.