Computing the maximum over these 2N values (with
f equal to Fdata(x) and g equal to F0(x) as defined
above) is clearly the most efficient way to compute
the Kolmogorov-Smirnov test statistic for a continuous
null distribution. When the function g is not
continuous, however, equality (3) does not hold in
general because we cannot replace limx!xi g(x) with
the value g(xi).
If it is known that g is a step function, it follows
that for some small e,