Definition
For arbitrary points the discrepancy is defined by, where the supremum is extended over all subintervals of, is times the number of points among falling into J and V(J) denotes the s-dimensional volume of J.
Until now, we had sequences of integers from 0 to T-1, in order to have sequences of, one can divide a sequences of integers by its period T.
From this definition, we can say that if the sequence is perfectly random then its well distributed on the interval then and all points are in J so hence but instead if the sequence is concentrated close to one point then the subinterval J is very small and so Then we have from the better and worst case: .
Read more about this topic: Inversive Congruential Generator
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