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
Famous quotes containing the word definition:
“The man who knows governments most completely is he who troubles himself least about a definition which shall give their essence. Enjoying an intimate acquaintance with all their particularities in turn, he would naturally regard an abstract conception in which these were unified as a thing more misleading than enlightening.”
—William James (1842–1910)
“One definition of man is “an intelligence served by organs.””
—Ralph Waldo Emerson (1803–1882)
“No man, not even a doctor, ever gives any other definition of what a nurse should be than this—”devoted and obedient.” This definition would do just as well for a porter. It might even do for a horse. It would not do for a policeman.”
—Florence Nightingale (1820–1910)