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:
“Although there is no universal agreement as to a definition of life, its biological manifestations are generally considered to be organization, metabolism, growth, irritability, adaptation, and reproduction.”
—The Columbia Encyclopedia, Fifth Edition, the first sentence of the article on “life” (based on wording in the First Edition, 1935)
“I’m beginning to think that the proper definition of “Man” is “an animal that writes letters.””
—Lewis Carroll [Charles Lutwidge Dodgson] (1832–1898)
“Perhaps the best definition of progress would be the continuing efforts of men and women to narrow the gap between the convenience of the powers that be and the unwritten charter.”
—Nadine Gordimer (b. 1923)