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:
“Beauty, like all other qualities presented to human experience, is relative; and the definition of it becomes unmeaning and useless in proportion to its abstractness. To define beauty not in the most abstract, but in the most concrete terms possible, not to find a universal formula for it, but the formula which expresses most adequately this or that special manifestation of it, is the aim of the true student of aesthetics.”
—Walter Pater (1839–1894)
“The definition of good prose is proper words in their proper places; of good verse, the most proper words in their proper places. The propriety is in either case relative. The words in prose ought to express the intended meaning, and no more; if they attract attention to themselves, it is, in general, a fault.”
—Samuel Taylor Coleridge (1772–1834)
“Mothers often are too easily intimidated by their children’s negative reactions...When the child cries or is unhappy, the mother reads this as meaning that she is a failure. This is why it is so important for a mother to know...that the process of growing up involves by definition things that her child is not going to like. Her job is not to create a bed of roses, but to help him learn how to pick his way through the thorns.”
—Elaine Heffner (20th century)