Crystallographic explorations into uniform distribution theory

Explorations in Learning & Instruction: The Theory Into Practice Database

13 Geometric Discrepancy Theory and Uniform Distribution

A sequence s1, s2, . . . in U = [0, 1) is said to be uniformly distributed if, in the limit, the number of sj falling in any given subinterval is proportional to its length. Equivalently, s1, s2, . . . is uniformly distributed if the sequence of equiweighted atomic probability measures μN (sj) = 1/N , supported by the initial N -segments s1, s2, . . . , sN , converges weakly to Lebesgue measure...

Foundations of the Theory of Uniform Distribution

The book Uniform distribution of sequences by Kuipers and Niederreiter, long out of print, has recently been made available again by Dover books. I came across a copy at the Borders bookstore in San Francisco and decided to give it a try (the price, as they say, was right). It turned out to be full of interesting results, so I decided to take some notes on what seemed to me to be the parts most...

10 Geometric Discrepancy Theory and Uniform Distribution

A sequence s1, s2, . . . in U = [0, 1) is said to be uniformly distributed if, in the limit, the number of sj falling in any given subinterval is proportional to its length. Equivalently, s1, s2, . . . is uniformly distributed if the sequence of equiweighted atomic probability measures μN (sj) = 1/N , supported by the initial N -segments s1, s2, . . . , sN , converges weakly to Lebesgue measure...

Record Range of Uniform Distribution

We consider a sequence of independent and identicaly distributed (iid) random variables with absolutely continuous distribution function F(x) and probability density function (pdf) f(x). Let Rnl be the largest observation after observing nth record and R(ns) be the smallest observation after observing the nth record. Then we say Wnr = Rnl− R(ns), n > 1, as the nth record range. We will c...