In mathematics, a sequence (s1, s2, s3, ...) of real numbers is said to be equidistributed, or uniformly distributed, if the proportion of terms falling...

base b if and only if the sequence ( b k x ) k = 0 ∞ {\displaystyle {\left(b^{k}x\right)}_{k=0}^{\infty }} is equidistributed modulo 1, or equivalently...

on average (but not for particular samples) in the case of an equidistributed sequence. Specific definitions of discrepancy differ regarding the choice...

distribution Discrete uniform distribution Uniform distribution (ecology) Equidistributed sequence All pages with titles containing uniform distribution Homogeneous...

multiples of an irrational α, 0, α, 2α, 3α, 4α, ... is equidistributed modulo 1. In other words, the sequence of the fractional parts of each term will be uniformly...

the reciprocal of its fractional part, and so on. Circle group Equidistributed sequence One-parameter group Pisot–Vijayaraghavan number Poussin proof Significand...

and the upper density is 5/9. (See Benford's law.) Consider an equidistributed sequence { α n } n ∈ N {\displaystyle \{\alpha _{n}\}_{n\in \mathbb {N}...

a period of 219 937 − 1 iterations (≈ 4.3×106001), is proven to be equidistributed in (up to) 623 dimensions (for 32-bit values), and at the time of its...

exists a subsequence of the van der Corput sequence that converges to that number. They are also equidistributed over the unit interval. def corput(n, base):...

equidistribution property of v-bit accuracy than MT but worse than WELL ("Well Equidistributed Long-period Linear"). It has quicker recovery from zero-excess initial...

distributed, equidistributed in residue classes, and even in smooth Bohr neighbourhoods. Erdős also showed that, for any particular infinite Sidon sequence A {\displaystyle...

Matsumoto, M.; Nishimura, T. (1998). "MersenneTwister: A623-dimensionally Equidistributed Uniform Pseudo-Random Number Generator". ACM Transactions on Modeling...

\infty }x_{n}=+1.} (This is because the sequence { 1 , 2 , 3 , … } {\displaystyle \{1,2,3,\ldots \}} is equidistributed mod 2π, a consequence of the equidistribution...

1933, proved that the generalization x + na, for almost all x, is equidistributed on any Lebesgue measurable subset of the unit interval. The corresponding...

and hence random variables. It is also useful in the study of equidistributed sequences, for example in the Weyl equidistribution estimate. Loosely stated...

xorshift128 generator is 2-dimensionally equidistributed, the xorshift128+ generator is only 1-dimensionally equidistributed. XSadd has some weakness in the low-order...

"Middle-Square Weyl Sequence RNG". arXiv:1704.00358 [cs.CR]. Matsumoto, M.; Nishimura, T. (1998). "MersenneTwister: A 623-dimensionally Equidistributed Uniform Pseudo-Random...

Nishimura, Takuji (January 1998). "Mersenne twister: a 623-dimensionally equidistributed uniform pseudo-random number generator" (PDF). ACM Transactions on...

consequence, it is a normal number, which means that its digits are equidistributed as if they were generated by tossing a fair coin. It is not a computable...

Nishimura, Takuji (January 1998). "Mersenne Twister: A 623-Dimensionally Equidistributed Uniform Pseudo-Random Number Generator". ACM Transactions on Modeling...

Makoto; Nishimura, Takuji (1998). "Mersenne Twister: A 623-dimensionally equidistributed uniform pseudo-random number generator". ACM Transactions on Modeling...

Chaitin has defined Chaitin's constant Ω, a real number whose digits are equidistributed and which is sometimes informally described as an expression of the...

procedure is that the period is a multiple of b, so the output is exactly equidistributed mod b. (The ordinary MWC, over its full period, produces each possible...

Generalized Inversive Congruential Pseudorandom Numbers are well equidistributed in one dimension. A reliable theoretical approach for assessing their...

Colin de Verdière and Zelditch states that on average, eigenfunctions equidistribute on S {\displaystyle S} . The unique quantum ergodicity conjecture of...