Related papers: Harmonic analysis of random number generators
The spectral test of random number generators (R.R. Coveyou and R.D. McPherson, 1967) is generalized. The sequence of random numbers is analyzed explicitly not just via their n-tupel distributions. The generalized analysis of many…
An important statistical test on the pseudo-random number generators is called the spectral test. The test is aimed at answering the question of distribution of the generated pseudo-random vectors in dimensions $d$ that are larger than the…
It is well-known that the quality of random number generators can often be improved by combining several generators, e.g. by summing or subtracting their results. In this paper we investigate the ratio of two random number generators as an…
Congruential pseudorandom number generators rely on good multipliers, that is, integers that have good performance with respect to the spectral test. We provide lists of multipliers with a good lattice structure up to dimension eight and up…
In this paper the spectral analysis of all possible linear congruent sequences with a maximum period is conducted and the best random number generators are selected among them.
In multiple testing, the family-wise error rate can be bounded under some conditions by the copula of the test statistics. Assuming that this copula is Archimedean, we consider two non-parametric Archimedean generator estimators. More…
A simple binary model to compute the degree of balancedness in the output sequence of LFSR-combinational generators has been developed. The computational method is based exclusively on the handling of binary strings by means of logic…
Random number generators (RNGs) are notoriously challenging to build and test, especially for cryptographic applications. While statistical tests cannot definitively guarantee an RNG's output quality, they are a powerful verification tool…
Revisions are almost entirely in the introduction and conclusion. Results are unchanged, however the comments and recommendations on different generators were changed, and more references were added.
We define two a priori tests of pseudo-random number generators for the class of linear matrix-recursions. The first desirable property of a random number generator is the smallness of serial or lagged correlations between generated…
We present results of an extensive test program of a group of pseudorandom number generators which are commonly used in the applications of physics, in particular in Monte Carlo simulations. The generators include public domain programs,…
A general method to produce uniformly distributed pseudorandom numbers with extended precision by combining two pseudorandom numbers with lower precision is proposed. In particular, this method can be used for pseudorandom number generation…
Pseudorandom number generators are required for many computational tasks, such as stochastic modelling and simulation. This paper investigates the serial CPU and parallel GPU implementation of a Linear Congruential Generator based on the…
Let $g$, $h$ be a random pair of generators of $G=Sym(n)$ or $G=Alt(n)$. We show that, with probability tending to $1$ as $n\to \infty$, (a) the diameter of $G$ with respect to $S = \{g,h,g^{-1},h^{-1}\}$ is at most $O(n^2 (\log n)^c)$, and…
Conventional random number generators provide the speed but not necessarily the high quality output streams needed for large-scale stochastic simulations. Cryptographically-based generators, on the other hand, provide superior quality…
The Mersenne Twister MT19937 pseudorandom number generator, introduced by the last two authors in 1998, is still widely used. It passes all existing statistical tests, except for the linear complexity test, which measures the ratio of the…
In a mixed generalized linear model, the goal is to learn multiple signals from unlabeled observations: each sample comes from exactly one signal, but it is not known which one. We consider the prototypical problem of estimating two…
High-performance streams of (pseudo) random numbers are crucial for the efficient implementation for countless stochastic algorithms, most importantly, Monte Carlo simulations and molecular dynamics simulations with stochastic thermostats.…
This paper has a practical aim. For a long time, implementations of pseudorandom number generators in standard libraries of programming languages had poor quality. The situation started to improve only recently. Up to now, a large number of…
A universal generator for integer-valued square-integrable random variables is introduced. The generator relies on a rejection technique based on a generalization of the inversion formula for integer-valued random variables. The proposal…