Analysis of Random Number Generators Using Monte Carlo Simulation

Abstract

Monte Carlo simulation is one of the main applications involving the use of random number generators. It is also one of the best methods of testing the randomness properties of such generators, by comparing results of simulations using different generators with each other, or with analytic results. Here we compare the performance of some popular random number generators by high precision Monte Carlo simulation of the 2-d Ising model, for which exact results are known, using the Metropolis, Swendsen-Wang, and Wolff Monte Carlo algorithms. Many widely used generators that perform well in standard statistical tests are shown to fail these Monte Carlo tests.

Estimation of Random Variable Distribution Parameters by the Monte Carlo Method

“…It is particularly important because of the finite lengths of the cycles of pseudo-random number generators used for data generation. In practice, the accuracy of the method is dependent on the number of data and the quality of the pseudo-random number generator [28]- [30]. The article presents results obtained with the use of LabVIEW.…”

A Nonempirical Test on the Weight of Pseudorandom Number Generators

“…These three-term GFSRs were introduced to the computational physics community by [8] suggesting the recursion x j = x j−103 ⊕ x j−250 , and became fairly popular. In middle 80's, physicists began to find the failure of these generators in simulations of physical models, such as Ising models [5][2] [1] and random walks [4]. These physical models are simplified and proposed as tests of randomness in [22], which we call physical tests here.…”

On Parallel Pseudo-Random Number Generation

“…Although multiple lagged Fibonacci generators using XOR operations can be combined to provide good quality sequences [4], the individual sequence obtained by using a lagged Fibonacci generator with XOR operations give the worst pseudo-random numbers, in terms of their randomness properties [5,1,11]. Multiplicative lagged Fibonacci generators have been shown to have superior properties compared to additive lagged Fibonacci generators [5].…”

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