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Random number generation
"... Random numbers are the nuts and bolts of simulation. Typically, all the randomness required by the model is simulated by a random number generator whose output is assumed to be a sequence of independent and identically distributed (IID) U(0, 1) random variables (i.e., continuous random variables dis ..."
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Random numbers are the nuts and bolts of simulation. Typically, all the randomness required by the model is simulated by a random number generator whose output is assumed to be a sequence of independent and identically distributed (IID) U(0, 1) random variables (i.e., continuous random variables distributed uniformly over the interval
22 TestU01: A C Library for Empirical Testing of Random Number Generators
"... We introduce TestU01, a software library implemented in the ANSI C language, and offering a collection of utilities for the empirical statistical testing of uniform random number generators (RNGs). It provides general implementations of the classical statistical tests for RNGs, as well as several ot ..."
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We introduce TestU01, a software library implemented in the ANSI C language, and offering a collection of utilities for the empirical statistical testing of uniform random number generators (RNGs). It provides general implementations of the classical statistical tests for RNGs, as well as several others tests proposed in the literature, and some original ones. Predefined tests suites for sequences of uniform random numbers over the interval (0, 1) and for bit sequences are available. Tools are also offered to perform systematic studies of the interaction between a specific test and the structure of the point sets produced by a given family of RNGs. That is, for a given kind of test and a given class of RNGs, to determine how large should be the sample size of the test, as a function of the generator’s period length, before the generator starts to fail the test systematically. Finally, the library provides various types of generators implemented in generic form, as well as many specific generators proposed in the literature or found in widely used software. The tests can be applied to instances of the generators predefined in the library, or to userdefined generators, or to streams of random numbers produced by any kind of device or stored in files. Besides introducing TestU01, the article provides a survey and a classification of statistical tests for RNGs. It also applies batteries of tests to a long list of widely used RNGs.
Comparison of Point Sets and Sequences for QuasiMonte Carlo and for Random Number Generation
"... Algorithmic random number generators require recurring sequences with very long periods and good multivariate uniformity properties. Point sets and sequences for quasiMonte Carlo numerical integration need similar multivariate uniformity properties as well. It then comes as no surprise that both ty ..."
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Algorithmic random number generators require recurring sequences with very long periods and good multivariate uniformity properties. Point sets and sequences for quasiMonte Carlo numerical integration need similar multivariate uniformity properties as well. It then comes as no surprise that both types of applications share common (or similar) construction methods. However, there are some differences in both the measures of uniformity and the construction methods used in practice. We briefly survey these methods and explain some of the reasons for the differences.