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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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Cited by 139 (30 self)
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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
TestU01: A C library for empirical testing of random number generators
 ACM Transactions on Mathematical Software
, 2007
"... 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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Cited by 32 (1 self)
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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 widelyused 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 paper 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.
TestU01: A Software Library in ANSI C for Empirical Testing of Random Number Generators
, 2007
"... This document describes the software library TestU01, implemented in the ANSI C language, and offering a collection of utilities for the (empirical) statistical testing of uniform random number generators (RNG). The library implements several types of generators in generic form, as well as many spec ..."
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Cited by 19 (2 self)
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This document describes the software library TestU01, implemented in the ANSI C language, and offering a collection of utilities for the (empirical) statistical testing of uniform random number generators (RNG). The library implements several types of generators in generic form, as well as many specific generators proposed in the literature or found in widelyused software. It provides general implementations of the classical statistical tests for random number generators, as well as several others proposed in the literature, and some original ones. These tests can be applied to the generators predefined in the library and to userdefined generators. Specific tests suites for either sequences of uniform random numbers in [0, 1] or bit sequences are also available. Basic tools for plotting vectors of points produced by generators are provided as well. Additional software permits one 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.
A Collection of Selected Pseudorandom Number Generators with Linear Structures
, 1997
"... This is a collection of selected linear pseudorandom number that were implemented in commercial software, used in applications, and some of which have extensively been tested. The quality of these generators is examined using scatter plots and the spectral test. In addition, the spectral test is app ..."
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Cited by 14 (2 self)
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This is a collection of selected linear pseudorandom number that were implemented in commercial software, used in applications, and some of which have extensively been tested. The quality of these generators is examined using scatter plots and the spectral test. In addition, the spectral test is applied to study the applicability of linear congruential generators on parallel architectures. Additional Key Words and Phrases: Pseudorandom number generator, linear congruential generator, multiple recursive generator, combined pseudorandom number generators, parallel pseudorandom number generator, lattice structure, spectral test. 0 0.0001 0 0.0001 0 0.0001 0 0.0001 0 0.0001 Research supported by the Austrian Science Foundation (FWF), project no. P11143MAT. Contents 1 Linear congruential generator: LCG 5 1.1 LCG(2 31 ; 1103515245; 12345; 12345) ANSIC : : : : : : : : : : : : : : : : 5 1.2 LCG(2 31 \Gamma1; a = 7 5 = 16807; 0; 1) MINSTD : : : : : : : : : : : : : : : : 5 1.3 LCG...
Uniform Random Number Generators: A Review
"... Thispapersummarizesthecurrentstateoftheart onuniformrandomnumbergenerationforstochasticsimulation. Itrecallsthebasicideas,discusses somelinearmethodsandtheirtheoreticalanalysis, andprovidespointerstofurtherdetailsandtorecommendedimplementations. 1 WHATISAGOODRNG? Withoutagoodrandomnumbergenerato ..."
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Cited by 8 (0 self)
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Thispapersummarizesthecurrentstateoftheart onuniformrandomnumbergenerationforstochasticsimulation. Itrecallsthebasicideas,discusses somelinearmethodsandtheirtheoreticalanalysis, andprovidespointerstofurtherdetailsandtorecommendedimplementations. 1 WHATISAGOODRNG? Withoutagoodrandomnumbergenerator(RNG), simulationresultsareoftenmeaningless.Andquestionablegeneratorsarestillallovertheplace, somany experimentsrestonshakyfoundations.Whythis problemwasnotsolvedlongago?Becauseitisnot soeasy.AsocalledRNGactuallyproducesatotally deterministicandperiodicsequenceofnumbers,once itsinitialstate(orseed)ischosen.Thisisintotal contradictionwiththeassumptionofasequenceofindependentandidenticallydistributed (i.i.d.)random variables,andthereisnocleanwaytocompletely reconcilethesetwooppositeaspects.Therefore,everythingwedointhiscontextisheuristic. Thisbeingsaid, theheuristicargumentsleadtocriteriathat needtheorytobeanalyzed.
Random Number Generators and Empirical Tests
"... We recall some requirements for "good" random number generators and argue that while the construction of generators and the choice of their parameters must be based on theory, a posteriori empirical testing is also important. We then give examples of tests failed by some popular generato ..."
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Cited by 5 (3 self)
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We recall some requirements for "good" random number generators and argue that while the construction of generators and the choice of their parameters must be based on theory, a posteriori empirical testing is also important. We then give examples of tests failed by some popular generators and examples of generators passing these tests.
What is a Random Sequence
 The Mathematical Association of America, Monthly
, 2002
"... there laws of randomness? These old and deep philosophical questions still stir controversy today. Some scholars have suggested that our difficulty in dealing with notions of randomness could be gauged by the comparatively late development of probability theory, which had a ..."
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Cited by 4 (1 self)
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there laws of randomness? These old and deep philosophical questions still stir controversy today. Some scholars have suggested that our difficulty in dealing with notions of randomness could be gauged by the comparatively late development of probability theory, which had a
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 ..."
Abstract
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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.
ABSTRACT UNIFORM RANDOM NUMBER GENERATORS: A REVIEW
"... This paper summarizes the current stateoftheart on uniform random number generation for stochastic simulation. It recalls the basic ideas, discusses some linear methods and their theoretical analysis, and provides pointers to further details and to recommended implementations. 1. WHAT IS A GOOD R ..."
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This paper summarizes the current stateoftheart on uniform random number generation for stochastic simulation. It recalls the basic ideas, discusses some linear methods and their theoretical analysis, and provides pointers to further details and to recommended implementations. 1. WHAT IS A GOOD RNG? Without a good random number generator (RNG), simulation results are often meaningless. And questionable generators are still all over the place, so many experiments rest on shaky foundations. Why this problem was not solved long ago? Because it is not so easy. A socalled RNG actually produces a totally deterministic and periodic sequence of numbers, once its initial state (or seed) is chosen. This is in total contradiction with the assumption of a sequence of independent andidentically distributed (i.i.d.) random variables, and there is no clean way to completely reconcile these two opposite aspects. Therefore, everything we dointhiscontext is heuristic. This being said, the heuristic arguments lead to criteria that need theory to be analyzed. ARNGhas a state that evolves in a nite state space S, according to a recurrence of the form sn = f(sn;1), n 1, where the initial state s0 2 S is called the seed, and f: S! S is the transition function. At step n, the generator outputs un = g(sn), where g: S! [0 � 1] is the output function. The output sequence of the RNG is thus fun � n 0g. The output space could be more general, but we shall assume here that it is the real interval [0 � 1]. Since S is nite, the sequence must be periodic (possibly after some initial transient). Let be the period length. Typically, one has near jSj, that is, 2 b if the state is represented over b bits, otherwise there is a waste of computer memory. We now momentarily forget the deterministic na