Bibliography

1

P. Acworth, M. Broadie, and P. Glasserman.
A Comparison of Some Monte Carlo and Quasi Monte Carlo Techniques for Option Pricing.
In H. Niederreiter, P. Hellekalek, G. Larcher, and P. Zinterhof, editors, Monte Carlo and Quasi-Monte Carlo Methods 1996, volume 127 of Lecture Notes in Statistics, pages 1-18. Springer, 1998.

2

L. Afflerbach.
Criteria for the assessment of random number generators.
J. Comput. Appl. Math., 31(1):3-10, 1990.

3

L. Afflerbach.
Die Gütebewertung von Pseudo-Zufallszahlen-Generatoren aufgrund theoretischer Analysen und algorithmischer Berechnungen.
Grazer Mathematische Berichte, 309, University Graz, Austria, 1990.
(in German).

4

L. Afflerbach and G. Gruber.
Assessment of random number generators in high accuracy.
In S. Morito, H. Sakasegawa, M. Fushimi, and K. Nakano, editors, New Directions in Simulation for Manufacturing and Communications, pages 128-133. OR Society of Japan, 1994.

5

L. Afflerbach and R. Weilbächer.
The Exact Determination of Rectangle Discrepancy for Linear Congruential Pseudorandom Numbers.
Math. Comp., 53(187):343-354, 1989.

6

J. Ahrens, U. Dieter, and A. Grube.
Pseudo-random numbers: a new proposal for the choice of multiplicators.
Computing, 6:121-138, 1970.

7

N.S. Altman.
Bit-wise behavior of random number generators.
SIAM J. Sci. Stat. Comput., 9:941-949, 1988.

8

S.L. Anderson.
Random number generators on vector supercomputers and other advanced architectures.
SIAM Rev., 32:221-251, 1990.

9

F. Anscombe.
Computing in Statistical Science through APL.
Springer Series in Statistics. Springer, New York, Heidelberg, Berlin, 1981.

10

A.C. Atkinson.
Tests of Pseudo-random Numbers.
Appl. Statist., 29(2):164-171, 1980.

11

A.C. Atkinson.
A simulation experiment for comparing tests of regression transformation.
J. Comput. Appl. Math., 31(1):11-14, 1990.

12

L.T. Bernhofen, E.J. Dudewicz, J. Levendovszky, and E.C. van der Meulen.
Ranking of the best random number generators via entropy-uniformity theory.
American Journal of Mathematical and Management Sciences, 16(1,2):49-88, 1996.

13

J.R. Birge.
Quasi-Monte Carlo Approaches to Option Pricing.
Technical report 94-19, Department of Industrial and Operations Engineering, University of Michigan, 1994 (Revised 1995).
Available at: http://www.umich.edu/~fep/papers.html.

14

R.F. Boisvert, M. McClain, and Miller B.
GAMS The Guide to Available Mathematical Software.
National Institute of Standards and Technology, , Gaithersburg, MD, USA, 1998.
http://math.nist.gov/gams/.

15

I. Borosh and H. Niederreiter.
Optimal multipliers for pseudo-random number generation by the linear congruential method.
BIT, 23:65-74, 1983.

16

K.O. Bowman and M.T. Robinson.
Studies of random number generators for parallel processing.
In M.T. Heath, editor, Proc. Second Conference on Hypercube Multiprocessors, pages 445-453, Philadelphia, 1987. SIAM.

17

P. Bratley, B.L. Fox, and L.E. Schrage.
A Guide to Simulation.
Springer, New York, 2nd edition, 1987.

18

R. P. Brent.
Uniform Random Number Generators for Supercomputers.
In Proceedings Fifth Australian Supercomputer Conference, pages 95-104, Melbourne, 1992. 5ASC Organising Committee.
Available at: http://www.comlab.ox.ac.uk/oucl/people/richard.brent.html.

19

R. P. Brent.
Random Number Generation and Simultion on Vector and Parallel computers (extended abstract).
Invited paper to be presented at Euro-Par'98, Southampton, 1-4 Sept., 1998.
Final version to appear in Lecture Notes in Computer Science, Springer Verlag, available at: http://www.comlab.ox.ac.uk/oucl/people/richard.brent.html.

20

M. Brown and H. Solomon.
On combining pseudorandom number generators.
Annals of Statistics, 1:691-695, 1979.

21

D. Brunner and A. Uhl.
Optimal multipliers for linear congruential pseudo-random number generators with prime moduli: parallel computation and properties.
BIT, 39(2):193-209, 1999.

22

D.G. Carta.
Two fast implementations of the ``minimal standard'' random number generator.
Comm. ACM, 33 :87-88, 1990.

23

D. Ceperley, M. Mascagni, and A. Srinivasan.
SPRNG: Scalable Parallel Random Number Generators.
NCSA, University of Illinois at Urbana-Champaign and University of Southern Mississippi, 1997.
http://www.ncsa.uiuc.edu/Apps/SPRNG/.

24

P. Chang, S. Hwang, and Kao C.
Some good multipliers for random number generator for 16-bit microcomputers.
Computers Ops Res., 21 :199-204, 1994.

25

CN division/CERN, CH-1211 Geneva 23, Switzerland.
CERN Program Library, 1998.
http://wwwinfo.cern.ch/asd/index.html.

26

P. Coddington.
Analysis of Random Number Generators Using Monte Carlo Simulation.
Int. J. Mod. Phys., C 5:547, 1994.

27

P. Coddington.
Random Number Generators for Parallel Computers.
NHSE Review, Second Issue, Northeast Parallel Architectures Center, 1996.
Available at: http://nhse.cs.rice.edu/NHSEreview/RNG/.

28

P. Coddington.
Tests of Random Number Generators using Ising Model Simulations.
In D.P. Landau and M. Suzuki, editors, Proceedings of the 1995 US-Japan Bilateral Seminar on New Trends in Computer Simulations of Spin Systems, volume C 7. Int. J. Mod. Phys., 1996.

29

P. Coddington and S-H. Ko.
Techniques for Empirical Testing of Parallel Random Number Genterators.
In Proc. of the ACM International Conference on Supercomputing (ICS) '98, Melbourne, Australia, 1998, to appear.
Available at http://www.cs.adelaide.edu.au/users/paulc/.

30

B.J. Collings.
Compound random number generators.
J. Amer. Statist. Assoc., 82:525-527, 1987.

31

A. Compagner.
Operational conditions for random-number generation.
Phys. Rev. E., 52:5634-5645, 1995.

32

R. Couture and P. L'Ecuyer.
On the lattice structure of certain linear congruential sequences related to AWC/SWB generators.
Math. Comp., 62:799-808, 1994.

33

R. Couture and P. L'Ecuyer.
Linear Recurrences with Carry as Uniform Random Number Generators.
In C. Alexopoulos and D. Goldsman K. Kang, W.R. Lilegdon, editors, Proceedings of the 1995 Winter Simulation Conference, pages 263-267, 1995.

34

R. Couture and P. L'Ecuyer.
Orbits and Lattices for Linear Random Number Generators with Composite Moduli.
Math. Comp., 65:189-201, 1996.

35

R. Couture and P. L'Ecuyer.
Distribution Properties of Multiply-with-Carry Random Number Generators.
Math. Comp., 66:591-607, 1997.

36

R.R. Coveyou and R.D. MacPherson.
Fourier analysis of uniform random number generators.
J. Assoc. Comput. Mach., 14:100-119, 1967.

37

J. Dagpunar.
Principles of Random Variate Generation.
Clarendon Press, Oxford, 1988.

38

A. DeMatteis, J. Eichenauer-Herrmann, and H. Grothe.
Computation of critical distances within multiplicative congruential pseudorandom number sequences.
J. Comp. Appl. Math., 39:49-55, 1992.

39

A. DeMatteis and S. Pagnutti.
Parallelization of random number generators and long-range correlations.
Numer. Math., 53:595-608, 1988.

40

A. DeMatteis and S. Pagnutti.
A class of parallel random number generators.
Parallel Comput., 13:193-198, 1990.

41

A. DeMatteis and S. Pagnutti.
Long-range correlations in linear and non-linear random number generators.
Parallel Comput., 14:207-210, 1990.

42

A. DeMatteis and S. Pagnutti.
Critical distances in pseudorandom sequences generated with composite moduli.
Intern. J. Computer Math., 43:189-196, 1992.

43

A. DeMatteis and S. Pagnutti.
Long-range correlation analysis of the Wichmann-Hill random number generator.
Statistics and Computing, 3:67-70, 1993.

44

A. DeMatteis and S. Pagnutti.
Controlling correlations in parallel Monte Carlo.
Parallel Comput., 21:73-84, 1995.

45

L. Devroye.
Random variate generation for multivariate unimodal densities.
ACM Transactions on Modeling and Computer Simulation, 7:447-477, 1997.

46

U. Dieter.
Pseudo-Random Numbers: The Exact Distribution of Pairs.
Math. Comp., 25(116):855-883, 1971.

47

U. Dieter.
How to Calculate Shortest Vectors in a Lattice.
Math. Comp., 29(131):827-833, 1975.

48

U. Dieter.
Probleme bei der Erzeugung gleichverteilter Zufallszahlen.
In L. Afflerbach and J. Lehn, editors, Kolloquium über Zufallszahlen und Simulationen, pages 7-20. Teubner-Verlag, Stuttgart, 1986.

49

U. Dieter.
Erzeugung von gleichverteilten Zufallszahlen.
In Jahrbuch Überblicke Mathematik 1993, pages 25-44, Braunschweig, 1993. Vieweg.

50

U. Dieter and J.H. Ahrens.
Uniform random numbers.
Inst. f. Math. Stat., Technische Hochschule Graz, Graz, 1974.

51

E.J. Dudewicz and T.G. Ralley.
The Handbook of Random Number Generation and Testing With TESTRAND Computer Code, volume 4 of American Series in Mathematical and Management Sciences.
American Sciences Press, Inc., Columbus, Ohio, 1981.

52

E.J. Dudewicz, E.C. van der Meulen, M.G. SriRam, and N.K.W. Teoh.
Entropy-based random number evaluation.
American Journal of Mathematical and Management Sciences, 15(1,2):115-153, 1995.

53

M.J. Durst.
Using linear congruential generators for parallel random number generation.
In E.A. MacNair, K.J. Musselman, and P. Heidelberger, editors, Proceedings of the 1989 Winter Simulation Conference, pages 462-466, 1989.

54

W.F. Eddy.
Random number generators for parallel processors.
J. Comp. Appl. Math., 31:63-71, 1990.

55

J. Eichenauer and J. Lehn.
A non-linear congruential pseudo random number generator.
Statist. Papers, 27:315-326, 1986.

56

J. Eichenauer-Herrmann.
Inversive congruential pseudorandom numbers avoid the planes.
Math. Comp., 56:297-301, 1991.

57

J. Eichenauer-Herrmann.
Statistical independence of a new class of inversive congruential pseudorandom numbers.
Math. Comp., 60:375-384, 1993.

58

J. Eichenauer-Herrmann.
Compound nonlinear congruential pseudorandom numbers.
Monatsh. Math., 117:213-222, 1994.

59

J. Eichenauer-Herrmann and H. Grothe.
A remark on long-range correlations in multiplicative congruential pseudo random number generators.
Numer. Math., 56:609-611, 1989.

60

J. Eichenauer-Herrmann and H. Grothe.
Upper bounds for the beyer ratios of linear congruential generators.
J. Comput. Appl. Math., 31(1):73-80, 1990.

61

K. Entacher.
Selected random number generators in run tests.
Preprint, Department of Mathematics, University of Salzburg, Austria.

62

K. Entacher.
The PLAB Picturebook: Part III, Bad Subsequences of LCGs - The Results.
Report no. 06, PLAB - reports, University of Salzburg, 1997.
Available on the internet at http://random.mat.sbg.ac.at/team/.

63

K. Entacher.
Bad subsequences of well-known linear congruential pseudorandom number generators.
ACM Transactions on Modeling and Computer Simulation, 7(1):61-70, 1998.

64

K. Entacher.
On the Cray-System Random Number Generator.
SIMULATION, 72(3):163-169, 1999.

65

K. Entacher.
Parallel Streams of Linear Random Numbers in the Spectral Test.
ACM Transactions on Modeling and Computer Simulation, 9(1):31-44, 1999.

66

K. Entacher, P. Hellekalek, and P. L'Ecuyer.
Quasi-Monte Carlo Node Sets from Linear Congruential Generators.
In [187], pp. 188-198.

67

K. Entacher, A. Uhl, and S. Wegenkittl.
Analyzing Streams of Pseudorandom Numbers for Parallel Monte Carlo Integration.
In R. Wyrzykowski, H. Piech, M. Vajteršic, and P. Zinterhof, editors, Proceedings of the international Workshop Parallel Numerics' 97, pages 59-71, Zakopane, Poland, 1997.
Available at http://random.mat.sbg.ac.at.

68

K. Entacher, A. Uhl, and S. Wegenkittl.
Linear and Inversive Pseudorandom Numbers for Parallel and Distributed Simulation.
In Twelfth Workshop on Parallel and Distributed Simultation PADS'98, May 26th - 29th, Simulation Digest 28(1), ACM SIGSIM Newsletter, pages 90-97, Banff, Alberta, Canada, 1998. IEEE Computer Society, Los Alamitos, California.

69

K. Entacher, A. Uhl, and S. Wegenkittl.
Linear Congruential Generators for Parallel Monte-Carlo: the Leap-Frog Case.
Monte Carlo Methods and Appl., 4(1):1-16, 1998.

70

K. Entacher and S. Wegenkittl.
On the Relevance of Splitting Properties and the Compound Method in Parallel Applications of Pseudorandom Number Generators.
In M. Trobec, M. Vajtersic, P. Zinterhof, and B. Robic, editors, Proceedings of the international Workshop Parallel Numerics' 96, pages 64-74, Gozd Martuljek-Slovenia, 1996.

71

A. M. Ferrenberg, D.P. Landau, and Y.J. Wong.
Monte carlo simulations: hidden errors from ``good'' random number generators.
Phys. Rev. Lett., 69:3382-3384, 1992.

72

G.S. Fishman.
Multiplicative congruential random number generators with modulus $2^\beta$: an exhaustive analysis for $\beta = 32$ and a partial analysis for $\beta = 48$.
Math. Comp., 54:331-344, 1990.

73

G.S. Fishman.
Monte Carlo: Concepts, Algorithms, and Applications, volume 1 of Springer Series in Operations Research.
Springer, New York, 1996.

74

G.S. Fishman and L.R. Moore.
A statistical evaluation of multiplicative congruential random number generators with modulus $2^{31}-1$.
J. Amer. Statist. Assoc., 77:129-136, 1982.

75

G.S. Fishman and L.R. Moore.
An exhaustive analysis of multiplicative congruential random number generators with modulus $2^{31}-1$.
SIAM J. Sci. Stat. Comput., 7:24-45, 1986.
See erratum, ibid., 7:1058, 1986.

76

B.L. Fox.
Algorithm 647: Implementation and Efficientcy of Quasirandom Sequence Genterators.
ACM Transactions on Mathematical Software, 12(4):362-376, 1986.

77

W. Freiberger and U. Grenander.
A Short Course in Computational Probability and Statistics.
Springer-Verlag, 1971.

78

B. Gärtner.
Ein Reinfall mit Computer-Zufallszahlen.
Mitteilungen der Deutschen Mathematiker-Vereinigung (DMV), 2:55-60, 1999.
(In German).

79

J.E. Gentle.
Computer implementation of random number generators.
J. Comput. Appl. Math., 31(1):119-125, 1990.

80

H. Grothe.
Matrixgeneratoren zur Erzeugung gleichverteilter Pseudozufallsvektoren.
PhD thesis, Technische Hochschule Darmstadt, 1988.

81

A. Grube.
Mehrfach rekursiv-erzeugte Pseudo-Zufallszahlen.
Z. für angewandte Math. und Mechanik, 53:T223-T225, 1973.

82

A. Grube.
Mehrfach rekursiv erzeugte Zufallszahlen.
PhD thesis, University of Karlruhe, 1973.

83

R. Hamming.
Mathematical methods in large-scale computing units, by D.H. Lehmer.
Math. Rev., 13(1):495, 1952.

84

F. Härtel.
On combined random number generators.
In International Workshop on Mathematical Methods and Tools in Computer Simulation, pages 7-8. V. I. Smirnov Scientific Research Institute of Mathematics and Mechancis, 1994.

85

F. Härtel.
Zufallszahlen für Simulationsmodelle.
PhD thesis, Hochschule St. Gallen für Wirtschafts-, Rechts- und Sozialwissenschaften, St. Gallen, 1994.

86

M.J.R. Healy.
GLIM An Introduction.
Clarendon Press, Oxford, 1988.

87

P. Hellekalek.
Correlations between pseudorandom numbers: theory and numerical practice.
In P. Hellekalek, G. Larcher, and P. Zinterhof, editors, Proceedings of the 1st Salzburg Minisymposium on Pseudorandom Number Generation and Quasi-Monte Carlo Methods, Salzburg, Nov 18, 1994, volume ACPC/TR 95-4 of Technical Report Series, pages 43-73. ACPC - Austrian Center for Parallel Computation, University of Vienna, Austria, 1995.

88

P. Hellekalek.
Inversive pseudorandom number generators: concepts, results and links.
In C. Alexopoulos and D. Goldsman K. Kang, W.R. Lilegdon, editors, Proceedings of the 1995 Winter Simulation Conference, pages 255-262, 1995.

89

P. Hellekalek.
A Note on Pseudorandom Number Generators.
EUROSIM Simulations News Europe, 20:8-10, 1997.

90

P. Hellekalek.
Don't Trust Parallel Monte Carlo.
In Twelfth Workshop on Parallel and Distributed Simultation PADS'98, May 26th - 29th, pages 82-89, Banff, Alberta, Canada, 1998. IEEE Computer Society, Los Alamitos, California.

91

P. Hellekalek.
Good random number generators are (not so) easy to find.
Mathematics and Computers in Simulation, 46:485-505, 1998.

92

P. Hellekalek.
On the Assessment of Random and Quasi-Random Point Sets.
In P. Hellekalek and G. Larcher, editors, Random and Quasi-Random Point Sets, Lecture Notes in Statistics. Springer-Verlag, New York, 1998.

93

P. Hellekalek, K. Entacher, H. Leeb, O. Lendl, and S. Wegenkittl.
The PLAB www-server, Dept. of Mathematics, University Salzburg, Austria.
http://random.mat.sbg.ac.at, 1995.
Also accessible via ftp.

94

P. Hellekalek and G. Larcher (eds.).
Random and Quasi-Random Point Sets, volume 138 of Lecture Notes in Statistics.
Springer, Berlin, 1998.

95

M. Hennecke.
Parallel Random Number Generation on KSR1.
In R. Schumacher, editor, One Year KSR1 at the University of Mannheim, pages 34-39, Mannheim, 1993.
Available at http://www.uni-karlsruhe.de/~Michael.Hennecke/.

96

M. Hennecke.
RANEXP: experimental random number generator package.
Comp. Phys. Comm., 79:261-267, 1994.

97

M. Hennecke.
Parallel Random Number Generation and High Performance Fortran.
preprint, 1998.
submitted to Parallel Computing; available at http://www.uni-karlsruhe.de/~Michael.Hennecke/.

98

C. Herring and J.I. Palmore.
Random Number Generators are Caotic.
Communications of the ACM, 38(1):121-122, 1995.

99

D. Hoaglin.
Theoretical Properties of Congruential Random-Number Generators: An Empirical View.
Memorandum NS-340. Harvard University, Department of Statistics, 1976.

100

J. Honerkamp.
Stochastische Dynamische Systeme.
VCH Verlagsgesellschaft, Weinheim, 1990.

101

W. Hörmann.
The quality of non-uniform random numbers.
In H. Dyckhoff, U. Derigs, M. Salomon, and H.C. Tijms, editors, Operations Research Proceedings 1993, DGOR/NSOR, pages 329-335. Springer-Verlag, 1993.

102

W. Hörmann.
A Note on the Quality of Random Variates Generated by the Ratio of Uniforms Method.
ACM Transactions on Modeling and Computer Simulation, 4(1):96-106, 1994.

103

W. Hörmann.
The Transformed Rejection Method for Generating Poisson Random Variables.
Communications in Statistics: Simulation and Computation, 23(3):847-860, 1994.

104

W. Hörmann and G. Derflinger.
A portable uniform random number generator well suited for the rejection method.
ACM Transactions on Mathematical Software, 19(4):489-495, December 1993.

105

P.F. Hulquist.
A good random number generator for microcomputers.
Simulation, 57:4 :258-259, 1991.

106

D.W. Hutchinson.
A new uniform pseudo-random number generator.
Communications of the ACM, 9(6):432-433, 1966.

107

F. James.
A review of pseudorandom number generators.
Comp. Phys. Comm., 60:329-344, 1990.

108

F. James.
RANLUX: A Fortran implementation of the high-quality pseudorandom number generator of Lüscher.
Comp. Phys. Comm., 79:111-114, 1994.

109

B. Jansson.
Random number generators.
PhD thesis, University of Stockholm, 1966.
Victor Pettersons Bokindustri AB, also published by Almqvist and Wiksell.

110

L.P. Jennergren.
Another method for random number generation on microcomputers.
Simulation, 41 :79, 1983.

111

K. Kankaala, T. Ala-Nissila, and I. Vattulainen.
Bit-level correlations in some pseudorandom number generators.
Phys. Rev. E, 48:4211-4214, 1993.

112

C. Kao.
Decomposition with simulated division for effeciently generating random numbers.
Computers Ops Res., 21 (10):1089-1093, 1994.

113

C. Kao and H.C. Tang.
Symmetry property of multiplicative congruential random number generator in chi-square test.
Intern. J. Computer Math., 55 :113-118, 1995.

114

C. Kao and H.C. Tang.
Systematic searches for good multiple recursive random number generators.
Computers Ops Res., 24 (10):899-905, 1997.

115

C. Kao and H.C. Tang.
Upper Bounds in Spectral Test for Multiple Recursive Random Number Generators with Missing Terms.
Computers Math. Applic., 33 (4):119-125, 1997.

116

C. Kao and J.Y. Wong.
Several extensively tested random number generators.
Computers Ops Res., 21 :1035-1039, 1994.

117

C. Kao and J.Y Wong.
Random Number Generators with Long Period and Sound Statistical Properties.
Computers Math. Applic., 36 (3):113-121, 1998.

118

A. Karian and E. J. Dudewicz.
Modern Statistical Systems, and GPSS Simulation.
Computer Science Press, 1990.

119

W.D. Kelton, R.P. Sadowski, and D.A. Sadowski.
Simulation with Arena.
WCB/McGraw-Hill, 1998.

120

W.J. Kennedy and J.E. Gentle.
Statistical Computing.
Dekker, New York, 1980.

121

S. Kirkpatrick and E.P. Stoll.
A very fast shift-register sequence random number generator.
J. Comp. Physics, 40:517-526, 1981.

122

J.P.C. Kleijnen.
Pseudorandom number generation on supercomputers.
Supercomputer, 6:34-40, 1989.

123

J.P.C. Kleijnen.
Regression Metamodels for Simulation with Common Random Numbers: Comparison of Validation Tests and Confidence Intervals.
Management Science, 38(8):1164-1185, 1992.

124

J.P.C. Kleijnen and B. Annink.
Pseudorandom number generators for supercomputers and classical computers: A practical introduction.
European Journal of Operational Research, 63:76-85, 1992.

125

J.P.C. Kleijnen and B. Annink.
Vector Computers, Monte Carlo Simulation and Regression Analysis: An Introduction.
Management Science, 38(2):170-181, 1992.

126

D.E. Knuth.
The Art of Computer Programming, volume 2: Seminumerical Algorithms.
Addison-Wesley, Reading, MA, 2nd edition, 1981.

127

H. Kobayashi.
Modeling and Analysis: An Introduction to System Performance Evaluation Methodology.
Addison-Wesley, Reading, MA, 1978.

128

P. Labbe and M.J. Bureau.
Results from Statistical Analysis of Popular Pseudorandom Number Generators for Simulation.
In 1993 Canadian Conference on Electrical and Computer Engineering, volume 1, pages 131-135, Vancouver, 1993. IEEE Canada.

129

J.C. Lagarias.
Pseudorandom numbers.
Statistical Science, 8:31-39, 1993.

130

A.M. Law and W.D. Kelton.
Simulation Modeling and Analysis.
McGraw-Hill, New York, 2 edition, 1991.

131

P. L'Ecuyer.
Efficient and portable combined random number generators.
Comm. ACM, 31:742-749 and 774, 1988.

132

P. L'Ecuyer.
Random numbers for simulation.
Comm. ACM, 33:85-97, 1990.

133

P. L'Ecuyer.
Testing random number generators.
In Proceedings of the 1992 Winter Simulation Conference, pages 305-313. IEEE Press, 1992.

134

P. L'Ecuyer.
Uniform random number generation.
Ann. Oper. Res., 53:77-120, 1994.

135

P. L'Ecuyer.
Combined Multiple Recursive Random Number Generators.
Operations Research, 44:816-822, 1996.

136

P. L'Ecuyer.
Bad Lattice Structures for Vectors of Non-Successive Values Produced by Some Linear Recurrences.
INFORMS Journal on Computing, 9:57-60, 1997.

137

P. L'Ecuyer.
Tests Based on Sum-Functions of Spacings for Uniform Random Numbers.
Journal of Statistical Computation and Simulation, 59:251-269, 1997.

138

P. L'Ecuyer.
Good Parameter Sets for Combined Multiple Recursive Random Number Generators.
Manuscript from http://www.iro.umontreal.ca/; a shorter version will appear in Operations Research., 1998.

139

P. L'Ecuyer.
Random Number Generation.
In Jerry Banks, editor, Handbook of Simulation, Chapter 4. Wiley, 1998.

140

P. L'Ecuyer.
Random Number Generators and Empirical Tests.
In H. Niederreiter, P. Hellekalek, G. Larcher, and P. Zinterhof, editors, Monte Carlo and Quasi-Monte Carlo Methods 1996, volume 127 of Lecture Notes in Statistics, pages 124-138. Springer, 1998.

141

P. L'Ecuyer.
Tables of Linear Congruential Generators of Different Sizes and Good Lattice Structure.
Mathematics of Computation, 68(225):249-260, 1999.

142

P. L'Ecuyer and T.H. Andres.
A random number generator based on the combination of four LCGs.
Mathematics and Computers in Simulation, 44:99-107, 1997.

143

P. L'Ecuyer and F. Blouin.
Linear congruential generators of order $k>1$.
In M. Abrams, P. Haigh, and J. Comfort, editors, Proceedings of the 1988 Winter Simulation Conference, IEEE Press, pages 432-439, 1988.

144

P. L'Ecuyer, F. Blouin, and R. Couture.
A Search for Good Multiple Recursive Generators.
ACM Transactions on Modeling and Computer Simulation, 3:87-98, 1993.

145

P. L'Ecuyer, J. Cordeau, and R. Simard.
Close-Points Spatial Tests for Random Number Generators.
Manuscript from http://www.iro.umontreal.ca/; to appear in Operations Research., 1998.

146

P. L'Ecuyer, J.F. Cordeau, and A. Compagner.
Entropy-Based tests for Random Number Generators, 1998.
Manuscript available at http://www.iro.umontreal.ca/~lecuyer/papers.html.

147

P. L'Ecuyer and S. Côte.
Implementing a Random Number Package with Splitting Facilities.
ACM Transactions on Mathematical Software, 17(1):98-111, 1991.

148

P. L'Ecuyer and R. Couture.
An Implementation of the Lattice and Spectral Tests for Multiple Recursive Linear Random Number Generators.
INFORMS Journal on Computing, 9(2):209-217, 1997.

149

P. L'Ecuyer and Tezuka S.
Structural properties for two classes of combined random number generators.
Math. Comp., 57(196):735-746, 1991.

150

H. Leeb.
On the digit test.
In P. Hellekalek, G. Larcher, and P. Zinterhof, editors, Proceedings of the 1st Salzburg Minisymposium on Pseudorandom Number Generation and Quasi-Monte Carlo Methods, Salzburg, Nov 18, 1994, volume ACPC/TR 95-4 of Technical Report Series, pages 109-121. ACPC - Austrian Center for Parallel Computation, University of Vienna, Austria, 1995.

151

H. Leeb and S. Wegenkittl.
Inversive and linear congruential pseudorandom number generators in selected empirical tests.
ACM Transactions on Modeling and Computer Simulation, 7(2):272-286, 1997.

152

D.H. Lehmer.
Mathematical methods in large-scale computing units.
In Proc. 2nd Sympos. on Large-Scale Digital Calculating Machinery, Cambridge, MA, 1949, pages 141-146, Cambridge, MA, 1951. Harvard University Press.

153

D.H. Lehmer.
Random number generation on the BRL high-speed computing machines, by M.L. Juncosa.
Math. Rev., 15:559, 1954.

154

C. Lemieux and P. L'Ecuyer.
On Selection Criteria for Lattice Rules and Other Quasi-Monte Carlo Point Sets.
Mathematics and Computers in Simulation, to appear, 2000.

155

P.A. Lewis, A.S. Goodman, and J.M. Miller.
A pseudo-random number generator for the System/360.
IBM Syst. J., 8 :136-146, 1969.

156

J. Leydold, H. Leeb, and W. Hörmann.
Higher-Dimensional Properties of Non-Uniform Pseudo-Random Variates.
In [187], pp. 341-355.

157

P. Lorenz.
Begleitmaterial für den Kurs: Simulation und Animation.
http://simsrv.cs.uni-magdeburg.de/, 1997.

158

M. Lüscher.
A portable high-quality random number generator for lattice field theory simulations.
Comput. Phys. Comm., 74:100-110, 1994.

159

Ch. Ma.
Implementation of a Monte Carlo code on a parallel computer system.
Parallel Computing, 20:991-1005, 1994.

160

P.K. MacKeown.
Stochastic Simulation in Physics.
Springer-Verlag, Singapore, 1997.

161

N.M. Maclaren.
The Generation of Multiple Independent Sequences of Pseudorandom Numbers.
Appl. Statist., 38:351-359, 1989.

162

N.M. Maclaren.
A limit on the usable length of a pseudorandom sequence.
J. Statist. Comput. Simul., 42:47-54, 1992.

163

G. Marsaglia.
The structure of linear congruential sequences.
In S. K. Zaremba, editor, Applications of Number Theory to Numerical Analysis, pages 248-285. Academic Press, New York, 1972.

164

G. Marsaglia.
A current view of random number generators.
In L. Billard, editor, Computer Science and Statistics: The Interface, pages 3-10, Amsterdam, 1985. Elsevier Science Publishers B.V.

165

G. Marsaglia.
DIEHARD Random Number CD-ROM.
Department of Statistics and Supercomputer Computations Research Institute, Florida State University, 1995.
Can be downloaded from http://stat.fsu.edu/~geo/diehard.html (see also http://euler.bd.psu.edu/~naras/diehard/snapshots.html).

166

G. Marsaglia, B. Narasimhan, and A. Zaman.
A Random Number Generator for PC's.
Comp. Phys. Comm., 60:345-349, 1990.

167

G. Marsaglia and A. Zaman.
A new class of random number generators.
The Annals of Applied Probability, 1:462-480, 1991.

168

G. Marsaglia and A. Zaman.
Monkey tests for random number generators.
Computers Math. Applic., 26:1-10, 1993.

169

K.J. Marse and S.D. Roberts.
Implementing a portable FORTRAN Uniform (0,1) Generator.
Simulation, 14(4):135-139, 1983.

170

M. Mascagni.
Parallel linear congruential generators with prime moduli.
Parallel Computing, 24(5-6):923-936, 1998.

171

N. Masuda and F. Zimmermann.
PRNGlib: A Parallel Random Number Generator Library.
Technical report, Swiss Center for Scientific Computing, 1996.
Available at http://www.cscs.ch/Official/Publications.html.

172

The MathWorks, Inc.
MATLAB 4.0, 1992.
Homepage: http://www.mathworks.com/.

173

M. Matsumoto and Y. Kurita.
Twisted GFSR generators.
ACM Transactions on Modeling and Computer Simulation, 2(3):179-194, 1992.

174

M. Matsumoto and Y. Kurita.
Twisted GFSR generators II.
ACM Transactions on Modeling and Computer Simulation, 4:254-266, 1994.

175

M. Matsumoto and T. Nishimura.
Mersenne Twister: A 623-dimensionally equidistributed uniform pseudorandom number generator.
ACM Transactions on Modeling and Computer Simulation, 7(1):3-30, 1998.

176

O. Moeschlin, E. Grycko, C. Pohl, and F. Steinert.
Experimental Stochastics.
Springer-Verlag, Berlin Heidelberg, 1998.

177

C. Moler.
Cleve's Corner: Random thoughts.
MATLAB News & Notes, Fall 1998.
See http://www.mathworks.com/.

178

J.F. Monahan.
Accuracy in Random Number Generation.
Math. Comp., 45:559-568, 1985.

179

B.J.T. Morgan.
Elements of simulation.
Chapman and Hall, London, New York, 1986.

180

H.R. Neave.
On using the Box-Müller Transformation with Multiplicative Congruential Pseudo-random Number Generators.
Appl. Statist., 22:92-97, 1973.

181

H. Niederreiter.
Quasi-Monte Carlo methods and pseudo-random numbers.
Bull. Amer. Math. Soc., 84:957-1041, 1978.

182

H. Niederreiter.
Recent trends in random number generation and random vector generation.
Ann. Oper. Res., 31:323-345, 1991.

183

H. Niederreiter.
New methods for pseudorandom number and pseudorandom vector generation.
Proc. 1992 Winter Simulation Conference (Arlington, Va., 1992), IEEE Press, Piscataway, N.J., pages 264-269, 1992.

184

H. Niederreiter.
Random Number Generation and Quasi-Monte Carlo Methods.
SIAM, Philadelphia, 1992.

185

H. Niederreiter.
On a new class of pseudorandom numbers for simulation methods.
J. Comput. Appl. Math., 56:159-167, 1994.

186

H. Niederreiter.
New developments in uniform pseudorandom number and vector generation.
In H. Niederreiter and P. Jau-Shyong Shiue, editors, Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, volume 106 of Lecture Notes in Statistics. Springer, 1995.

187

H. Niederreiter and J. Spanier (eds.).
Monte Carlo and Quasi-Monte Carlo Methods 1998.
Springer, Berlin, 2000.

188

O.O. Odeyemi and P. Coddington.
Implementation of a Random Number Generator for High Performance Fortran.
In P.D. Coddington, editor, Journal of Undergraduate Research in High-Performance Computing, volume 5 of Technical Report SCCS-747. Northeast Parallel Architectures Center at Syracuse University, 1995.
Available at http://www.npac.syr.edu/projects/reu/.

189

S.K. Park and K.W. Miller.
Random number generators: good ones are hard to find.
Comm. ACM, 31:1192-1201, 1988.

190

S.H. Paskov.
New Methodologies for Valuing Derivatives.
In S. Pliska and M. Dempster, editors, Mathematics of Derivative Securities, pages 103-115, Cambridge, 1997. Cambridge University Press.

191

S.H. Paskov and J. Traub.
Faster Valuation of Financial Derivatives.
Journal of Portfolio Management, 22(1):113-120, 1995.

192

W.H. Payne, J.R. Rabung, and T.P. Bogyo.
Coding the lehmer pseudo-random number generator.
Communications of the ACM, 12 :85-86, 1969.

193

W. Pei-Chi.
Multiplicative, Congruential Random-Number Generators with Multiplier $\pm 2^{k_1} \pm 2^{k_2}$ and Modulus $2^p-1$.
ACM Transactions on Mathematical Software, 23(2):255-265, 1997.

194

O. E. Percus and P. A. Whitlock.
Theory and Application of Marsaglia's Monkey Test for Pseudorandom Number Generators.
ACM Transactions on Modeling and Computer Simulation, 5 (2):87-100, 1995.

195

O.E. Percus and M.H. Kalos.
Random Number Generators for MIMD Parallel Processors.
Journal of Parallel and Distributed Computing, 6:477-497, 1989.

196

O.E. Percus and J.K. Percus.
Intrinsice relations in the structure of linear congruential generators modulo $2^{\beta}$.
Statistics & Probability Letters, 15:381-383, 1992.

197

W.P. Petersen.
Some Vectorized Random Number Generators for Uniform, Normal, and Poisson Distributions for CRAY X-MP.
The Journal of Supercomputing, 1:327-335, 1988.

198

W.P. Petersen.
Some evaluations of Random Number Generators in real*8 Format.
Technical report, Swiss Center for Scientific Computing, 1996.
Available at http://www.cscs.ch/Official/Publication.html.

199

Pittsburgh Supercomputing Center, 4400 Fifth Avenue Pittsburgh, PA 15213, USA.
RANPACK a collection of random number generators, 1998.
http://www.psc.edu/general/software/packages/ranpack/ranpack.html.

200

W.H. Press, S.A. Teukolsky, W.T. Vetterling, and B.P. Flannery.
Numerical Recipes in C.
The Art of Scientific Computing. Cambridge University Press, 2 edition, 1992.
See also the online PostScript Edition http://cfatab.harvard.edu/nr/bookc.html.

201

B.D. Ripley.
The lattice structure of pseudo-random number generators.
Proc. Roy. Soc. London Ser. A, 389:197-204, 1983.

202

B.D. Ripley.
Uses and abuses of statistical simulation.
Mathematical Programming, 42:53-68, 1988.

203

B.D. Ripley.
Thoughts on pseudorandom number generators.
J. Comput. Appl. Math., 31:153-163, 1990.

204

S.M. Ross.
A Course in Simulation.
Macmillan Publishing Company, New York, 1990.

205

A. Rotenberg.
A new pseudo-random number generator.
J. Assoc. Comput. Mach., 7:75-77, 1960.

206

RWTH Communication Networks, Rheinisch-Westfälisch Technische Hochschule Aachen.
CNCL Communication Networks Class Library, 1.9 edition, 1997.
http://www.comnets.rwth-aachen.de/doc/cncl.html.

207

T.J. Schriber.
An Introduction to Simulation Using GPSS/H.
John Wiley, New York, 1990.

208

R. Sedgewick.
Algorithms.
Addison-Wesley, Reading, MA, 1983.
The german version Algorithmen appeared in 1991.

209

F. Sezgin.
Some comments on computer implementation of random number generators.
J. Comput. Appl. Math., 39:384-386, 1992.

210

F. Sezgin.
A random number generator for 16-bit microcomputers.
Computers Ops Res., 23 (2):193-198, 1996.

211

Y.S. Sherif and R.G. Dear.
Development of a new composite pseudo random number generator.
Microelectronics and Reliability, 30:545-553, 1990.

212

Yu.A. Shreider.
The Monte Carlo Method.
Pergamon Press Ltd., 1967.

213

J.T. Smith.
C++ For Scientists & Engeneers.
McGraw-Hill Book Company, New York, 1991.

214

I.M. Sobol' and Yu. L. Levitan.
A Pseudo-Random Number Generator for Personal Computers.
Comput. Math. Appl., 37:33-40, 1999.

215

A. Srinivasan, D.M. Ceperley, and M. Mascagni.
Random Number Generators for Parallel Applications.
In D. Ferguson, J.I. Siepmann, and D.G. Truhlar, editors, Monte Carlo Methods in Chemical Physics, Advances in Chemical Physics series. Wiley, New York, 1998, to appear.

216

E. Stadlober.
Die Gitterstruktur linearer und kombinierter Kongruenzgeneratoren.
Manuscript, Department of Statistics, TU Graz, Austria, 1992.

217

E. Stadlober and R. Kremer.
Sampling from discrete and continuous distributions with C-Rand.
In G. Pflug and U. Dieter, editors, Simulation and Optimization, volume 374 of Lecture Notes in Economics and Math. Systems, pages 154-162. Springer-Verlag, Berlin, 1992.

218

E. Stadlober and F. Niederl.
C-Rand: A package for generating nonuniform random variates.
In Compstat '94, Software Descriptions, pages 63-64, 1994.

219

R.S. Szankovich.
Ein statistischer Vergleich vierer Typen von Pseudozufallszahlen-Generatoren.
Master's thesis, Sozial- und Wirtschaftswissenschaftliche Fakultät, Universität Wien, Austria, 1996.

220

R.C. Tausworthe.
Random numbers generated by linear recurrence modulo two.
Math. Comp., 19:201-209, 1965.

221

S. Tezuka.
Financial Applications of Monte Carlo and Quasi-Monte Carlo Methods.
In [94].

222

S. Tezuka.
Uniform Random Numbers: Theory And Practice.
Kluwer Academic Publishers, 1995.

223

S. Tezuka and P. L'Ecuyer.
Analysis of Add-with-carry and Subtract-with-borrow generators.
In Proceedings of the 1992 Winter Simulation Conference, pages 443-447. IEEE Press, 1992.

224

S. Tezuka, P. L'Ecuyer, and R. Couture.
On Add-with-Carry and Subtract-with-Borrow Random Number Generators.
ACM Transactions on Modeling and Computer Simulation, 3:315-331, 1993.

225

The Numerical Algorithms Group Limited.
The NAG Fortran Library Manual, Mark 15, 1 edition, 1991.

226

K. Tocher.
The Art of Simulation.
English U. Press, London, 1963.

227

G. Ugrin-Šparac.
Stochastic Investigations of Pseudo-Random Number Generators.
Computing, 46:53-65, 1991.

228

G. Ugrin-Šparac and D. Ugrin-Šparac.
On a Possible Error of Type II in Statistical Evaluation of Pseudo-Random Number Generators.
Computing, 56:105-116, 1996.

229

I. Vattulainen.
Framework for Testing Random Numbers in Parallel Calculations.
To appear in Physical Review E, 1999.

230

I. Vattulainen, T. Ala-Nissila, and K. Kankaala.
Physical tests for random numbers in simulations.
Phys. Rev. Lett., 73:2513-2516, 1994.

231

I. Vattulainen, T. Ala-Nissila, and K. Kankaala.
Physical models as tests of randomness.
Phys. Rev. E, 52:3205-3214, 1995.

232

I. Vattulainen, K. Kankaala, J. Saarinen, and T. Ala-Nissila.
Influence of Implementation on the Properties of Pseudorandom Number Generators with a Carry Bit.
Manuscript hep-lat/9306008 v2, University of Helsinki, Finland, 1993.

233

I. Vattulainen, K. Kankaala, J. Saarinen, and T. Ala-Nissila.
A comparative study of some pseudorandom number generators.
Comp. Phys. Comm., 86:209-226, 1995.

234

S. Wegenkittl.
Empirical testing of pseudorandom number generators.
Master's thesis, University of Salzburg, 1995.

235

B.A. Wichmann and I.D. Hill.
An efficient and portable pseudo-random number generator.
Appl. Statist., 31:188-190, 1982.
Corrections and remarks in the same journal by Wichmann and Hill 33 (1984) 123; McLeod 34 (1985) 198-200; Zeisl 35 (1986) 89.

Acknowledgments:

Research supported by the Austrian Science Foundation (FWF), project no. P11143-MAT and P12441-MAT. The author wishes to thank the PLAB-group, Salzburg, for supporting his work, especially the head of the group Peter Hellekalek for many helpfull suggestions. Many thanks to Jürgen Eichenauer-Herrmann, Technische Hochschule Darmstadt, Germany, for the strong support with theoretical verifications of certain spectral tests.

Many thanks also to several people for their support concerning informations on random number generators: Ulrich Dieter, Technische Universität Graz; Daniel Dubois, Waterloo Maple Inc.; Neal Gaarder, Cray Research; Jörg Hintelman, Universität Essen; Jack P.C. Kleijnen, Tilburg University; Gerhard Larcher, Universität Salzburg; Pierre L`Ecuyer, University of Montreal; Michael Mascagni, University of Southern Mississippi; Cleve Moler, MathWorks, Inc.; Geoffrey Morgan and Gareth Shaw, NAG Ltd.; Jim Mott, SPSS Inc.; Peter J. Moylan, University of Newcastle; Harald Niederreiter, Austrian Academy of Sciences; Jean O'Reilly, SYMIX-APS & Simulation Development; Albert D. Rich, Soft Warehouse, Inc.; Ernst Stadlober, Technische Universität Graz; Robert G. Sargent, Syracuse University; Christoph Singer, Universität Passau;