next up previous contents
Next: About this document Up: A collection of selected Previous: Conclusion

References

1
L. Afflerbach. Die Gütebewertung von Pseudo-Zufallszahlen-Generatoren aufgrund theoretischer Analysen und algorithmischer Berechnungen. Grazer Mathematische Berichte, 309, 1990.

2
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.

3
L. Afflerbach and R. Weilbächer. The Exact Determination of Rectangle Discrepancy for Linear Congruential Pseudorandom Numbers. Math. Comp., 53(187):343-354, 1989.

4
J. Ahrens, U. Dieter, and A. Grube. Pseudo-random numbers: a new proposal for the choice of multiplicators. Computing, 6:121-138, 1970.

5
N.S. Altman. Bit-wise behavior of random number generators. SIAM J. Sci. Stat. Comput., 9:941-949, 1988.

6
S.L. Anderson. Random number generators on vector supercomputers and other advanced architectures. SIAM Rev., 32:221-251, 1990.

7
F. Anscombe. Computing in Statistical Science through APL. Springer Series in Statistics. Springer, New York, Heidelberg, Berlin, 1981.

8
A.C. Atkinson. Tests of Pseudo-random Numbers. Appl. Statist., 29(2):164-171, 1980.

9
I. Borosh and H. Niederreiter. Optimal multipliers for pseudo-random number generation by the linear congruential method. BIT, 23:65-74, 1983.

10
P. Bratley, B.L. Fox, and L.E. Schrage. A Guide to Simulation. Springer, New York, 2nd edition, 1987.

11
M. Brown and H. Solomon. On combining pseudorandom number generators. Annals of Statistics, 1:691-695, 1979.

12
D.G. Carta. Two fast implementations of the ``minimal standard'' random number generator. Comm. ACM, 33 :87-88, 1990.

13
B.J. Collings. Compound random number generators. J. Amer. Statist. Assoc., 82:525-527, 1987.

14
A. Compagner. Operational conditions for random-number generation. Phys. Rev. E., 52:5634-5645, 1995.

15
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.

16
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.

17
R. Couture and P. L'Ecuyer. Orbits and Lattices for Linear Random Number Generators with Composite Moduli. Math. Comp., 65:189-201, 1996.

18
R. Couture and P. L'Ecuyer. Distribution Properties of Multiply-with-Carry Random Number Generators. Math. Comp., 66:591-607, 1997.

19
R.R. Coveyou and R.D. MacPherson. Fourier analysis of uniform random number generators. J. Assoc. Comput. Mach., 14:100-119, 1967.

20
A. De Matteis, J. Eichenauer-Herrmann, and H. Grothe. Computation of critical distances within multiplicative congruential pseudorandom number sequences. J. Comp. Appl. Math., 39:49-55, 1992.

21
A. De Matteis and S. Pagnutti. Parallelization of random number generators and long-range correlations. Numer. Math., 53:595-608, 1988.

22
A. De Matteis and S. Pagnutti. A class of parallel random number generators. Parallel Comput., 13:193-198, 1990.

23
A. De Matteis and S. Pagnutti. Long-range correlations in linear and non-linear random number generators. Parallel Comput., 14:207-210, 1990.

24
A. De Matteis and S. Pagnutti. Critical distances in pseudorandom sequences generated with composite moduli. Intern. J. Computer Math., 43:189-196, 1992.

25
A. De Matteis and S. Pagnutti. Long-range correlation analysis of the Wichmann-Hill random number generator. Statistics and Computing, 3:67-70, 1993.

26
A. De Matteis and S. Pagnutti. Controlling correlations in parallel Monte Carlo. Parallel Comput., 21:73-84, 1995.

27
U. Dieter. How to calculate shortest vectors in a lattice. Math. Comp., 29:827-833, 1975.

28
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.

29
U. Dieter. Erzeugung von gleichverteilten Zufallszahlen. In Jahrbuch Überblicke Mathematik 1993, pages 25-44, Braunschweig, 1993. Vieweg.

30
U. Dieter and J.H. Ahrens. Uniform random numbers. Inst. f. Math. Stat., Technische Hochschule Graz, Graz, 1974.

31
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.

32
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.

33
W.F. Eddy. Random number generators for parallel processors. J. Comp. Appl. Math., 31:63-71, 1990.

34
J. Eichenauer and J. Lehn. A non-linear congruential pseudo random number generator. Statist. Papers, 27:315-326, 1986.

35
J. Eichenauer-Herrmann. Inversive congruential pseudorandom numbers avoid the planes. Math. Comp., 56:297-301, 1991.

36
J. Eichenauer-Herrmann. Statistical independence of a new class of inversive congruential pseudorandom numbers. Math. Comp., 60:375-384, 1993.

37
J. Eichenauer-Herrmann. Compound nonlinear congruential pseudorandom numbers. Monatsh. Math., 117:213-222, 1994.

38
K. Entacher. Selected random number generators in run tests. Preprint, Department of Mathematics, University of Salzburg, Austria.

39
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/.

40
K. Entacher. A Remark on a Cray System Pseudorandom Number Generator. Preprint, Department of Mathematics, University of Salzburg, Austria, submitted for publication, 1998.

41
K. Entacher. Bad subsequences of well-known linear congruential pseudorandom number generators. ACM Transactions on Modeling and Computer Simulation, 8(1), 1998, to appear.

42
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.

43
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.

44
G.S. Fishman. Multiplicative congruential random number generators with modulus tex2html_wrap_inline2535: an exhaustive analysis for tex2html_wrap_inline2537 and a partial analysis for tex2html_wrap_inline2539. Math. Comp., 54:331-344, 1990.

45
G.S. Fishman. Monte Carlo: Concepts, Algorithms, and Applications, volume 1 of Springer Series in Operation Research. Springer, New York, 1996.

46
G.S. Fishman and L.R. Moore. A statistical evaluation of multiplicative congruential random number generators with modulus tex2html_wrap_inline2541. J. Amer. Statist. Assoc., 77:129-136, 1982.

47
G.S. Fishman and L.R. Moore. An exhaustive analysis of multiplicative congruential random number generators with modulus tex2html_wrap_inline2541. SIAM J. Sci. Statist. Comput., 7:24-45, 1986. See erratum, ibid., 7:1058, 1986.

48
W. Freiberger and U. Grenander. A Short Course in Computational Probability and Statistics. Springer-Verlag, 1971.

49
H. Grothe. Matrixgeneratoren zur Erzeugung gleichverteilter Pseudozufallsvektoren. PhD thesis, Technische Hochschule Darmstadt, 1988.

50
A. Grube. Mehrfach rekursiv-erzeugte Pseudo-Zufallszahlen. Z. für angewandte Math. und Mechanik, 53:T223-T225, 1973.

51
A. Grube. Mehrfach rekursiv erzeugte Zufallszahlen. PhD thesis, University of Karlruhe, 1973.

52
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.

53
F. Härtel. Zufallszahlen für Simulationsmodelle. PhD thesis, Hochschule St. Gallen für Wirtschafts-, Rechts- und Sozialwissenschaften, St. Gallen, 1994.

54
P. Hellekalek. Inversive pseudorandom number generators. In C. Alexopoulos and D. Goldsman K. Kang, W.R. Lilegdon, editors, Proceedings of the 1995 Winter Simulation Conference, 1995.

55
P. Hellekalek, K. Entacher, H. Leeb, O. Lendl, and S. Wegenkittl. The PLAB www-server. http://random.mat.sbg.ac.at, 1995. Also accessible via ftp.

56
D. Hoaglin. Theoretical Properties of Congruential Random-Number Generators: An Empirical View. Memorandum NS-340. Harvard University, Department of Statistics, 1976.

57
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.

58
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.

59
W. Hörmann and G. Derflinger. A portable random number generator well suited for the rejection method. ACM Transactions on Mathematical Software, 19(4):489-495, December 1993.

60
P.F. Hulquist. A good random number generator for microcomputers. Simulation, 57:4 :258-259, 1991.

61
F. James. A review of pseudorandom number generators. Comp. Phys. Comm., 60:329-344, 1990.

62
L.P. Jennergren. Another method for random number generation on microcomputers. Simulation, 41 :79, 1983.

63
K. Kankaala, T. Ala-Nissila, and I. Vattulainen. Bit-level correlations in some pseudorandom number generators. Phys. Rev. E, 48:4211-4214, 1993.

64
A. Karian and E. J. Dudewicz. Modern Statistical Systems, and GPSS Simulation. Computer Science Press, 1990.

65
W.J. Kennedy and J.E. Gentle. Statistical Computing. Dekker, New York, 1980.

66
S. Kirkpatrick and E.P. Stoll. A very fast shift-register sequence random number generator. J. Comp. Physics, 40:517-526, 1981.

67
D.E. Knuth. The Art of Computer Programming, volume 2: Seminumerical Algorithms. Addison-Wesley, Reading, MA, 2nd edition, 1981.

68
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.

69
J.C. Lagarias. Pseudorandom numbers. Statistical Science, 8:31-39, 1993.

70
P. L'Ecuyer. Efficient and portable combined random number generators. Comm. ACM, 31:742-749 and 774, 1988.

71
P. L'Ecuyer. Random numbers for simulation. Comm. ACM, 33:85-97, 1990.

72
P. L'Ecuyer. Testing random number generators. In Proceedings of the 1992 Winter Simulation Conference, pages 305-313. IEEE Press, 1992.

73
P. L'Ecuyer. Uniform random number generation. Ann. Oper. Res., 53:77-120, 1994.

74
P. L'Ecuyer. Combined Multiple Recursive Random Number Generators. Operations Research, 44:816-822, 1996.

75
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.

76
P. L'Ecuyer. Tables of Linear Congruential Generators of Different Sizes and Good Lattice Structure. Mathematics of Computation, to appear, 1998.

77
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.

78
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.

79
P. L'Ecuyer, A. Compagner, and J.F. Cordeau. Entropy-Based tests for Random Number Generators, 1997. Submitted for publication.

80
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):206-217, 1997.

81
P. L'Ecuyer and Tezuka S. Structural properties for two classes of combined random number generators. Math. Comp., 57(196):735-746, 1991.

82
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.

83
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.

84
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.

85
Ch. Ma. Implementation of a Monte Carlo code on a parallel computer system. Parallel Computing, 20:991-1005, 1994.

86
N.M. MacLaren. The Generation of Multiple Independent Sequences of Pseudorandom Numbers. Appl. Statist., 38:351-359, 1989.

87
N.M. MacLaren. A limit on the usable length of a pseudorandom sequence. J. Statist. Comput. Simul., 42:47-54, 1992.

88
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.

89
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.

90
G. Marsaglia, B. Narasimhan, and A. Zaman. A random number generator for pc's. Comp. Phys. Comm., 60:345-349, 1990.

91
G. Marsaglia and A. Zaman. A new class of random number generators. The Annals of Applied Probability, 1:462-480, 1991.

92
M. Matsumoto and Y. Kurita. Twisted GFSR generators. ACM Transactions on Modeling and Computer Simulation, 2(3):179-194, 1992.

93
M. Matsumoto and Y. Kurita. Twisted GFSR generators II. ACM Transactions on Modeling and Computer Simulation, 4:254-266, 1994.

94
M. Matsumoto and T. Nishimura. Mersenne Twister: A 623-dimensionally equidistributed uniform pseudorandom number generator. ACM Transactions on Modeling and Computer Simulation, 8(1), 1998, to appear.

95
H. Niederreiter. Quasi-Monte Carlo methods and pseudo-random numbers. Bull. Amer. Math. Soc., 84:957-1041, 1978.

96
H. Niederreiter. Recent trends in random number generation and random vector generation. Ann. Oper. Res., 31:323-345, 1991.

97
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.

98
H. Niederreiter. Random Number Generation and Quasi-Monte Carlo Methods. SIAM, Philadelphia, 1992.

99
H. Niederreiter. On a new class of pseudorandom numbers for simulation methods. J. Comput. Appl. Math., 56:159-167, 1994.

100
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.

101
S.K. Park and K.W. Miller. Random number generators: good ones are hard to find. Comm. ACM, 31:1192-1201, 1988.

102
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.

103
W. H. et al Press. Numerical Recipes in C. The Art of Scientific Computing. Cambridge University Press, 1992.

104
B.D. Ripley. The lattice structure of pseudo-random number generators. Proc. Roy. Soc. London Ser. A, 389:197-204, 1983.

105
B.D. Ripley. Uses and abuses of statistical simulation. Mathematical Programming, 42:53-68, 1988.

106
B.D. Ripley. Thoughts on pseudorandom number generators. J. Comput. Appl. Math., 31:153-163, 1990.

107
Y.S. Sherif and R.G. Dear. Development of a new composite pseudo random number generator. Microelectronics and Reliability, 30:545-553, 1990.

108
E. Stadlober. Die Gitterstruktur linearer und kombinierter Kongruenzgeneratoren. Preprint, Department of Statistics, TU Graz, Austria, 1992.

109
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.

110
E. Stadlober and F. Niederl. C-Rand: A package for generating nonuniform random variates. In Compstat '94, Software Descriptions, pages 63-64, 1994.

111
R.S. Szankovich. Ein statistischer Vergleich vierer Typen von Pseudozufallszahlen-Generatoren. Master's thesis, Sozial- und Wirtschaftswissenschaftliche Fakultät, Universität Wien, Austria, 1996.

112
R.C. Tausworthe. Random numbers generated by linear recurrence modulo two. Math. Comp., 19:201-209, 1965.

113
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.

114
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.

115
The Numerical Algorithms Group Limited. The NAG Fortran Library Manual, Mark 15, 1 edition, 1991.

116
G. Ugrin-Sparac. Stochastic Investigations of Pseudo-Random Number Generators. Computing, 46:53-65, 1991.

117
G. Ugrin-Sparac and D. Ugrin-Sparac. On a Possible Error of Type II in Statistical Evaluation of Pseudo-Random Number Generators. Computing, 56:105-116, 1996.

118
I. Vattulainen, T. Ala-Nissila, and K. Kankaala. Physical tests for random numbers in simulations. Phys. Rev. Lett., 73:2513-2516, 1994.

119
I. Vattulainen, T. Ala-Nissila, and K. Kankaala. Physical models as tests of randomness. Phys. Rev. E, 52:3205-3214, 1995.

120
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.

121
S. Wegenkittl. Empirical testing of pseudorandom number generators. Master's thesis, University of Salzburg, 1995.

122
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.


Overview * Team * Generators * Tests * News * Literature * Links



Karl Entacher
Tue Jan 13 18:10:31 MET 1998