Sum-discrepancy test on pseudorandom number generators

Mathematics and Computers in Simulation

Volumn 62, Issue 3-6, 2003, Pages 431-442

  Matsumoto, Makoto ^a   Nishimura, Takuji ^b  

^a HIROSHIMA UNIVERSITY   (Japan)

^b YAMAGATA UNIVERSITY   (Japan)

Author keywords

Fourier transform; Random number generation; Statistical test

Indexed keywords

COMPUTER SIMULATION; DISCRETE FOURIER TRANSFORMS; POISSON DISTRIBUTION; RECURSIVE FUNCTIONS; SAMPLING; STATISTICAL METHODS;

SUM-DISCREPANCY TESTS;

RANDOM PROCESSES;

EID: 0037417024     PISSN: 03784754     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0378-4754(02)00227-6     Document Type: Conference Paper

References (14)

1. P. Billingsley, Probability and Measure, Wiley, New York, 2nd ed., 1986.
2. Couture R., L'Ecuyer P., On the lattice structure of certain linear congruential sequences related to AWC/SWB generators. Math. Computat. 62:1994;798-808.
3. P. L'Ecuyer, P. Hellekalek, Random number generators: selection criteria and testing, in: P. Hellekalek, G. Larcher (Eds.), Random and Quasi-Random Point Sets, Lecture Notes in Statistics, vol. 138, Springer, New York, 1998, pp. 223-265.
4. P. L'Ecuyer, R. Simard, S. Wegenkittl, Sparse serial tests of uniformity for random number generators. SIAM J. Sci. Comput. 24 (2002) 652-668.
5. James F., RANLUX: A Fortran implementation of the high-quality pseudo-random number generator of Lüscher. Comput. Phys. Commun. 79:1994;111-114.
6. D.E. Knuth, The Art of Computer Programming, vol. 2, Seminumerical Algorithms. 3rd ed., Addison-Wesley, Reading, Mass., 1997.
7. H. Linhart, W. Zucchini, Model Selection, Wiley, New York, 1986.
8. Lüscher M., A portable high-quality random number generator for lattice field theory simulations. Comput. Phys. Commun. 79:1994;100-110.
9. Marsaglia G., Zaman A., A new class of random number generators. Ann. Appl. Prob. 1:1991;462-480.
10. Matsumoto M., Nishimura T., Mersenne Twister: A 623-dimensionally equidistributed uniform pseudo-random number generator. ACM Trans. Model. Comput. Simul. 8:1998;3-30.
11. M. Matsumoto, T. Nishimura, A nonempirical test on the weight of pseudorandom number generators, in: K.T. Fang, F.J. Hickernel, H. Niederreiter (Eds.), Monte Carlo and Quasi-Monte Carlo Methods 2000, Springer, New York, 2002, pp. 381-395.
12. S. Reiter, J.D. Stegeman, Classical Harmonic Analysis and Locally Compact Groups, Oxford Science Publications, Oxford, 2000.
13. Tezuka S., L'Ecuyer P., Couture R., On the add-with-carry and subtract-with-borrow random number generators. ACM Trans. Model. Comput. Simul. 3:1994;315-331.
14. M. Tiku, Noncentral Chi-square distribution, in: S. Kots, N.L. Johnson (Eds.), Encyclopedia of Statistical Sciences, vol. 6, Wiley, New York, 1981, pp. 276-278.