A Statistical Evaluation of Multiplicative Congruential Generators with Modulus 2 Super 31-1.
NORTH CAROLINA UNIV AT CHAPEL HILL
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This paper presents the results of empirically testing eight alternative multipliers for a multiplicative congruential generator with modulus 2 Super 31-1. The LLRANDOM number package Learmonth and Lewis 1973 uses one of the multipliers, the simulating programming language SIMSCRIPT II uses a second and the remaining six are the best of 50 candidate multipliers studied by Hoaglin 1976 using the theoretical spectral and lattice tests. The battery of tests raises serious doubts about three of the multipliers, including the one in LLRANDOM. The power of the tests is demonstrated by their rejection of RANDU, a notably poor random number generator. A comparison of the results for the eight multipliers with the eight worst multipliers with regard to 2-tuples in Hoaglin1976 failed to show any apparent gross differences. Since examination of performance on the lattice test revealed that the 16 multipliers clustered in performance when compared to RANDU, one may conjecture that the poorer lattice test performance for the worst eight is too subtle for detection by our empirical tests. Since this failure may not be as serious as the lattice test implies, one may want to revise upward the criteria for acceptable performance on the lattice tests and similarly on the spectral test.
- Statistics and Probability