Sum-discrepancy test on pseudorandom number generators

Makoto Matsumoto and Takuji Nishimura

Mathematics and Computers in Simulation (MATCOM), 2003, vol. 62, issue 3, 431-442

Abstract: We introduce a non-empirical test on pseudorandom number generators (prng), named sum-discrepancy test. We compute the distribution of the sum of consecutive m outputs of a prng to be tested, under the assumption that the initial state is uniformly randomly chosen. We measure its discrepancy from the ideal distribution, and then estimate the sample size which is necessary to reject the generator. These tests are effective to detect the structure of the outputs of multiple recursive generators with small coefficients, in particular that of lagged Fibonacci generators such as random() in BSD-C library, as well as add-with-carry and subtract-with-borrow generators like RCARRY. The tests show that these generators will be rejected if the sample size is of order 106.

Keywords: Random number generation; Statistical test; Fourier transform (search for similar items in EconPapers)
Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:62:y:2003:i:3:p:431-442

DOI: 10.1016/S0378-4754(02)00227-6

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