On the Performance of Birthday Spacings Tests with Certain Families of Random Number Generators
نویسندگان
چکیده
We examine how a statistical test based on discrete spacings between points, in 1 or more dimensions, detects the regularities in certain popular classes of random number generators. We provide a rule of thumb giving the minimal sample size for the test to reject the generator systematically, as a function of the generator's size (or period length), for generator families such as the linear congruential, Taus-worthe, nonlinear inversive, etc. Full period linear congruential generators with a good behavior in the spectral test, for example, start to fail the 2-dimensional test decisively at sample sizes approximately equal to the cubic root of their period length (or modulus).
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