Abstract:

Testing the quality of pseudo random number generators is an important issue. In general, PRNGs' randomness is measured by whether it passes the statistical test of testing uniformity and independence. In 1998, Rudnick and Sarnak proposed the concept of Poissonian pair correlations of real number sequences in [0, 1), an i.i.d. random sequence (sampled from the uniform distribution in (0, 1)) has Poissonian pair correlations. In this paper we propose a single-level statistical test for the real number sequences in (0, 1) based on the Poissonian pair correlations. We carried out PPC test on common PRNGs (Linear Congruential Generators, Mersenne Twister, Matlab.rand function, and PRNG based on the overlap of irrational numbers $\pi$, etc), introducing the selection method of convergence criterion. The test results show that the statistical test can effectively test the uniformity and independence of the pseudo-random number sequence at the same time.

Key words: Poissonian Pair Correlations, Pseudo Random Number Generators, Statistical test, Single-level testing