Asymptotic non-negative correlation of some statistics used in testing the quality of random number generators - Savelov, Maxim P. (Journal of the Belarusian State University. Mathematics and Informatics, 2026)
The problem of testing the hypothesis, stating that the tested sequence consists of independent random variables with a given polynomial distribution, is considered. To solve this problem four types of statistics that are generalisations of statistics of tests of the NIST STS, TestU01 and other packages are used. It is proved that many of these statistics, including 10 statistics of the NIST STS, are asymptotically non-negatively correlated, and some of them, in particular some of the 10 statistics of the NIST STS, are asymptotically uncorrelated.
Keywords: NIST STS; asymptotically non-negatively correlated statistics; asymptotically uncorrelated statistics; joint distribution of statistics; limit distributions; TestU01 package; random number generators