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The limit joint distributions of some statistics used in testing the quality of random number generators

Published: December 8, 2025 | arXiv ID: 2512.08002v1

By: M. P. Savelov

Potential Business Impact:

Checks if computer numbers are truly random.

Business Areas:
A/B Testing Data and Analytics

The limit joint distribution of statistics that are generalizations of some statistics from the NIST STS, TestU01, and other packages is found under the following hypotheses $H_0$ and $H_1$. Hypothesis $H_0$ states that the tested sequence is a sequence of independent random vectors with a known distribution, and the simple alternative hypothesis $H_1$ converges in some sense to $H_0$ with increasing sample size. In addition, an analogue of the Berry-Esseen inequality is obtained for the statistics under consideration, and conditions for their asymptotic independence are found.

Country of Origin
🇷🇺 Russian Federation

Page Count
24 pages

Category
Mathematics:
Statistics Theory