Asymptotic non-negative correlation of some statistics used in testing the quality of random number generators

Authors

  • Maxim P. Savelov Steklov Mathematical Institute of Russian Academy of Sciences, 8 Gubkina Street, Moscow 119333, Russia

Keywords:

NIST STS, asymptotically non-negatively correlated statistics, asymptotically uncorrelated statistics, joint distribution of statistics, limit distributions, TestU01 package, random number generators
Supporting Agencies
The author expresses his gratitude to doctor of science (physics and mathematics) A. M. Zubkov for constant assistance in preparing work.

Abstract

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.

Author Biography

  • Maxim P. Savelov, Steklov Mathematical Institute of Russian Academy of Sciences, 8 Gubkina Street, Moscow 119333, Russia

    PhD (physics and mathematics); senior researcher at the department of discrete mathematics

References

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  10. Savelov MP. Limit joint distribution of the statistics of «Monobit test», «Frequency test within a block» and «Test for the longest run of ones in a block». Discrete Mathematics and Applications. 2024;34(5):291–301. DOI: 10.1515/dma-2024-0026.
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Published

2026-05-19

Issue

No. 1 (2026): Journal of the Belarusian State University. Mathematics and Informatics

Section

Computer Data Analysis

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Copyright (c) 2026 Journal of the Belarusian State University. Mathematics and Informatics

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How to Cite

[1]
Savelov, M.P. 2026. Asymptotic non-negative correlation of some statistics used in testing the quality of random number generators. Journal of the Belarusian State University. Mathematics and Informatics. 1 (May 2026), 16–21.