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Limit joint distribution of the statistics of «Monobit test», «Frequency Test within a Block» and «Binary Matrix Rank Test»

  • Maksim P. Savelov EMAIL logo
Published/Copyright: September 6, 2025

Abstract

In the case when the tested sequence consists of independent random variables having a Bernoulli distribution with the parameter p=12 the limit joint distribution of the statistics T1, T2, T3 of the following three tests of the NIST package is obtained: «Monobit Test», «Frequency Test within a Block» and «Binary Matrix Rank Test». Necessary and sufficient conditions for asymptotic uncorrelatedness and/or asymptotic independence of these statistics are obtained. It is proved that the covariance matrix C = ‖Cij‖ of the limit distribution of the vector (T1, T2, T3) satisfies the relations C12 = C21 = C13 = C31 = 0, C23 = C32 ≥ 0. The limit behavior of the vector (T1, T2, T3) is described for a wide class of values p12.


Originally published in Diskretnaya Matematika (2022) 34, №4, 84–98 (in Russian).


Acknowledgment

The author is grateful to A.M. Zubkov for constant attention.

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Received: 2022-06-14
Published Online: 2025-09-06
Published in Print: 2025-08-26

© 2025 Walter de Gruyter GmbH, Berlin/Boston

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