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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»

  • Maksim P. Savelov EMAIL logo
Published/Copyright: October 17, 2024

Abstract

For a sequence consisting 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 «Test for the Longest Run of Ones in a Block». It is proved that the covariance matrix C of the limit distribution of the vector (T1, T2, T3) satisfies the relations C12 = C21 = C13 = C31 = 0, C23 = C32 ≥ 0. For arbitrary p necessary and sufficient conditions for asymptotic uncorrelatedness and/or asymptotic independence of these statistics are obtained. The limit behavior of the vector (T1, T2, T3) is described for a wide class of values p 12 .


Originally published in Diskretnaya Matematika (2022) 34, №3, 70–84 (in Russian).


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Received: 2022-06-14
Published Online: 2024-10-17
Published in Print: 2024-10-28

© 2024 Walter de Gruyter GmbH, Berlin/Boston

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