Geodesic
The limit joint distributions of statistics of four tests of the NIST package
Diskretnaya Matematika, Tome 33 (2021) no. 2, pp. 141-154

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For sequences of independent random variables having a Bernoulli distribution with parameter $p$ the limit joint distribution of statistics of four tests of the NIST statistical package («Monobit Test», «Frequency Test within a Block», «Runs Test» and a generalization of «Non-overlapping Template Matching Test») is obtained. Conditions of asymptotic uncorrelatedness and/or asymptotic independence of these statistics are given.
Keywords: joint distribution of statistics, NIST package, «Monobit Test», «Frequency Test within a Block», «Non-overlapping Template Matching Test», «Runs Test», asymptotically independent statistics, asymptotically uncorrelated statistics. 
@article{DM_2021_33_2_a9,
     author = {M. P. Savelov},
     title = {The limit joint distributions of statistics of four tests of the {NIST} package},
     journal = {Diskretnaya Matematika},
     pages = {141--154},
     publisher = {mathdoc},
     volume = {33},
     number = {2},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2021_33_2_a9/}
}
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M. P. Savelov. The limit joint distributions of statistics of four tests of the NIST package. Diskretnaya Matematika, Tome 33 (2021) no. 2, pp. 141-154. http://geodesic.mathdoc.fr/item/DM_2021_33_2_a9/