Geodesic
Limit joint distribution of $\phi$-entropy test>> statistics
Diskretnaya Matematika, Tome 35 (2023) no. 3, pp. 60-70

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Consider a sequence of independent polynomial trials with $s$ outcomes. «Approximate Entropy Test» is one of the tools used to test the hypothesis of the equiprobability of outcomes. In 2000 A.L. Rukhin proposed a more general «Approximate $\phi$-Entropy Test» and found the limiting distribution of its statistic $T^{\phi}$. In the present paper a generalization of this result is obtained in a simpler way. In addition, the limiting joint distribution $(T^{\phi_1}, \ldots, T^{\phi_r}$) is obtained in the situation with equiprobable outcomes. As a corollary, in the case $s=2$ the limiting joint distribution of the statistics of two NIST package tests «Approximate Entropy Test» and «Serial Test» is found for a sequence of independent Bernoulli trials with parameter $\frac12$.
Keywords: goodness of fit test, «Approximate Entropy Test», «Approximate $\phi$-Entropy Test», «Serial Test», NIST package. 
@article{DM_2023_35_3_a5,
     author = {M. P. Savelov},
     title = {Limit joint distribution of {<<Approximate} $\phi$-entropy test>> statistics},
     journal = {Diskretnaya Matematika},
     pages = {60--70},
     publisher = {mathdoc},
     volume = {35},
     number = {3},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2023_35_3_a5/}
}
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M. P. Savelov. Limit joint distribution of <> statistics. Diskretnaya Matematika, Tome 35 (2023) no. 3, pp. 60-70. http://geodesic.mathdoc.fr/item/DM_2023_35_3_a5/