{"ID":2831843,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.08002","arxiv_id":"2512.08002","title":"The limit joint distributions of some statistics used in testing the quality of random number generators","abstract":"The limit joint distribution of statistics that are generalizations of some statistics from the NIST STS, TestU01, and other packages is found under the following hypotheses $H_0$ and $H_1$. Hypothesis $H_0$ states that the tested sequence is a sequence of independent random vectors with a known distribution, and the simple alternative hypothesis $H_1$ converges in some sense to $H_0$ with increasing sample size. In addition, an analogue of the Berry-Esseen inequality is obtained for the statistics under consideration, and conditions for their asymptotic independence are found.","short_abstract":"The limit joint distribution of statistics that are generalizations of some statistics from the NIST STS, TestU01, and other packages is found under the following hypotheses $H_0$ and $H_1$. Hypothesis $H_0$ states that the tested sequence is a sequence of independent random vectors with a known distribution, and the s...","url_abs":"https://arxiv.org/abs/2512.08002","url_pdf":"https://arxiv.org/pdf/2512.08002v2","authors":"[\"M. P. Savelov\"]","published":"2025-12-08T19:46:35Z","proceeding":"math.ST","tasks":"[\"math.ST\",\"stat.AP\"]","methods":"[]","has_code":false}