Geodesic
Random partitions with two-side bounds and $(r,s)$-Bell polynomials in a parametric probabilistic model
Matematičeskie voprosy kriptografii, Tome 13 (2022) no. 3, pp. 77-92 Cet article a éte moissonné depuis la source Math-Net.Ru

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On the set of all partitions of an $n$-element set $X_n = \{1,2,\ldots,n\}$ into blocks with sizes exceeding the number $r \geq 0$ and not exceeding the number $s \leq n$ a probability measure is defined such that the probability of each partition with $k$ blocks is proportional to $\theta^k$, where $\theta > 0$ is the parameter of measure. The $(r,s)$-Bell polynomials are introduced and their asymptotic are investigated for $n,r,s \to \infty$. The asymptotic normality of the numbers of blocks in a random partition of $X_n$ in this model is proved, a statistical test for the uniformity hypothesis $H_0\colon \theta = 1$ against the alternatives $H_0\colon \theta \ne 1$ is constructed. 
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G. I. Ivchenko; Yu. I. Medvedev. Random partitions with two-side bounds and $(r,s)$-Bell polynomials in a parametric probabilistic model. Matematičeskie voprosy kriptografii, Tome 13 (2022) no. 3, pp. 77-92. http://geodesic.mathdoc.fr/item/MVK_2022_13_3_a4/

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