Geodesic
Limit distributions of the number of sets of $H$-equivalent segments in an equiprobable polynomial scheme of arrays
Diskretnaya Matematika, Tome 14 (2002) no. 1, pp. 82-98

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In this paper we study random variables which characterise collections of segments in an equiprobable polynomial scheme related by the $H$-equivalence. We give an upper bound for the variation distance between the distribution of the random variable $\xi_k(H)$ equal to the number of collections of $H$-equivalent segments and the Poisson distribution. We present sufficient conditions for the convergence of the distribution functions of the number of $H$-equivalent segments in the triangular array scheme of equiprobable polynomial trials to the normal law, the Poisson law, and the compound Poisson law. 
@article{DM_2002_14_1_a6,
     author = {A. M. Shoitov},
     title = {Limit distributions of the number of sets of $H$-equivalent segments in an equiprobable polynomial scheme of arrays},
     journal = {Diskretnaya Matematika},
     pages = {82--98},
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     volume = {14},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2002_14_1_a6/}
}
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A. M. Shoitov. Limit distributions of the number of sets of $H$-equivalent segments in an equiprobable polynomial scheme of arrays. Diskretnaya Matematika, Tome 14 (2002) no. 1, pp. 82-98. http://geodesic.mathdoc.fr/item/DM_2002_14_1_a6/