Geodesic
On the limiting behaviour of extreme order statistics in polynomial scheme
Teoriâ veroâtnostej i ee primeneniâ, Tome 14 (1969) no. 3, pp. 476-487

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A sequence of $n$ independent trials with $N$ equiprobable events $E_1,\dots,E_N$ is considered. Let $\eta_i$ be the number of occurances of the event $E_i$ and $\eta_{(i)}$ be the $i$th order statistic for the sample $\eta_1,\dots,\eta_N$. The asymptotic behaviour of $\eta_{(i)}$ and $\eta_{(N-i+1)}$ as $n,\ N\to\infty$ is investigated by means of conversion to the analogous problem for order statistics for independent Poisson random variables. 
@article{TVP_1969_14_3_a6,
     author = {V. F. Kolchin},
     title = {On the limiting behaviour of extreme order statistics in polynomial scheme},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {476--487},
     publisher = {mathdoc},
     volume = {14},
     number = {3},
     year = {1969},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1969_14_3_a6/}
}
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V. F. Kolchin. On the limiting behaviour of extreme order statistics in polynomial scheme. Teoriâ veroâtnostej i ee primeneniâ, Tome 14 (1969) no. 3, pp. 476-487. http://geodesic.mathdoc.fr/item/TVP_1969_14_3_a6/