Geodesic
Limit distributions of the number of not appeared $s$-tuples in a multinomial scheme
Teoriâ veroâtnostej i ee primeneniâ, Tome 19 (1974) no. 4, pp. 855-864 Cet article a éte moissonné depuis la source Math-Net.Ru

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Let $\mu_0(s,n,p_1\dots,p_N)$ be the number of not appeared $s$-tuples in a sequence of $n+s-1$ independent trials, at each trial the probability of event $i$ being $p_i$, $i=1,\dots,N$. We consider asymptotic behaviour of $\mu_0(s,n,p_1\dots,p_N)$ as $n,N$ and $n/N\to\infty$. In particular, we obtain conditions under which the distributions of $\mu_0(s,n,p_1\dots,p_N)$ converge to a Poisson distribution without assuming $p_1\dots,p_N$ to be close to $1/N$. 
@article{TVP_1974_19_4_a18,
     author = {V. F. Kolchin and V. P. Chistyakov},
     title = {Limit distributions of the number of not appeared $s$-tuples in a~multinomial scheme},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {855--864},
     year = {1974},
     volume = {19},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1974_19_4_a18/}
}
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V. F. Kolchin; V. P. Chistyakov. Limit distributions of the number of not appeared $s$-tuples in a multinomial scheme. Teoriâ veroâtnostej i ee primeneniâ, Tome 19 (1974) no. 4, pp. 855-864. http://geodesic.mathdoc.fr/item/TVP_1974_19_4_a18/