Teoriâ veroâtnostej i ee primeneniâ, Tome 19 (1974) no. 4, pp. 855-864
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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/
@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/}
}
TY - JOUR
AU - V. F. Kolchin
AU - V. P. Chistyakov
TI - Limit distributions of the number of not appeared $s$-tuples in a multinomial scheme
JO - Teoriâ veroâtnostej i ee primeneniâ
PY - 1974
SP - 855
EP - 864
VL - 19
IS - 4
UR - http://geodesic.mathdoc.fr/item/TVP_1974_19_4_a18/
LA - ru
ID - TVP_1974_19_4_a18
ER -
%0 Journal Article
%A V. F. Kolchin
%A V. P. Chistyakov
%T Limit distributions of the number of not appeared $s$-tuples in a multinomial scheme
%J Teoriâ veroâtnostej i ee primeneniâ
%D 1974
%P 855-864
%V 19
%N 4
%U http://geodesic.mathdoc.fr/item/TVP_1974_19_4_a18/
%G ru
%F TVP_1974_19_4_a18
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 $1/N$.
