Geodesic
Integral limit theorems on large deviations for multidimensional hypergeometric distribution
Teoriâ veroâtnostej i ee primeneniâ, Tome 47 (2002) no. 1, pp. 71-79

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Integral large deviation theorems are obtained for multidimensional hypergeometric distribution. These theorems allow us to evaluate the probabilities of large deviations with the remainder term of order $O(1/N)$. The corresponding hypergeometric distribution of a random vector $(\mu_1,\dots,\mu_s)$ has the form $$ \mathbf{P}\{(\mu_1,\dots,\mu_s)=(k_1,\dots,k_s)\}=\frac{C_{M_1}^{k_1}\dotsb C_{M_s}^{k_s}}{C_N^n}\,, $$ and $k_j\le M_j$, $j=1,\dots,s$; 0 in the remaining cases.
Keywords: saddle-point method, hypergeometric distribution, large deviations, asymptotic estimates. 
@article{TVP_2002_47_1_a4,
     author = {A. N. Timashev},
     title = {Integral limit theorems on large deviations for multidimensional hypergeometric distribution},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {71--79},
     publisher = {mathdoc},
     volume = {47},
     number = {1},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2002_47_1_a4/}
}
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A. N. Timashev. Integral limit theorems on large deviations for multidimensional hypergeometric distribution. Teoriâ veroâtnostej i ee primeneniâ, Tome 47 (2002) no. 1, pp. 71-79. http://geodesic.mathdoc.fr/item/TVP_2002_47_1_a4/