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Teor. Veroyatnost. i Primenen., 2002, Volume 47, Issue 1, Pages 71–79 (Mi tvp2988)  

Integral limit theorems on large deviations for multidimensional hypergeometric distribution

A. N. Timashev

Academy of Federal Security Service of Russian Federation

Abstract: 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 $(\mu_1,…,\mu_s)$ has the form
$$ \mathbf{P}\{(\mu_1,…,\mu_s)=(k_1,…,k_s)\}=\frac{C_{M_1}^{k_1}\dotsb C_{M_s}^{k_s}}{C_N^n} , $$
and $k_j\le M_j$, $j=1,…,s$; 0 in the remaining cases.

Keywords: saddle-point method, hypergeometric distribution, large deviations, asymptotic estimates.

DOI: https://doi.org/10.4213/tvp2988

Full text: PDF file (697 kB)

English version:
Theory of Probability and its Applications, 2003, 47:1, 91–98

Bibliographic databases:

Received: 02.12.1998
Revised: 25.01.2000

Citation: A. N. Timashev, “Integral limit theorems on large deviations for multidimensional hypergeometric distribution”, Teor. Veroyatnost. i Primenen., 47:1 (2002), 71–79; Theory Probab. Appl., 47:1 (2003), 91–98

Citation in format AMSBIB
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\jour Theory Probab. Appl.
\yr 2003
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\pages 91--98
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