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The tail of the hypergeometric distribution

✍ Scribed by V. Chvátal

Publisher: Elsevier Science
Year: 1979
Tongue: English
Weight: 160 KB
Volume: 25
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(79)90084-0

No coin nor oath required. For personal study only.

✦ Synopsis

Investigating random discrete structures, one often needs upper bounds on the tail of the hypergeometric distribution, with k = (p+ t)n for p = M/N and some t 20. A particularly useful bound,

[l] W. Ha&ding, Probability inequalities far sums af bounded randam variables, J. Am, Statist.

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## Abstract An asymptotic representation is obtained for the hypergeometric function ${\bf F}(a+\lambda,b‐\lambda,c,1/2‐1/2z)$\nopagenumbers\end as $|\lambda|\rightarrow\infty$\nopagenumbers\end with $|{\rm ph}\,\lambda|<\pi$\nopagenumbers\end. It is uniformly valid in the __z__‐plane cut in an app