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Teoriya Veroyatnostei i ee Primeneniya, 1957, Volume 2, Issue 4, Pages 470–472
(Mi tvp4978)
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Short Communications
A Nomogram for the Incomplete $\Gamma$-Function and the $\chi^2$ Probability Function
S. V. Smirnov, M. K. Potapov Moscow
Abstract:
A nomogram is constructed of the function $P(\chi^2,n)=1-\Gamma(m,y)$. For $n\geq30$ the function $\Pi$ is introduced, which is obtained from $P$ by means of the transformation $t=\sqrt{2\chi^2}-\sqrt{2n},x=\sqrt{2/n}$, while for $1\leq n\leq30$ the function $P$ itself is considered.
The nomogram is valid for the following values of $n,t,\chi^2$ and $P$: $1\leq n\leq\infty$; $|t|\leq3.1$;
$1\leq\chi^2\leq30$; $0.001\leq P\leq0.999$. The absolute error in the entire nomogram for $0.01\leq P\leq0.99$ is found not to exceed $0.005$.
Received: 21.06.1957
Citation:
S. V. Smirnov, M. K. Potapov, “A Nomogram for the Incomplete $\Gamma$-Function and the $\chi^2$ Probability Function”, Teor. Veroyatnost. i Primenen., 2:4 (1957), 470–472; Theory Probab. Appl., 2:4 (1957), 461–465
Linking options:
https://www.mathnet.ru/eng/tvp4978 https://www.mathnet.ru/eng/tvp/v2/i4/p470
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Statistics & downloads: |
Abstract page: | 146 | Full-text PDF : | 57 |
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