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Teoriya Veroyatnostei i ee Primeneniya, 1957, Volume 2, Issue 4, Pages 470–472 (Mi tvp4978)  

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
English version:
Theory of Probability and its Applications, 1957, Volume 2, Issue 4, Pages 461–465
DOI: https://doi.org/10.1137/1102032
Document Type: Article
Language: Russian
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
Citation in format AMSBIB
\Bibitem{SmiPot57}
\by S.~V.~Smirnov, M.~K.~Potapov
\paper A Nomogram for the Incomplete $\Gamma$-Function and the $\chi^2$ Probability Function
\jour Teor. Veroyatnost. i Primenen.
\yr 1957
\vol 2
\issue 4
\pages 470--472
\mathnet{http://mi.mathnet.ru/tvp4978}
\transl
\jour Theory Probab. Appl.
\yr 1957
\vol 2
\issue 4
\pages 461--465
\crossref{https://doi.org/10.1137/1102032}
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