A Nomogram for the Incomplete $\Gamma$-Function and the $\chi^2$ Probability Function
Teoriâ veroâtnostej i ee primeneniâ, Tome 2 (1957) no. 4, pp. 470-472
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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 $0.005$.
@article{TVP_1957_2_4_a3,
author = {S. V. Smirnov and M. K. Potapov},
title = {A {Nomogram} for the {Incomplete} $\Gamma${-Function} and the $\chi^2$ {Probability} {Function}},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {470--472},
year = {1957},
volume = {2},
number = {4},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1957_2_4_a3/}
}
TY - JOUR AU - S. V. Smirnov AU - M. K. Potapov TI - A Nomogram for the Incomplete $\Gamma$-Function and the $\chi^2$ Probability Function JO - Teoriâ veroâtnostej i ee primeneniâ PY - 1957 SP - 470 EP - 472 VL - 2 IS - 4 UR - http://geodesic.mathdoc.fr/item/TVP_1957_2_4_a3/ LA - ru ID - TVP_1957_2_4_a3 ER -
S. V. Smirnov; M. K. Potapov. A Nomogram for the Incomplete $\Gamma$-Function and the $\chi^2$ Probability Function. Teoriâ veroâtnostej i ee primeneniâ, Tome 2 (1957) no. 4, pp. 470-472. http://geodesic.mathdoc.fr/item/TVP_1957_2_4_a3/