\(\normalsize Noncentral\ F{\tiny-}distribution\ F(x,\nu_{1},\nu_{2},\lambda)\\
(1) probability\ density\\
f(x,\nu_1,\nu_2,\lambda){\small=}{\large\displaystyle \sum_{\small j=0}^{\small\infty} \frac{e^{-\frac{\lambda}{2}} (\frac{\lambda}{2})^j {\nu_{\tiny j}}^{\frac{\nu_{\tiny j}}{2}}{\nu_2}^{\frac{\nu_2}{2}} x^{\frac{\nu_{\tiny j}}{2}-1}}{j!B(\frac{\nu_{\tiny j}}{2},\frac{\nu_2}{2}) (\nu_2+\nu_{\tiny j}x)^{\frac{\nu_{\tiny j}+\nu_2}{2}}} }\\
\hspace{80px}\nu_j=\nu_1+2j\\
(2) lower\ cumulative\ distribution\\
\hspace{30px}P(x,\nu_1,\nu_2,\lambda)={\large\int_{\small 0}^{\small x}}f(t,\nu_1,\nu_2,\lambda)dt\\
(3) upper\ cumulative\ distribution\\
\hspace{30px}Q(x,\nu_1,\nu_2,\lambda)={\large\int_{\small x}^{\small\infty}}f(t,\nu_1,\nu_2,\lambda)dt\\\) |
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ゲストさん
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