# Noncentral F-distribution (chart)

## Calculates a table of the probability density function, or lower or upper cumulative distribution function of the noncentral F-distribution, and draws the chart.

select function
 probability density f lower cumulative distribution P upper cumulative distribution Q
degree of freedom ν1
 ν1＞0
degree of freedom ν2
 ν2＞0
noncentrality λ
 λ≧0
[ initial percentile x
 x≧0
increment
 repetition ]

 $\normal Noncentral\ F{\tiny-}distribution\ F(x,\nu_{1},\nu_{2},\lambda)\\[10](1)\qquad probability\ density\\[10]f(x,\nu_1,\nu_2,\lambda){\small=}{\large\sum_{\small j=0}^{\small\infty} \frac{e^{-\frac{\lambda}{2}} (\frac{\lambda}{2})^j {\nu_{\tiny j}}^{\frac{\nu_{\tiny j}}{2}}{\nu_2}^{\frac{\nu_2}{2}} x^{\frac{\nu_{\tiny j}}{2}-1}}{j!B(\frac{\nu_{\tiny j}}{2},\frac{\nu_2}{2}) (\nu_2+\nu_{\tiny j}x)^{\frac{\nu_{\tiny j}+\nu_2}{2}}} }\\\hspace{80}\nu_j=\nu_1+2j\\[10](2)\qquad lower\ cumulative\ distribution\\\hspace{30}P(x,\nu_1,\nu_2,\lambda)={\large\int_{\small 0}^{\hspace{25}\small x}}f(t,\nu_1,\nu_2,\lambda)dt\\(3)\qquad upper\ cumulative\ distribution\\\hspace{30}Q(x,\nu_1,\nu_2,\lambda)={\large\int_{\small x}^{\hspace{25}\small\infty}}f(t,\nu_1,\nu_2,\lambda)dt\\$

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