Returns the value of the noncentrality parameter of an F distribution.

Category: | Mathematical |

The FNONCT function
returns the nonnegative noncentrality parameter from a noncentral F distribution whose parameters are x, ndf, ddf, and nc. If prob is greater than the probability from the central F distribution whose parameters are x, ndf, and ddf, a root to this
problem does not exist. In this case a missing value is returned.
A Newton-type algorithm is used to find a nonnegative root nc of the equation

$\begin{array}{c}{P}_{f}\left(x\right|ndf,ddf,nc)={\epsilon}^{\frac{-nc}{2}}\underset{j=0}{\overset{\infty}{\Sigma}}\frac{{\left(\frac{nc}{2}\right)}^{j}}{j!}{I}_{\frac{\left(ndf\right)x}{ddf+\left(ndf\right)x}}(\frac{ddf}{2}+j,\frac{ddf}{2})\hfill \end{array}$

In the equation, I (. . .) is the probability from the beta distribution
that is given by the following equation:

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