# 3.5.3.3.4 Finv

## Definition:

$f_p=finv(p, df1, df2)$ computes the inverse of $F$ cdf at $p$, with parameters $df1$ and $df2$ .

The deviate, $f_p$, associated with the lower tail probability $p$ of the $F$ distribution with $\nu_1$ and $\nu_2$ degrees of freedom is defined as the solution to

$P(F\leq f_p)=p=$ $\frac{\nu _1^{\nu _{1/2}}\nu _2^{\nu _2/2}\Gamma ((\nu _1+\nu _2)/2)}{\Gamma (\nu _1/2)\Gamma (\nu _2/2)}\int_0^{f_p}F^{(\nu _1-2)/2}(\nu _1F+\nu _2)^{-(\nu _1+\nu _2)/2}dF$

where

$\nu_1,\nu_2 > 0$ ; $0 \le f_p < \infty$

## Parameters:

$p$ (input, double)
the probability,$p$, from the required F-distribution. $0 \le p<1$
$df1$ (input, double)
the degrees of freedom of the numerator variance, $\nu_1$, must be positive ($df1>0$ ).
$df2$ (input, double)
the degrees of freedom of the denominator variance, $\nu_2$, must be positive($df2>0$).
$f_p$ (output, double)
the deviate,$f_p$.