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# finv

F inverse cumulative distribution function

## Syntax

X = finv(P,V1,V2)

## Description

X = finv(P,V1,V2) computes the inverse of the F cdf with numerator degrees of freedom V1 and denominator degrees of freedom V2 for the corresponding probabilities in P. P, V1, and V2 can be vectors, matrices, or multidimensional arrays that all have the same size. A scalar input is expanded to a constant array with the same dimensions as the other inputs.

V1 and V2 parameters must contain real positive values, and the values in P must lie on the interval [0 1].

The F inverse function is defined in terms of the F cdf as

$x={F}^{-1}\left(p|{\nu }_{1},{\nu }_{2}\right)=\left\{x:F\left(x|{\nu }_{1},{\nu }_{2}\right)=p\right\}$

where

$p=F\left(x|{\nu }_{1},{\nu }_{2}\right)=\underset{0}{\overset{x}{\int }}\frac{\Gamma \left[\frac{\left({\nu }_{1}+{\nu }_{2}\right)}{2}\right]}{\Gamma \left(\frac{{\nu }_{1}}{2}\right)\Gamma \left(\frac{{\nu }_{2}}{2}\right)}{\left(\frac{{\nu }_{1}}{{\nu }_{2}}\right)}^{\frac{{\nu }_{1}}{2}}\frac{{t}^{\frac{{\nu }_{1}-2}{2}}}{{\left[1+\left(\frac{{\nu }_{1}}{{\nu }_{2}}\right)t\right]}^{\frac{{\nu }_{1}+{\nu }_{2}}{2}}}dt$

## Examples

Find a value that should exceed 95% of the samples from an F distribution with 5 degrees of freedom in the numerator and 10 degrees of freedom in the denominator.

```x = finv(0.95,5,10)
x =
3.3258
```

You would observe values greater than 3.3258 only 5% of the time by chance.