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# fstat

F mean and variance

## Syntax

[M,V] = fstat(V1,V2)

## Description

[M,V] = fstat(V1,V2) returns the mean of and variance for the F distribution with numerator degrees of freedom V1 and denominator degrees of freedom V2. V1 and V2 can be vectors, matrices, or multidimensional arrays that all have the same size, which is also the size of M and V. A scalar input for V1 or V2 is expanded to a constant arrays with the same dimensions as the other input.

The mean of the F distribution for values of ν2 greater than 2 is

$\frac{{\nu }_{2}}{{\nu }_{2}-2}$

The variance of the F distribution for values of ν2 greater than 4 is

$\frac{2{\nu }_{2}^{2}\left({\nu }_{1}+{\nu }_{2}-2\right)}{{\nu }_{1}{\left({\nu }_{2}-2\right)}^{2}\left({\nu }_{2}-4\right)}$

The mean of the F distribution is undefined if ν2 is less than 3. The variance is undefined for ν2 less than 5.

## Examples

fstat returns NaN when the mean and variance are undefined.

```[m,v] = fstat(1:5,1:5)
m =
NaN  NaN  3.0000  2.0000  1.6667
v =
NaN  NaN  NaN  NaN  8.8889```