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```