Documentation

# ncfstat

Noncentral F mean and variance

## Syntax

```[M,V] = ncfstat(NU1,NU2,DELTA) ```

## Description

`[M,V] = ncfstat(NU1,NU2,DELTA)` returns the mean of and variance for the noncentral F pdf with corresponding numerator degrees of freedom in `NU1`, denominator degrees of freedom in `NU2`, and positive noncentrality parameters in `DELTA`. `NU1`, `NU2`, and `DELTA` 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 `NU1`, `NU2`, or `DELTA` is expanded to a constant array with the same dimensions as the other input.

The mean of the noncentral F distribution with parameters ν1, ν2, and δ is

`$\frac{{\nu }_{2}\left(\delta +{\nu }_{1}\right)}{{\nu }_{1}\left({\nu }_{2}-2\right)}$`

where ν2 > 2.

The variance is

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

where ν2 > 4.

## Examples

```[m,v]= ncfstat(10,100,4) m = 1.4286 v = 0.4252```

## References

[1] Evans, M., N. Hastings, and B. Peacock. Statistical Distributions. 2nd ed., Hoboken, NJ: John Wiley & Sons, Inc., 1993, pp. 73–74.

[2] Johnson, N., and S. Kotz. Distributions in Statistics: Continuous Univariate Distributions-2. Hoboken, NJ: John Wiley & Sons, Inc., 1970, pp. 189–200.