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# 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.

## See Also

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