Documentation

# ncfrnd

Noncentral F random numbers

## Syntax

```R = ncfrnd(NU1,NU2,DELTA) R = ncfrnd(NU1,NU2,DELTA,m,n,...) R = ncfrnd(NU1,NU2,DELTA,[m,n,...]) ```

## Description

`R = ncfrnd(NU1,NU2,DELTA)` returns a matrix of random numbers chosen from the noncentral F distribution 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 have the same size, which is also the size of `R`. A scalar input for `NU1`, `NU2`, or `DELTA` is expanded to a constant matrix with the same dimensions as the other inputs.

`R = ncfrnd(NU1,NU2,DELTA,m,n,...)` or ```R = ncfrnd(NU1,NU2,DELTA,[m,n,...])``` generates an `m`-by-`n`-by-... array. The `NU1`, `NU2`, `DELTA` parameters can each be scalars or arrays of the same size as `R`.

## Examples

Compute six random numbers from a noncentral F distribution with 10 numerator degrees of freedom, 100 denominator degrees of freedom and a noncentrality parameter, δ, of 4.0. Compare this to the F distribution with the same degrees of freedom.

```r = ncfrnd(10,100,4,1,6) r = 2.5995 0.8824 0.8220 1.4485 1.4415 1.4864 r1 = frnd(10,100,1,6) r1 = 0.9826 0.5911 1.0967 0.9681 2.0096 0.6598```

## References

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