FNONCT

# FNONCT

Returns the value of the noncentrality parameter of an F distribution

 Category: Mathematical

## Syntax

 FNONCT(x,ndf,ddf,prob)

### Arguments

x
is a numeric random variable.
 Range: x 0

ndf
is a numeric numerator degrees-of-freedom parameter.
 Range: ndf > 0

ddf
is a numeric denominator degrees-of-freedom parameter.
 Range: ddf > 0

prob
is a probability.
 Range: 0 < prob < 1

The FNONCT function returns the nonnegative noncentrality parameter from a noncentral F distribution whose parameters are x, ndf, ddf, and nc. If prob is greater than the probability from the central F distribution whose parameters are x, ndf, and ddf, a root to this problem does not exist. In this case a missing value is returned. A Newton-type algorithm is used to find a nonnegative root nc of the equation

where

where I (. . .) is the probability from the beta distribution that is given by

If the algorithm fails to converge to a fixed point, a missing value is returned.

```data work;
x=2;
df=4;
ddf=5;
do nc=1 to 3 by .5;
prob=probf(x,df,ddf,nc);
ncc=fnonct(x,df,ddf,prob);
output;
end;
run;
proc print;
run;```

 ``` OBS x df ddf nc prob ncc 1 2 4 5 1.0 0.69277 1.0 2 2 4 5 1.5 0.65701 1.5 3 2 4 5 2.0 0.62232 2.0 4 2 4 5 2.5 0.58878 2.5 5 2 4 5 3.0 0.55642 3.0```