FNONCT Function

Returns the value of the noncentrality parameter of an F distribution

Category: Mathematical

Syntax

FNONCT ( x , ndf , ddf , prob )

Arguments

is a numeric random variable.
Range: x ‰

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

Details

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.

Examples

 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;

Output 4.24: FNONCT Example Output

 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