SAS 9.1 Language Reference Dictionary, Volumes 1, 2 and 3

FNONCT Function

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 ‰

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