Functions and CALL Routines

FNONCT Function

Returns the value of the noncentrality parameter of an F distribution.

Category:

Mathematical

Syntax
Arguments
Details
Examples

Syntax

FNONCT(x,ndf,ddf,prob)

Arguments

x

is a numeric random variable.

Range:

ndf

is a numeric numerator degree of freedom parameter.

Range:

ndf > 0

ddf

is a numeric denominator degree 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

[equation]

where

[equation]

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

[equation]

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;

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

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