FNONCT Function

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

Category: Mathematical

Syntax

FNONCT(x,ndf,ddf,prob)

Required Arguments

x

is a numeric random variable.

Range x ≥ 0

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
P f ( x | n d f , d d f , n c ) - p r o b = 0
The following relationship applies to the preceding equation:
P f ( x | n d f , d d f , n c ) = ε - n c 2 Σ j = 0 ( n c 2 ) j j ! I ( n d f ) x d d f + ( n d f ) x ( d d f 2 + j , d d f 2 )
In the equation, I (. . .) is the probability from the beta distribution that is given by the following equation:
I x ( a , b ) = Γ ( a ) Γ ( b ) Γ ( a + b ) 0 x t a - 1 ( 1 - t ) b - 1 d t
If the algorithm fails to converge to a fixed point, a missing value is returned.

Example

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
FNONCT Example Output