FNONCT

FNONCT

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 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

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where

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

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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;

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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