fdtri

Inverse of complemented F distribution.

SYNOPSIS:

int df1, df2;
double x, p, fdtri();
x = fdtri(df1, df2, p);

DESCRIPTION:

Finds the F density argument x, such that the integral from x to infinity of the F density is equal to the given probability p.
This is accomplished using the inverse beta integral function and the relations:

      z = incbi(df2/2, df1/2, p)
      x = df2 (1-z) / (df1 z).

Note: These relations hold for the inverse of the uncomplemented F distribution:

      z = incbi(df1/2, df2/2, p)
      x = df2 z / (df1 (1-z)).

ACCURACY:

Tested at random points (a,b,p).

              a,b                     Relative error:
arithmetic domain     # trials      peak         rms
For p between .001 and 1:
    IEEE     1,100       100000      8.3e-15     4.7e-16
    IEEE     1,10000     100000      2.1e-11     1.4e-13
For p between 10^-6 and 10^-3:
    IEEE     1,100        50000      1.3e-12     8.4e-15
    IEEE     1,10000      50000      3.0e-12     4.8e-14

See the fdtrc Help topic.

ERROR MESSAGES:

   message         condition        value returned
   domain        p <= 0 or p > 1         0.0
                     v < 1