fdtrc

Complemented F distribution.

SYNOPSIS:

int df1, df2;
double x, y, fdtrc();
y = fdtrc(df1, df2, x);

DESCRIPTION:

Returns the area from x to infinity under the F density function (also known as Snedcor's density or the variance ratio density).

                      inf.
                       -
              1       | | a-1      b-1
1-P(x) = ------    |   t    (1-t)    dt
            B(a,b) | |
                     -
                      x

The incomplete beta integral is used, according to the formula

P(x) = incbet( df2/2, df1/2, (df2/(df2 + df1*x) ).

ACCURACY:

Tested at random points (a,b,x) in the indicated intervals.

                x     a,b                     Relative error:
arithmetic domain domain     # trials      peak         rms
    IEEE      0,1    1,100       100000      3.7e-14     5.9e-16
    IEEE      1,5    1,100       100000      8.0e-15     1.6e-15
    IEEE      0,1    1,10000     100000      1.8e-11     3.5e-13
    IEEE      1,5    1,10000     100000      2.0e-11     3.0e-12

ERROR MESSAGES:

message     condition      value returned
domain     a<0, b<0, x<0         0.0