fdtr

F distribution.

SYNOPSIS:

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

DESCRIPTION:

Returns the area from zero to x under the F density function (also known as Snedcor's density, or the variance ratio density).
This is the density of x = (u1/df1)/(u2/df2), where u1 and u2 are random variables having Chi square distributions with df1 and df2 degrees of freedom, respectively.

The incomplete beta integral is used, according to the formula

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

The arguments a and b are greater than zero, and x is nonnegative.

ACCURACY:

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

                x     a,b                     Relative error:
arithmetic domain domain     # trials      peak         rms
    IEEE      0,1    0,100       100000      9.8e-15     1.7e-15
    IEEE      1,5    0,100       100000      6.5e-15     3.5e-16
    IEEE      0,1    1,10000     100000      2.2e-11     3.3e-12
    IEEE      1,5    1,10000     100000      1.1e-11     1.7e-13

See the incbet Help topic.

ERROR MESSAGES:

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