stdtr

Student's t distribution.

SYNOPSIS:

double t, stdtr();
short k;
y = stdtr(k, t);

DESCRIPTION:

Computes the integral from minus infinity to t of the Student t distribution with integer k > 0 degrees of freedom:

                                  t
                                  -
                                 | |
          -                      |          2   -(k+1)/2
         | ((k+1)/2)             | (      x )
       -----------------         | ( 1 + --- )          dx
                   -             | (      k )
       sqrt(k pi) | (k/2)        |
                               | |
                                -
                               -inf.

Relation to incomplete beta integral:

        1 - stdtr(k,t) = 0.5 * incbet(k/2, 1/2, z)
where
        z = k/(k + t**2).

For t < -2, this is the method of computation.
For higher t, a direct method is derived from integration by parts.
Since the function is symmetric about t=0, the area under the right tail of the density is found by calling the function with -t instead of t.

ACCURACY:

Tested at random 1 <= k <= 25. The 'domain' refers to t.
                      Relative error:
arithmetic   domain     # trials      peak         rms
    IEEE     -100,-2      50000       5.9e-15     1.4e-15
    IEEE     -2,100      500000       2.7e-15     4.9e-17