﻿ stdtr | Enterprise Architect User Guide

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# 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