# Category : C Source Code

Archive : CEPHES22.ZIP

Filename : STDTR.C

*

* 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 < -1, 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 "range" refers to t:

* Relative error:

* arithmetic domain # trials peak rms

* DEC 0,24 12000 4.7e-17 8.9e-18

* DEC -24,0 11000 2.3e-15 2.7e-16

* IEEE 0,24 30000 4.5e-16 8.0e-17

* IEEE -24,0 30000 1.9e-14 2.3e-15

*/

/*

Cephes Math Library Release 2.0: April, 1987

Copyright 1984, 1987 by Stephen L. Moshier

Direct inquiries to 30 Frost Street, Cambridge, MA 02140

*/

#include "mconf.h"

extern double PI, MACHEP;

double stdtr( k, t )

int k;

double t;

{

double x, rk, z, f, tz, p, xsqk;

double sqrt(), atan(), incbet();

int j;

if( k <= 0 )

{

mtherr( "stdtr", DOMAIN );

return(0.0);

}

if( t == 0 )

return( 0.5 );

if( t < -1.0 )

{

rk = k;

z = rk / (rk + t * t);

p = 0.5 * incbet( 0.5*rk, 0.5, z );

return( p );

}

/* compute integral from -t to + t */

if( t < 0 )

x = -t;

else

x = t;

rk = k; /* degrees of freedom */

z = 1.0 + ( x * x )/rk;

/* test if k is odd or even */

if( (k & 1) != 0)

{

/* computation for odd k */

xsqk = x/sqrt(rk);

p = atan( xsqk );

if( k > 1 )

{

f = 1.0;

tz = 1.0;

j = 3;

while( (j<=(k-2)) && ( (tz/f) > MACHEP ) )

{

tz *= (j-1)/( z * j );

f += tz;

j += 2;

}

p += f * xsqk/z;

}

p *= 2.0/PI;

}

else

{

/* computation for even k */

f = 1.0;

tz = 1.0;

j = 2;

while( ( j <= (k-2) ) && ( (tz/f) > MACHEP ) )

{

tz *= (j - 1)/( z * j );

f += tz;

j += 2;

}

p = f * x/sqrt(z*rk);

}

/* common exit */

if( t < 0 )

p = -p; /* note destruction of relative accuracy */

p = 0.5 + 0.5 * p;

return(p);

}

Very nice! Thank you for this wonderful archive. I wonder why I found it only now. Long live the BBS file archives!

This is so awesome! 😀 I’d be cool if you could download an entire archive of this at once, though.

But one thing that puzzles me is the “mtswslnkmcjklsdlsbdmMICROSOFT” string. There is an article about it here. It is definitely worth a read: http://www.os2museum.com/wp/mtswslnk/