[Rd] Density function for non-central t distribution

[Claus Ekstroem]

Hi,

I've written some C code for density evaluation of the non-central t distribution. It works 
with the R-1.7.1 source code if placed in the src/nmath directory and after appropriate 
changes are made to Makefiles, to the dt function in src/library/base/R/distn.R etc. 
I haven't read a lot of R source code so it may need some R-ification, but I've tried to use the 
dt.c file as a standard.

Use and abuse.

Claus


===> File dnt.c <===

/*
 *  AUTHOR
 *    Claus Ekstrøm, ekstrom at dina.kvl.dk
 *    July 15, 2003.
 *
 *  This program is free software; you can redistribute it and/or modify
 *  it under the terms of the GNU General Public License as published by
 *  the Free Software Foundation; either version 2 of the License, or
 *  (at your option) any later version.
 *
 *  This program is distributed in the hope that it will be useful,
 *  but WITHOUT ANY WARRANTY; without even the implied warranty of
 *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 *  GNU General Public License for more details.
 *
 *  You should have received a copy of the GNU General Public License
 *  along with this program; if not, write to the Free Software
 *  Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307 USA.
 *
 *
 *  NOTE
 *
 *    Requires the following auxiliary routines:
 *
 *      lgammafn(x)     - log gamma function
 *      pnt(x, df, ncp) - the distribution function for the non-central t distribution
 *
 *
 * DESCRIPTION
 *
 *    The non-central t density is 
 *
 *         f(x, df, ncp) = 
df^(df/2)*exp(-.5*ncp^2)/(sqrt(pi)*gamma(df/2)*(df+x^2)^((df+1)/2))*sum_{k=0}^Infinity gamma((df + 
k + df)/2)*ncp^k/prod(1:k)*(2*x^2/(df+x^2))^(k/2)
 *
 *    The functional relationship
 *
 *         f(x, df, ncp) = df/x*(F(sqrt((df+2)/df)*x, df+2, ncp) - F(x, df, ncp))
 *
 *    is used to evaluate the density at x != 0 and 
 *
 *         f(0, df, ncp) = exp(-.5*ncp^2) / (sqrt(pi)*sqrt(df)*gamma(df/2))*gamma((df+1)/2)
 *
 *    is used for x=0.
 *
 *    All calculations are done on log-scale to increase stability.
 *
 */

#include "nmath.h"
#include "dpq.h"

double dnt(double x, double df, double ncp, int give_log)
{ 
    double u;
#ifdef IEEE_754
    if (ISNAN(x) || ISNAN(df))
	return x + df;
#endif

    // If non-positive df then error
   if (df <= 0) ML_ERR_return_NAN;

    // If x is infinite then return 0
    if(!R_FINITE(x))
      return R_D__0;

    // If infinite df then the density is identical to a 
    // normal distribution with mean = ncp
    if(!R_FINITE(df))
	return dnorm(x, ncp, 1., give_log);

    // Consider two cases: x==0 or not
    // Do calculations on log scale to stabilize
    if (x!=0) {
      u = log(df)-log(fabs(x)) + log(fabs(pnt(x*sqrt((df+2)/df), df+2, ncp, 1, 0) - pnt(x, df, ncp, 
1, 0)));
    }
    else {
      u = lgammafn((df+1)/2) - lgammafn(df/2) - .5*(log(M_PI) + log(df) + ncp*ncp);
    }
    
    return (give_log ? u : exp(u));
}

-- 
*****************************************
Claus Thorn Ekstrøm <ekstrom at dina.kvl.dk>
Dept of Mathematics and Physics, KVL
Thorvaldsensvej 40
DK-1871 Frederiksberg C
Denmark
Phone:[+45] 3528 2341
Fax:  [+45] 3528 2350