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 Ekstr?m, ekstrom@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 Ekstr?m <ekstrom@dina.kvl.dk>
Dept of Mathematics and Physics, KVL
Thorvaldsensvej 40
DK-1871 Frederiksberg C
Denmark
Phone:[+45] 3528 2341
Fax: [+45] 3528 2350
Martin Maechler
2003-Aug-19 19:00 UTC
[Rd] Density function for non-central t distribution
>>>>> "Claus" == Claus Ekstroem <claus@ekstroem.dk> >>>>> on Wed, 16 Jul 2003 09:35:50 +0200 writes:Claus> Hi, I've written some C code for density evaluation Claus> of the non-central t distribution. It works with the Claus> R-1.7.1 source code if placed in the src/nmath Claus> directory and after appropriate changes are made to Claus> Makefiles, to the dt function in Claus> src/library/base/R/distn.R etc. I haven't read a lot Claus> of R source code so it may need some R-ification, but Claus> I've tried to use the dt.c file as a standard. Claus> Use and abuse. Claus> Claus So, this is a donation to the R project, right? I'm about to incorporate it into R-devel which will become R 1.8.0 in October. Claus> <<<<< file dnt.c -- skipped here -- >>>>> That looks pretty good. We'll need some experiments to check if it's ok. I'll try some plausibility checks and then plan to compare pt(*, ncp= NN) with integrate("dt(*, ncp=NN)"). Thanks again for your contribution -- in the name of the R community! Claus> ***************************************** Claus> Claus Thorn Ekstr?m <ekstrom@dina.kvl.dk> Claus> Dept of Mathematics and Physics, KVL Claus> Thorvaldsensvej 40 Claus> DK-1871 Frederiksberg C Claus> Denmark Claus> Phone:[+45] 3528 2341 Claus> Fax: [+45] 3528 2350 Martin Maechler <maechler@stat.math.ethz.ch> http://stat.ethz.ch/~maechler/ Seminar fuer Statistik, ETH-Zentrum LEO C16 Leonhardstr. 27 ETH (Federal Inst. Technology) 8092 Zurich SWITZERLAND phone: x-41-1-632-3408 fax: ...-1228 <><
At 19:01 19-08-2003 +0200, Martin Maechler wrote:>So, this is a donation to the R project, right?Yep. That's exactly right.>We'll need some experiments to check if it's ok. >I'll try some plausibility checks and then plan to compare > pt(*, ncp= NN) with integrate("dt(*, ncp=NN)").Sure. Let me know if I can help in any way with constructing verification tests. Claus