1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
|
/* randist/fdist.c
*
* Copyright (C) 1996, 1997, 1998, 1999, 2000 James Theiler, Brian Gough
*
* 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., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
*/
#include <config.h>
#include <math.h>
#include <gsl/gsl_sf_gamma.h>
#include <gsl/gsl_rng.h>
#include <gsl/gsl_randist.h>
/* The F distribution has the form
p(x) dx = (nu1^(nu1/2) nu2^(nu2/2) Gamma((nu1 + nu2)/2) /
Gamma(nu1/2) Gamma(nu2/2)) *
x^(nu1/2 - 1) (nu2 + nu1 * x)^(-nu1/2 -nu2/2) dx
The method used here is the one described in Knuth */
double
gsl_ran_fdist (const gsl_rng * r, const double nu1, const double nu2)
{
double Y1 = gsl_ran_gamma (r, nu1 / 2, 2.0);
double Y2 = gsl_ran_gamma (r, nu2 / 2, 2.0);
double f = (Y1 * nu2) / (Y2 * nu1);
return f;
}
double
gsl_ran_fdist_pdf (const double x, const double nu1, const double nu2)
{
if (x < 0)
{
return 0 ;
}
else
{
double p;
double lglg = (nu1 / 2) * log (nu1) + (nu2 / 2) * log (nu2) ;
double lg12 = gsl_sf_lngamma ((nu1 + nu2) / 2);
double lg1 = gsl_sf_lngamma (nu1 / 2);
double lg2 = gsl_sf_lngamma (nu2 / 2);
p = exp (lglg + lg12 - lg1 - lg2)
* pow (x, nu1 / 2 - 1) * pow (nu2 + nu1 * x, -nu1 / 2 - nu2 / 2);
return p;
}
}
|
