1 /* randist/hyperg.c
2  *
3  * Copyright (C) 1996, 1997, 1998, 1999, 2000, 2007 James Theiler, Brian Gough
4  *
5  * This program is free software; you can redistribute it and/or modify
6  * it under the terms of the GNU General Public License as published by
7  * the Free Software Foundation; either version 3 of the License, or (at
8  * your option) any later version.
9  *
10  * This program is distributed in the hope that it will be useful, but
11  * WITHOUT ANY WARRANTY; without even the implied warranty of
12  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
13  * General Public License for more details.
14  *
15  * You should have received a copy of the GNU General Public License
16  * along with this program; if not, write to the Free Software
17  * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
18  */
19 
20 #include "gsl__config.h"
21 #include <math.h>
22 #include "gsl_rng.h"
23 #include "gsl_randist.h"
24 #include "gsl_sf_gamma.h"
25 
26 /* The hypergeometric distribution has the form,
27 
28    prob(k) =  choose(n1,t) choose(n2, t-k) / choose(n1+n2,t)
29 
30    where choose(a,b) = a!/(b!(a-b)!)
31 
32    n1 + n2 is the total population (tagged plus untagged)
33    n1 is the tagged population
34    t is the number of samples taken (without replacement)
35    k is the number of tagged samples found
36 
37 */
38 
39 unsigned int
gsl_ran_hypergeometric(const gsl_rng * r,unsigned int n1,unsigned int n2,unsigned int t)40 gsl_ran_hypergeometric (const gsl_rng * r, unsigned int n1, unsigned int n2,
41                         unsigned int t)
42 {
43   const unsigned int n = n1 + n2;
44 
45   unsigned int i = 0;
46   unsigned int a = n1;
47   unsigned int b = n1 + n2;
48   unsigned int k = 0;
49 
50   if (t > n)
51     {
52       t = n ;
53     }
54 
55   if (t < n / 2)
56     {
57       for (i = 0 ; i < t ; i++)
58         {
59           double u = gsl_rng_uniform(r) ;
60 
61           if (b * u < a)
62             {
63               k++ ;
64               if (k == n1)
65                 return k ;
66               a-- ;
67             }
68           b-- ;
69         }
70       return k;
71     }
72   else
73     {
74       for (i = 0 ; i < n - t ; i++)
75         {
76           double u = gsl_rng_uniform(r) ;
77 
78           if (b * u < a)
79             {
80               k++ ;
81               if (k == n1)
82                 return n1 - k ;
83               a-- ;
84             }
85           b-- ;
86         }
87       return n1 - k;
88     }
89 
90 
91 }
92 
93 double
gsl_ran_hypergeometric_pdf(const unsigned int k,const unsigned int n1,const unsigned int n2,unsigned int t)94 gsl_ran_hypergeometric_pdf (const unsigned int k,
95                             const unsigned int n1,
96                             const unsigned int n2,
97                             unsigned int t)
98 {
99   if (t > n1 + n2)
100     {
101       t = n1 + n2 ;
102     }
103 
104   if (k > n1 || k > t)
105     {
106       return 0 ;
107     }
108   else if (t > n2 && k + n2 < t )
109     {
110       return 0 ;
111     }
112   else
113     {
114       double p;
115 
116       double c1 = gsl_sf_lnchoose(n1,k);
117       double c2 = gsl_sf_lnchoose(n2,t-k);
118       double c3 = gsl_sf_lnchoose(n1+n2,t);
119 
120       p = exp(c1 + c2 - c3) ;
121 
122       return p;
123     }
124 }
125