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
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
|
/*
* Copyright 2013 Brian Tjaden
*
* This file is part of Rockhopper.
*
* Rockhopper 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 3 of the License, or
* any later version.
*
* Rockhopper 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
* (in the file gpl.txt) along with Rockhopper.
* If not, see <http://www.gnu.org/licenses/>.
*/
/**
* Probability mass function of negative binomial distribution.
* Based on saddle point algorithm found in "Fast and Accurate
* Computation of Binomial Probabilities" by Catherine Loader, 2000.
*/
public class NegativeBinomial {
/*****************************************
********** CLASS VARIABLES **********
*****************************************/
private static double S0 = 0.08333333333333333333;
private static double S1 = 0.00277777777777777778;
private static double S2 = 0.00079365079365079365;
private static double S3 = 0.00059523809523809524;
private static double S4 = 0.00084175084175084175;
private static double[] sfe = {0.0, 0.081061466795327258219670264, 0.041340695955409294093822081, 0.0276779256849983391487892927, 0.020790672103765093111522771, 0.0166446911898211921631948653, 0.013876128823070747998945727, 0.0118967099458917700950557241, 0.010411265261972096497478567, 0.0092554621827127329177286366, 0.008330563433362871256469318, 0.0075736754879518407949720242, 0.006942840107209529865664152, 0.0064089941880042070684396370, 0.005951370112758847735624416, 0.0055547335519628013710386899};
/**********************************************
********** PUBLIC CLASS METHODS **********
**********************************************/
public static double pmf(double k, double n, double p, boolean b) {
if (p == 0.0) {
if (k == 0) return 1.0;
else return 0.0;
} else if (p == 1.0) {
if (k == n) return 1.0;
else return 0.0;
} else if (k == 0) {
return Math.exp(n * Math.log(1.0 - p));
} else if (k == n) {
return Math.exp(n * Math.log(p));
} else {
double lc = stirlerr(n) - stirlerr(k) - stirlerr(n - k) - bd0(k, n*p) - bd0(n-k, n*(1.0-p));
return p * Math.exp(lc) * Math.sqrt(n / (2.0*Math.PI*k*(n-k))); // We multiply by "p" here
}
}
public static double pmf(double k, double n, double p) {
if (p == 0.0) {
if (k == 0) return 1.0;
else return 0.0;
} else if (p == 1.0) {
if (k == n) return 1.0;
else return 0.0;
} else if (k == 0) {
return Math.exp(n * Math.log(1.0 - p));
} else if (k == n) {
return Math.exp(n * Math.log(p));
} else {
double lc = stirlerr(n) - stirlerr(k) - stirlerr(n - k) - bd0(k, n*p) - bd0(n-k, n*(1.0-p));
return p * Math.exp(lc) * Math.sqrt(n / (2.0*Math.PI*k*(n-k))); // We multiply by "p" here
}
}
/***********************************************
********** PRIVATE CLASS METHODS **********
***********************************************/
/**
* log(n!) - log(sqrt(2*pi*n)*(n/e)^n)
*/
private static double stirlerr(double n) {
if (n < 16) return sfe[(int)n];
double nn = n*n;
if (n > 500) return (S0 - S1/nn)/n;
if (n > 80) return (S0 - (S1/S2/nn)/nn)/n;
if (n > 35) return (S0 - (S1 - (S2-S3/nn)/nn)/nn)/n;
return (S0 - (S1 - (S2 - (S3 - S4/nn)/nn)/nn)/nn)/n;
}
/**
* Deviance term: k*lg(k/np) + np - k
*/
private static double bd0(double k, double np) {
if (Math.abs(k-np) < 0.1*(k+np)) {
double s = (k-np)*(k-np)/(k+np);
double v = (k-np)/(k+np);
double ej = 2*k*v;
int j = 1;
while (true) {
ej = ej*v*v;
double s1 = s+ej/(2*j+1);
if (s1 == s) return s;
s = s1;
j += 1;
}
}
return (k*Math.log(k/np)+np-k);
}
/*************************************
********** MAIN METHOD **********
*************************************/
public static void main(String[] args) {
if (args.length < 3) {
System.err.println("\nUSAGE: java NegativeBinomial <k> <r> <p>" + "\n");
System.err.println("NegativeBinomial computes the probability mass function for the negative binomial distribution with parameters (r,p) at value k.\n");
System.exit(0);
}
int k = Integer.parseInt(args[0]);
int r = Integer.parseInt(args[1]);
double p = Double.parseDouble(args[2]);
System.out.println(pmf(r-1, k+r-1, p));
}
}
|
