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
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
|
/* nbdtr.c
*
* Negative binomial distribution
*
*
*
* SYNOPSIS:
*
* int k, n;
* double p, y, nbdtr();
*
* y = nbdtr( k, n, p );
*
* DESCRIPTION:
*
* Returns the sum of the terms 0 through k of the negative
* binomial distribution:
*
* k
* -- ( n+j-1 ) n j
* > ( ) p (1-p)
* -- ( j )
* j=0
*
* In a sequence of Bernoulli trials, this is the probability
* that k or fewer failures precede the nth success.
*
* The terms are not computed individually; instead the incomplete
* beta integral is employed, according to the formula
*
* y = nbdtr( k, n, p ) = incbet( n, k+1, p ).
*
* The arguments must be positive, with p ranging from 0 to 1.
*
* ACCURACY:
*
* Tested at random points (a,b,p), with p between 0 and 1.
*
* a,b Relative error:
* arithmetic domain # trials peak rms
* IEEE 0,100 100000 1.7e-13 8.8e-15
* See also incbet.c.
*
*/
/* nbdtrc.c
*
* Complemented negative binomial distribution
*
*
*
* SYNOPSIS:
*
* int k, n;
* double p, y, nbdtrc();
*
* y = nbdtrc( k, n, p );
*
* DESCRIPTION:
*
* Returns the sum of the terms k+1 to infinity of the negative
* binomial distribution:
*
* inf
* -- ( n+j-1 ) n j
* > ( ) p (1-p)
* -- ( j )
* j=k+1
*
* The terms are not computed individually; instead the incomplete
* beta integral is employed, according to the formula
*
* y = nbdtrc( k, n, p ) = incbet( k+1, n, 1-p ).
*
* The arguments must be positive, with p ranging from 0 to 1.
*
* ACCURACY:
*
* Tested at random points (a,b,p), with p between 0 and 1.
*
* a,b Relative error:
* arithmetic domain # trials peak rms
* IEEE 0,100 100000 1.7e-13 8.8e-15
* See also incbet.c.
*/
/* nbdtrc
*
* Complemented negative binomial distribution
*
*
*
* SYNOPSIS:
*
* int k, n;
* double p, y, nbdtrc();
*
* y = nbdtrc( k, n, p );
*
* DESCRIPTION:
*
* Returns the sum of the terms k+1 to infinity of the negative
* binomial distribution:
*
* inf
* -- ( n+j-1 ) n j
* > ( ) p (1-p)
* -- ( j )
* j=k+1
*
* The terms are not computed individually; instead the incomplete
* beta integral is employed, according to the formula
*
* y = nbdtrc( k, n, p ) = incbet( k+1, n, 1-p ).
*
* The arguments must be positive, with p ranging from 0 to 1.
*
* ACCURACY:
*
* See incbet.c.
*/
/* nbdtri
*
* Functional inverse of negative binomial distribution
*
*
*
* SYNOPSIS:
*
* int k, n;
* double p, y, nbdtri();
*
* p = nbdtri( k, n, y );
*
* DESCRIPTION:
*
* Finds the argument p such that nbdtr(k,n,p) is equal to y.
*
* ACCURACY:
*
* Tested at random points (a,b,y), with y between 0 and 1.
*
* a,b Relative error:
* arithmetic domain # trials peak rms
* IEEE 0,100 100000 1.5e-14 8.5e-16
* See also incbi.c.
*/
/*
* Cephes Math Library Release 2.3: March, 1995
* Copyright 1984, 1987, 1995 by Stephen L. Moshier
*/
#include "mconf.h"
double nbdtrc(k, n, p)
int k, n;
double p;
{
double dk, dn;
if ((p < 0.0) || (p > 1.0))
goto domerr;
if (k < 0) {
domerr:
mtherr("nbdtr", DOMAIN);
return (NPY_NAN);
}
dk = k + 1;
dn = n;
return (incbet(dk, dn, 1.0 - p));
}
double nbdtr(k, n, p)
int k, n;
double p;
{
double dk, dn;
if ((p < 0.0) || (p > 1.0))
goto domerr;
if (k < 0) {
domerr:
mtherr("nbdtr", DOMAIN);
return (NPY_NAN);
}
dk = k + 1;
dn = n;
return (incbet(dn, dk, p));
}
double nbdtri(k, n, p)
int k, n;
double p;
{
double dk, dn, w;
if ((p < 0.0) || (p > 1.0))
goto domerr;
if (k < 0) {
domerr:
mtherr("nbdtri", DOMAIN);
return (NPY_NAN);
}
dk = k + 1;
dn = n;
w = incbi(dn, dk, p);
return (w);
}
|
