1 // neg_binomial_sample_sizes.cpp
2
3 // Copyright John Maddock 2006
4 // Copyright Paul A. Bristow 2007, 2010
5
6 // Use, modification and distribution are subject to the
7 // Boost Software License, Version 1.0.
8 // (See accompanying file LICENSE_1_0.txt
9 // or copy at http://www.boost.org/LICENSE_1_0.txt)
10
11 #include <boost/math/distributions/negative_binomial.hpp>
12 using boost::math::negative_binomial;
13
14 // Default RealType is double so this permits use of:
15 double find_minimum_number_of_trials(
16 double k, // number of failures (events), k >= 0.
17 double p, // fraction of trails for which event occurs, 0 <= p <= 1.
18 double probability); // probability threshold, 0 <= probability <= 1.
19
20 #include <iostream>
21 using std::cout;
22 using std::endl;
23 using std::fixed;
24 using std::right;
25 #include <iomanip>
26 using std::setprecision;
27 using std::setw;
28
29 //[neg_binomial_sample_sizes
30
31 /*`
32 It centres around a routine that prints out a table of
33 minimum sample sizes (number of trials) for various probability thresholds:
34 */
35 void find_number_of_trials(double failures, double p);
36 /*`
37 First define a table of significance levels: these are the maximum
38 acceptable probability that /failure/ or fewer events will be observed.
39 */
40 double alpha[] = { 0.5, 0.25, 0.1, 0.05, 0.01, 0.001, 0.0001, 0.00001 };
41 /*`
42 Confidence value as % is (1 - alpha) * 100, so alpha 0.05 == 95% confidence
43 that the desired number of failures will be observed.
44 The values range from a very low 0.5 or 50% confidence up to an extremely high
45 confidence of 99.999.
46
47 Much of the rest of the program is pretty-printing, the important part
48 is in the calculation of minimum number of trials required for each
49 value of alpha using:
50
51 (int)ceil(negative_binomial::find_minimum_number_of_trials(failures, p, alpha[i]);
52
53 find_minimum_number_of_trials returns a double,
54 so `ceil` rounds this up to ensure we have an integral minimum number of trials.
55 */
56
find_number_of_trials(double failures,double p)57 void find_number_of_trials(double failures, double p)
58 {
59 // trials = number of trials
60 // failures = number of failures before achieving required success(es).
61 // p = success fraction (0 <= p <= 1.).
62 //
63 // Calculate how many trials we need to ensure the
64 // required number of failures DOES exceed "failures".
65
66 cout << "\n""Target number of failures = " << (int)failures;
67 cout << ", Success fraction = " << fixed << setprecision(1) << 100 * p << "%" << endl;
68 // Print table header:
69 cout << "____________________________\n"
70 "Confidence Min Number\n"
71 " Value (%) Of Trials \n"
72 "____________________________\n";
73 // Now print out the data for the alpha table values.
74 for(unsigned i = 0; i < sizeof(alpha)/sizeof(alpha[0]); ++i)
75 { // Confidence values %:
76 cout << fixed << setprecision(3) << setw(10) << right << 100 * (1-alpha[i]) << " "
77 // find_minimum_number_of_trials
78 << setw(6) << right
79 << (int)ceil(negative_binomial::find_minimum_number_of_trials(failures, p, alpha[i]))
80 << endl;
81 }
82 cout << endl;
83 } // void find_number_of_trials(double failures, double p)
84
85 /*` finally we can produce some tables of minimum trials for the chosen confidence levels:
86 */
87
main()88 int main()
89 {
90 find_number_of_trials(5, 0.5);
91 find_number_of_trials(50, 0.5);
92 find_number_of_trials(500, 0.5);
93 find_number_of_trials(50, 0.1);
94 find_number_of_trials(500, 0.1);
95 find_number_of_trials(5, 0.9);
96
97 return 0;
98 } // int main()
99
100 //] [/neg_binomial_sample_sizes.cpp end of Quickbook in C++ markup]
101
102 /*
103
104 Output is:
105 Target number of failures = 5, Success fraction = 50.0%
106 ____________________________
107 Confidence Min Number
108 Value (%) Of Trials
109 ____________________________
110 50.000 11
111 75.000 14
112 90.000 17
113 95.000 18
114 99.000 22
115 99.900 27
116 99.990 31
117 99.999 36
118
119
120 Target number of failures = 50, Success fraction = 50.0%
121 ____________________________
122 Confidence Min Number
123 Value (%) Of Trials
124 ____________________________
125 50.000 101
126 75.000 109
127 90.000 115
128 95.000 119
129 99.000 128
130 99.900 137
131 99.990 146
132 99.999 154
133
134
135 Target number of failures = 500, Success fraction = 50.0%
136 ____________________________
137 Confidence Min Number
138 Value (%) Of Trials
139 ____________________________
140 50.000 1001
141 75.000 1023
142 90.000 1043
143 95.000 1055
144 99.000 1078
145 99.900 1104
146 99.990 1126
147 99.999 1146
148
149
150 Target number of failures = 50, Success fraction = 10.0%
151 ____________________________
152 Confidence Min Number
153 Value (%) Of Trials
154 ____________________________
155 50.000 56
156 75.000 58
157 90.000 60
158 95.000 61
159 99.000 63
160 99.900 66
161 99.990 68
162 99.999 71
163
164
165 Target number of failures = 500, Success fraction = 10.0%
166 ____________________________
167 Confidence Min Number
168 Value (%) Of Trials
169 ____________________________
170 50.000 556
171 75.000 562
172 90.000 567
173 95.000 570
174 99.000 576
175 99.900 583
176 99.990 588
177 99.999 594
178
179
180 Target number of failures = 5, Success fraction = 90.0%
181 ____________________________
182 Confidence Min Number
183 Value (%) Of Trials
184 ____________________________
185 50.000 57
186 75.000 73
187 90.000 91
188 95.000 103
189 99.000 127
190 99.900 159
191 99.990 189
192 99.999 217
193
194
195 Target number of failures = 5, Success fraction = 95.0%
196 ____________________________
197 Confidence Min Number
198 Value (%) Of Trials
199 ____________________________
200 50.000 114
201 75.000 148
202 90.000 184
203 95.000 208
204 99.000 259
205 99.900 324
206 99.990 384
207 99.999 442
208
209 */
210