[ceph.git] / ceph / src / boost / libs / math / example / neg_binomial_sample_sizes.cpp

// neg_binomial_sample_sizes.cpp

// Copyright John Maddock 2006
// Copyright Paul A. Bristow 2007, 2010

// Use, modification and distribution are subject to the
// Boost Software License, Version 1.0.
// (See accompanying file LICENSE_1_0.txt
// or copy at http://www.boost.org/LICENSE_1_0.txt)

#include <boost/math/distributions/negative_binomial.hpp>
using boost::math::negative_binomial;

// Default RealType is double so this permits use of:
double find_minimum_number_of_trials(
double k,     // number of failures (events), k >= 0.
double p,     // fraction of trails for which event occurs, 0 <= p <= 1.
double probability); // probability threshold, 0 <= probability <= 1.

#include <iostream>
using std::cout;
using std::endl;
using std::fixed;
using std::right;
#include <iomanip>
using std::setprecision;
using std::setw; 

//[neg_binomial_sample_sizes

/*`
It centres around a routine that prints out a table of 
minimum sample sizes (number of trials) for various probability thresholds:
*/
  void find_number_of_trials(double failures, double p);
/*`
First define a table of significance levels: these are the maximum 
acceptable probability that /failure/ or fewer events will be observed.
*/
  double alpha[] = { 0.5, 0.25, 0.1, 0.05, 0.01, 0.001, 0.0001, 0.00001 };
/*`
Confidence value as % is (1 - alpha) * 100, so alpha 0.05 == 95% confidence
that the desired number of failures will be observed.
The values range from a very low 0.5 or 50% confidence up to an extremely high
confidence of 99.999.

Much of the rest of the program is pretty-printing, the important part
is in the calculation of minimum number of trials required for each
value of alpha using:

  (int)ceil(negative_binomial::find_minimum_number_of_trials(failures, p, alpha[i]);

find_minimum_number_of_trials returns a double,
so `ceil` rounds this up to ensure we have an integral minimum number of trials.
*/
  
void find_number_of_trials(double failures, double p)
{
   // trials = number of trials
   // failures = number of failures before achieving required success(es).
   // p        = success fraction (0 <= p <= 1.).
   //
   // Calculate how many trials we need to ensure the
   // required number of failures DOES exceed "failures".

  cout << "\n""Target number of failures = " << (int)failures;
  cout << ",   Success fraction = " << fixed << setprecision(1) << 100 * p << "%" << endl;
   // Print table header:
   cout << "____________________________\n"
           "Confidence        Min Number\n"
           " Value (%)        Of Trials \n"
           "____________________________\n";
   // Now print out the data for the alpha table values.
  for(unsigned i = 0; i < sizeof(alpha)/sizeof(alpha[0]); ++i)
   { // Confidence values %:
      cout << fixed << setprecision(3) << setw(10) << right << 100 * (1-alpha[i]) << "      "
      // find_minimum_number_of_trials
      << setw(6) << right
      << (int)ceil(negative_binomial::find_minimum_number_of_trials(failures, p, alpha[i]))
      << endl;
   }
   cout << endl;
} // void find_number_of_trials(double failures, double p)

/*` finally we can produce some tables of minimum trials for the chosen confidence levels:
*/

int main()
{
    find_number_of_trials(5, 0.5);
    find_number_of_trials(50, 0.5);
    find_number_of_trials(500, 0.5);
    find_number_of_trials(50, 0.1);
    find_number_of_trials(500, 0.1);
    find_number_of_trials(5, 0.9);

    return 0;
} // int main()

//]  [/neg_binomial_sample_sizes.cpp end of Quickbook in C++ markup]

/*

Output is:
Target number of failures = 5,   Success fraction = 50.0%
  ____________________________
  Confidence        Min Number
   Value (%)        Of Trials 
  ____________________________
      50.000          11
      75.000          14
      90.000          17
      95.000          18
      99.000          22
      99.900          27
      99.990          31
      99.999          36
  
  
  Target number of failures = 50,   Success fraction = 50.0%
  ____________________________
  Confidence        Min Number
   Value (%)        Of Trials 
  ____________________________
      50.000         101
      75.000         109
      90.000         115
      95.000         119
      99.000         128
      99.900         137
      99.990         146
      99.999         154
  
  
  Target number of failures = 500,   Success fraction = 50.0%
  ____________________________
  Confidence        Min Number
   Value (%)        Of Trials 
  ____________________________
      50.000        1001
      75.000        1023
      90.000        1043
      95.000        1055
      99.000        1078
      99.900        1104
      99.990        1126
      99.999        1146
  
  
  Target number of failures = 50,   Success fraction = 10.0%
  ____________________________
  Confidence        Min Number
   Value (%)        Of Trials 
  ____________________________
      50.000          56
      75.000          58
      90.000          60
      95.000          61
      99.000          63
      99.900          66
      99.990          68
      99.999          71
  
  
  Target number of failures = 500,   Success fraction = 10.0%
  ____________________________
  Confidence        Min Number
   Value (%)        Of Trials 
  ____________________________
      50.000         556
      75.000         562
      90.000         567
      95.000         570
      99.000         576
      99.900         583
      99.990         588
      99.999         594
  
  
  Target number of failures = 5,   Success fraction = 90.0%
  ____________________________
  Confidence        Min Number
   Value (%)        Of Trials 
  ____________________________
      50.000          57
      75.000          73
      90.000          91
      95.000         103
      99.000         127
      99.900         159
      99.990         189
      99.999         217
  
  
  Target number of failures = 5,   Success fraction = 95.0%
  ____________________________
  Confidence        Min Number
   Value (%)        Of Trials 
  ____________________________
      50.000         114
      75.000         148
      90.000         184
      95.000         208
      99.000         259
      99.900         324
      99.990         384
      99.999         442

*/
Commit	Line	Data
7c673cae FG	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
	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
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	*/