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

// neg_binomial_confidence_limits.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)

// Caution: this file contains quickbook markup as well as code
// and comments, don't change any of the special comment markups!

//[neg_binomial_confidence_limits

/*`

First we need some includes to access the negative binomial distribution
(and some basic std output of course).

*/

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

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

/*`
First define a table of significance levels: these are the 
probabilities that the true occurrence frequency lies outside the calculated
interval:
*/

  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 true occurrence frequency lies *inside* the calculated interval.

We need a function to calculate and print confidence limits
for an observed frequency of occurrence 
that follows a negative binomial distribution.

*/

void confidence_limits_on_frequency(unsigned trials, unsigned successes)
{
   // trials = Total number of trials.
   // successes = Total number of observed successes.
   // failures = trials - successes.
   // success_fraction = successes /trials.
   // Print out general info:
   cout <<
      "______________________________________________\n"
      "2-Sided Confidence Limits For Success Fraction\n"
      "______________________________________________\n\n";
   cout << setprecision(7);
   cout << setw(40) << left << "Number of trials" << " =  " << trials << "\n";
   cout << setw(40) << left << "Number of successes" << " =  " << successes << "\n";
   cout << setw(40) << left << "Number of failures" << " =  " << trials - successes << "\n";
   cout << setw(40) << left << "Observed frequency of occurrence" << " =  " << double(successes) / trials << "\n";

   // Print table header:
   cout << "\n\n"
           "___________________________________________\n"
           "Confidence        Lower          Upper\n"
           " Value (%)        Limit          Limit\n"
           "___________________________________________\n";


/*`
And now for the important part - the bounds themselves.
For each value of /alpha/, we call `find_lower_bound_on_p` and 
`find_upper_bound_on_p` to obtain lower and upper bounds respectively. 
Note that since we are calculating a two-sided interval,
we must divide the value of alpha in two.  Had we been calculating a 
single-sided interval, for example: ['"Calculate a lower bound so that we are P%
sure that the true occurrence frequency is greater than some value"]
then we would *not* have divided by two.
*/

   // Now print out the upper and lower limits for the alpha table values.
   for(unsigned i = 0; i < sizeof(alpha)/sizeof(alpha[0]); ++i)
   {
      // Confidence value:
      cout << fixed << setprecision(3) << setw(10) << right << 100 * (1-alpha[i]);
      // Calculate bounds:
      double lower = negative_binomial::find_lower_bound_on_p(trials, successes, alpha[i]/2);
      double upper = negative_binomial::find_upper_bound_on_p(trials, successes, alpha[i]/2);
      // Print limits:
      cout << fixed << setprecision(5) << setw(15) << right << lower;
      cout << fixed << setprecision(5) << setw(15) << right << upper << endl;
   }
   cout << endl;
} // void confidence_limits_on_frequency(unsigned trials, unsigned successes)

/*`

And then call confidence_limits_on_frequency with increasing numbers of trials,
but always the same success fraction 0.1, or 1 in 10.

*/

int main()
{
  confidence_limits_on_frequency(20, 2); // 20 trials, 2 successes, 2 in 20, = 1 in 10 = 0.1 success fraction.
  confidence_limits_on_frequency(200, 20); // More trials, but same 0.1 success fraction.
  confidence_limits_on_frequency(2000, 200); // Many more trials, but same 0.1 success fraction.

  return 0;
} // int main()

//] [/negative_binomial_confidence_limits_eg end of Quickbook in C++ markup]

/*

______________________________________________
2-Sided Confidence Limits For Success Fraction
______________________________________________
Number of trials                         =  20
Number of successes                      =  2
Number of failures                       =  18
Observed frequency of occurrence         =  0.1
___________________________________________
Confidence        Lower          Upper
 Value (%)        Limit          Limit
___________________________________________
    50.000        0.04812        0.13554
    75.000        0.03078        0.17727
    90.000        0.01807        0.22637
    95.000        0.01235        0.26028
    99.000        0.00530        0.33111
    99.900        0.00164        0.41802
    99.990        0.00051        0.49202
    99.999        0.00016        0.55574
______________________________________________
2-Sided Confidence Limits For Success Fraction
______________________________________________
Number of trials                         =  200
Number of successes                      =  20
Number of failures                       =  180
Observed frequency of occurrence         =  0.1000000
___________________________________________
Confidence        Lower          Upper
 Value (%)        Limit          Limit
___________________________________________
    50.000        0.08462        0.11350
    75.000        0.07580        0.12469
    90.000        0.06726        0.13695
    95.000        0.06216        0.14508
    99.000        0.05293        0.16170
    99.900        0.04343        0.18212
    99.990        0.03641        0.20017
    99.999        0.03095        0.21664
______________________________________________
2-Sided Confidence Limits For Success Fraction
______________________________________________
Number of trials                         =  2000
Number of successes                      =  200
Number of failures                       =  1800
Observed frequency of occurrence         =  0.1000000
___________________________________________
Confidence        Lower          Upper
 Value (%)        Limit          Limit
___________________________________________
    50.000        0.09536        0.10445
    75.000        0.09228        0.10776
    90.000        0.08916        0.11125
    95.000        0.08720        0.11352
    99.000        0.08344        0.11802
    99.900        0.07921        0.12336
    99.990        0.07577        0.12795
    99.999        0.07282        0.13206
*/
Commit	Line	Data
7c673cae FG	1	// neg_binomial_confidence_limits.cpp
	2
	3	// Copyright John Maddock 2006
	4	// Copyright Paul A. Bristow 2007, 2010
	5	// Use, modification and distribution are subject to the
	6	// Boost Software License, Version 1.0.
	7	// (See accompanying file LICENSE_1_0.txt
	8	// or copy at http://www.boost.org/LICENSE_1_0.txt)
	9
	10	// Caution: this file contains quickbook markup as well as code
	11	// and comments, don't change any of the special comment markups!
	12
	13	//[neg_binomial_confidence_limits
	14
	15	/*`
	16
	17	First we need some includes to access the negative binomial distribution
	18	(and some basic std output of course).
	19
	20	*/
	21
	22	#include <boost/math/distributions/negative_binomial.hpp>
	23	using boost::math::negative_binomial;
	24
	25	#include <iostream>
	26	using std::cout; using std::endl;
	27	#include <iomanip>
	28	using std::setprecision;
	29	using std::setw; using std::left; using std::fixed; using std::right;
	30
	31	/*`
	32	First define a table of significance levels: these are the
	33	probabilities that the true occurrence frequency lies outside the calculated
	34	interval:
	35	*/
	36
	37	double alpha[] = { 0.5, 0.25, 0.1, 0.05, 0.01, 0.001, 0.0001, 0.00001 };
	38
	39	/*`
	40	Confidence value as % is (1 - alpha) * 100, so alpha 0.05 == 95% confidence
	41	that the true occurrence frequency lies inside the calculated interval.
	42
	43	We need a function to calculate and print confidence limits
	44	for an observed frequency of occurrence
	45	that follows a negative binomial distribution.
	46
	47	*/
	48
	49	void confidence_limits_on_frequency(unsigned trials, unsigned successes)
	50	{
	51	// trials = Total number of trials.
	52	// successes = Total number of observed successes.
	53	// failures = trials - successes.
	54	// success_fraction = successes /trials.
	55	// Print out general info:
	56	cout <<
	57	"______________________________________________\n"
	58	"2-Sided Confidence Limits For Success Fraction\n"
	59	"______________________________________________\n\n";
	60	cout << setprecision(7);
	61	cout << setw(40) << left << "Number of trials" << " = " << trials << "\n";
	62	cout << setw(40) << left << "Number of successes" << " = " << successes << "\n";
	63	cout << setw(40) << left << "Number of failures" << " = " << trials - successes << "\n";
	64	cout << setw(40) << left << "Observed frequency of occurrence" << " = " << double(successes) / trials << "\n";
65
66	// Print table header:
67	cout << "\n\n"
68	"___________________________________________\n"
69	"Confidence Lower Upper\n"
70	" Value (%) Limit Limit\n"
71	"___________________________________________\n";
72
73
74	/*`
75	And now for the important part - the bounds themselves.
76	For each value of /alpha/, we call `find_lower_bound_on_p` and
77	`find_upper_bound_on_p` to obtain lower and upper bounds respectively.
78	Note that since we are calculating a two-sided interval,
79	we must divide the value of alpha in two. Had we been calculating a
80	single-sided interval, for example: ['"Calculate a lower bound so that we are P%
81	sure that the true occurrence frequency is greater than some value"]
82	then we would not have divided by two.
83	*/
84
85	// Now print out the upper and lower limits for the alpha table values.
86	for(unsigned i = 0; i < sizeof(alpha)/sizeof(alpha[0]); ++i)
87	{
88	// Confidence value:
89	cout << fixed << setprecision(3) << setw(10) << right << 100 * (1-alpha[i]);
90	// Calculate bounds:
91	double lower = negative_binomial::find_lower_bound_on_p(trials, successes, alpha[i]/2);
92	double upper = negative_binomial::find_upper_bound_on_p(trials, successes, alpha[i]/2);
93	// Print limits:
94	cout << fixed << setprecision(5) << setw(15) << right << lower;
95	cout << fixed << setprecision(5) << setw(15) << right << upper << endl;
96	}
97	cout << endl;
98	} // void confidence_limits_on_frequency(unsigned trials, unsigned successes)
99
100	/*`
101
102	And then call confidence_limits_on_frequency with increasing numbers of trials,
103	but always the same success fraction 0.1, or 1 in 10.
104
105	*/
106
107	int main()
108	{
109	confidence_limits_on_frequency(20, 2); // 20 trials, 2 successes, 2 in 20, = 1 in 10 = 0.1 success fraction.
110	confidence_limits_on_frequency(200, 20); // More trials, but same 0.1 success fraction.
111	confidence_limits_on_frequency(2000, 200); // Many more trials, but same 0.1 success fraction.
112
113	return 0;
114	} // int main()
115
116	//] [/negative_binomial_confidence_limits_eg end of Quickbook in C++ markup]
117
118	/*
119
120	______________________________________________
121	2-Sided Confidence Limits For Success Fraction
122	______________________________________________
123	Number of trials = 20
124	Number of successes = 2
125	Number of failures = 18
126	Observed frequency of occurrence = 0.1
127	___________________________________________
128	Confidence Lower Upper
129	Value (%) Limit Limit
130	___________________________________________
131	50.000 0.04812 0.13554
132	75.000 0.03078 0.17727
133	90.000 0.01807 0.22637
134	95.000 0.01235 0.26028
135	99.000 0.00530 0.33111
136	99.900 0.00164 0.41802
137	99.990 0.00051 0.49202
138	99.999 0.00016 0.55574
139	______________________________________________
140	2-Sided Confidence Limits For Success Fraction
141	______________________________________________
142	Number of trials = 200
143	Number of successes = 20
144	Number of failures = 180
145	Observed frequency of occurrence = 0.1000000
146	___________________________________________
147	Confidence Lower Upper
148	Value (%) Limit Limit
149	___________________________________________
150	50.000 0.08462 0.11350
151	75.000 0.07580 0.12469
152	90.000 0.06726 0.13695
153	95.000 0.06216 0.14508
154	99.000 0.05293 0.16170
155	99.900 0.04343 0.18212
156	99.990 0.03641 0.20017
157	99.999 0.03095 0.21664
158	______________________________________________
159	2-Sided Confidence Limits For Success Fraction
160	______________________________________________
161	Number of trials = 2000
162	Number of successes = 200
163	Number of failures = 1800
164	Observed frequency of occurrence = 0.1000000
165	___________________________________________
166	Confidence Lower Upper
167	Value (%) Limit Limit
168	___________________________________________
169	50.000 0.09536 0.10445
170	75.000 0.09228 0.10776
171	90.000 0.08916 0.11125
172	95.000 0.08720 0.11352
173	99.000 0.08344 0.11802
174	99.900 0.07921 0.12336
175	99.990 0.07577 0.12795
176	99.999 0.07282 0.13206
177	*/
178