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math/example/Neg_binomial_confidence_limits.cpp
Paul A. Bristow ef67590773 Examples of confidence limits like binomial. 
[SVN r3425]
2006-11-21 17:18:45 +00:00

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// Copyright John Maddock 2006
// Copyright Paul A. Bristow 2006
// 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)
#ifdef _MSC_VER
# pragma warning(disable: 4512) // assignment operator could not be generated.
# pragma warning(disable: 4510) // default constructor could not be generated.
# pragma warning(disable: 4610) // can never be instantiated - user defined constructor required.
#endif
#include <iostream>
using std::cout;
using std::endl;
#include <iomanip>
#include <boost/math/distributions/negative_binomial.hpp>
void confidence_limits_on_frequency(unsigned trials, unsigned successes)
{
// trials = Total number of trials.
// successes = Total number of observed successes.
// failures = trials - successes.
//
// Calculate confidence limits for an observed
// frequency of occurance that follows a negative binomial distribution.
using namespace std;
using namespace boost::math;
// Print out general info:
cout <<
"___________________________________________\n"
"2-Sided Confidence Limits For Success Ratio\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 probability of occurrence" << " = " << double(successes) / trials << "\n";
// Define a table of significance levels:
double alpha[] = { 0.5, 0.25, 0.1, 0.05, 0.01, 0.001, 0.0001, 0.00001 };
// Print table header:
cout << "\n\n"
"___________________________________________\n"
"Confidence Lower Upper\n"
" Value (%) Limit Limit\n"
"___________________________________________\n";
// Now print out the data for the alpha table rows.
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 l = negative_binomial::estimate_lower_bound_on_p(trials, successes, alpha[i]/2);
double u = negative_binomial::estimate_upper_bound_on_p(trials, successes, alpha[i]/2);
// Print Limits:
cout << fixed << setprecision(5) << setw(15) << right << l;
cout << fixed << setprecision(5) << setw(15) << right << u << endl;
}
cout << endl;
} // void confidence_limits_on_frequency(unsigned trials, unsigned successes)
void estimate_number_of_trials(double failures, double p)
{
// Define a table of significance levels:
double alpha[] = { 0.5, 0.25, 0.1, 0.05, 0.01, 0.001, 0.0001, 0.00001 };
using namespace boost::math;
// static RealType estimate_number_of_trials(
//RealType k, // number of failures, k >= 0.
//RealType p, // success fraction 0 <= p <= 1.
//RealType probability) // probability threshold 0 <= p <= 0.
using namespace std;
cout << "\n""Number of failures = " << failures;
cout << ", Success ratio = " << 100 * p << "%" << endl;
cout << "Confidence % trials complement" << endl;
for(unsigned i = 0; i < sizeof(alpha)/sizeof(alpha[0]); ++i)
{ // Confidence values %:
cout << fixed << setprecision(3) << setw(10) << right << 100 * (1-alpha[i]) << " "
// estimate_number_of_trials
<< setw(6) << right<< int(negative_binomial::estimate_number_of_trials(failures, p, alpha[i]/2)) << " "
<< setw(6) << right<< int(negative_binomial::estimate_number_of_trials(boost::math::complement(failures, p, alpha[i]/2)))
<< endl;
}
cout << endl;
} // void estimate_number_of_trials(double fails, double p)
int main()
{
confidence_limits_on_frequency(20, 2);
confidence_limits_on_frequency(200, 20);
confidence_limits_on_frequency(2000, 200);
estimate_number_of_trials(5, 0.5);
estimate_number_of_trials(50, 0.5);
estimate_number_of_trials(500, 0.5);
estimate_number_of_trials(50, 0.1);
estimate_number_of_trials(500, 0.1);
estimate_number_of_trials(5, 0.9);
return 0;
} // int main()
/*
Output:
------ Build started: Project: neg_binomial_confidence_levels, Configuration: Debug Win32 ------
Compiling...
Neg_binomial_confidence_limits.cpp
Linking...
Autorun "i:\boost-06-05-03-1300\libs\math\test\Math_test\debug\neg_binomial_confidence_levels.exe"
___________________________________________
2-Sided Confidence Limits For Success Ratio
___________________________________________
Number of trials = 20
Number of successes = 2
Number of failures = 18
Observed probability of occurrence = 0.1
___________________________________________
Confidence Lower Upper
Value (%) Limit Limit
___________________________________________
50.000 0.08701 0.18675
75.000 0.06229 0.23163
90.000 0.04217 0.28262
95.000 0.03207 0.31698
99.000 0.01764 0.38713
99.900 0.00786 0.47093
99.990 0.00358 0.54084
99.999 0.00165 0.60020
___________________________________________
2-Sided Confidence Limits For Success Ratio
___________________________________________
Number of trials = 200
Number of successes = 20
Number of failures = 180
Observed probability of occurrence = 0.1000000
___________________________________________
Confidence Lower Upper
Value (%) Limit Limit
___________________________________________
50.000 0.08929 0.11824
75.000 0.08023 0.12959
90.000 0.07144 0.14199
95.000 0.06618 0.15021
99.000 0.05664 0.16698
99.900 0.04676 0.18756
99.990 0.03944 0.20571
99.999 0.03371 0.22226
___________________________________________
2-Sided Confidence Limits For Success Ratio
___________________________________________
Number of trials = 2000
Number of successes = 200
Number of failures = 1800
Observed probability of occurrence = 0.1000000
___________________________________________
Confidence Lower Upper
Value (%) Limit Limit
___________________________________________
50.000 0.09585 0.10491
75.000 0.09277 0.10822
90.000 0.08963 0.11172
95.000 0.08767 0.11399
99.000 0.08390 0.11850
99.900 0.07966 0.12385
99.990 0.07621 0.12845
99.999 0.07325 0.13256
Number of failures = 5.00000, Success ratio = 50.00000%
Confidence % trials complement
50.000 13 8
75.000 15 7
90.000 17 6
95.000 19 6
99.000 23 5
99.900 27 5
99.990 32 5
99.999 36 5
Number of failures = 50.000, Success ratio = 50.000%
Confidence % trials complement
50.000 108 94
75.000 113 90
90.000 118 85
95.000 122 83
99.000 130 78
99.900 139 73
99.990 147 69
99.999 155 65
Number of failures = 500.000, Success ratio = 50.000%
Confidence % trials complement
50.000 1022 979
75.000 1038 965
90.000 1054 950
95.000 1064 940
99.000 1085 922
99.900 1110 902
99.990 1131 885
99.999 1150 870
Number of failures = 50.000, Success ratio = 10.000%
Confidence % trials complement
50.000 553 462
75.000 588 432
90.000 626 403
95.000 651 385
99.000 701 352
99.900 763 317
99.990 818 289
99.999 869 266
Number of failures = 500.000, Success ratio = 10.000%
Confidence % trials complement
50.000 5150 4864
75.000 5254 4766
90.000 5364 4665
95.000 5434 4602
99.000 5574 4480
99.900 5739 4341
99.990 5880 4227
99.999 6006 4129
Number of failures = 5.000, Success ratio = 90.000%
Confidence % trials complement
50.000 6 5
75.000 7 5
90.000 7 5
95.000 8 5
99.000 9 5
99.900 10 5
99.990 12 5
99.999 13 5
Build Time 0:03
Build log was saved at "file://i:\boost-06-05-03-1300\libs\math\test\Math_test\neg_binomial_confidence_levels\Debug\BuildLog.htm"
neg_binomial_confidence_levels - 0 error(s), 0 warning(s)
========== Build: 1 succeeded, 0 failed, 0 up-to-date, 0 skipped ==========
*/
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