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// Copyright John Maddock 2006
// Copyright Paul A. Bristow 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)
#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>
using std::fixed; using std::left; using std::right; using std::right; using std::setw;
using std::setprecision;
#include <boost/math/distributions/binomial.hpp>
void confidence_limits_on_frequency(unsigned trials, unsigned successes)
{
//
// trials = Total number of trials.
// successes = Total number of observed successes.
//
// Calculate confidence limits for an observed
// frequency of occurrence that follows a binomial distribution.
//
//using namespace std; // Avoid
// using namespace boost::math; // potential name ambiguity with std <random>
using boost::math::binomial_distribution;
// 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 Observations" << "= " << trials << "\n";
cout << setw(40) << left << "Number of successes" << "= " << successes << "\n";
cout << setw(40) << left << "Sample frequency 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 CP Upper CP Lower JP Upper JP\n"
" Value (%) Limit Limit Limit Limit\n"
"_______________________________________________________________________\n";
//
// Now print out the data for the 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 Clopper Pearson bounds:
double l = binomial_distribution<>::find_lower_bound_on_p(trials, successes, alpha[i]/2);
double u = binomial_distribution<>::find_upper_bound_on_p(trials, successes, alpha[i]/2);
// Print Clopper Pearson Limits:
cout << fixed << setprecision(5) << setw(15) << right << l;
cout << fixed << setprecision(5) << setw(15) << right << u;
// Calculate Jeffreys Prior Bounds:
l = binomial_distribution<>::find_lower_bound_on_p(trials, successes, alpha[i]/2, binomial_distribution<>::jeffreys_prior_interval);
u = binomial_distribution<>::find_upper_bound_on_p(trials, successes, alpha[i]/2, binomial_distribution<>::jeffreys_prior_interval);
// Print Jeffreys Prior Limits:
cout << fixed << setprecision(5) << setw(15) << right << l;
cout << fixed << setprecision(5) << setw(15) << right << u << std::endl;
}
cout << endl;
} // void confidence_limits_on_frequency()
int main()
{
confidence_limits_on_frequency(20, 4);
confidence_limits_on_frequency(200, 40);
confidence_limits_on_frequency(2000, 400);
return 0;
} // int main()
/*
------ Build started: Project: binomial_confidence_limits, Configuration: Debug Win32 ------
Compiling...
binomial_confidence_limits.cpp
Linking...
Autorun "i:\boost-06-05-03-1300\libs\math\test\Math_test\debug\binomial_confidence_limits.exe"
___________________________________________
2-Sided Confidence Limits For Success Ratio
___________________________________________
Number of Observations = 20
Number of successes = 4
Sample frequency of occurrence = 0.2
_______________________________________________________________________
Confidence Lower CP Upper CP Lower JP Upper JP
Value (%) Limit Limit Limit Limit
_______________________________________________________________________
50.000 0.12840 0.29588 0.14974 0.26916
75.000 0.09775 0.34633 0.11653 0.31861
90.000 0.07135 0.40103 0.08734 0.37274
95.000 0.05733 0.43661 0.07152 0.40823
99.000 0.03576 0.50661 0.04655 0.47859
99.900 0.01905 0.58632 0.02634 0.55960
99.990 0.01042 0.64997 0.01530 0.62495
99.999 0.00577 0.70216 0.00901 0.67897
___________________________________________
2-Sided Confidence Limits For Success Ratio
___________________________________________
Number of Observations = 200
Number of successes = 40
Sample frequency of occurrence = 0.2000000
_______________________________________________________________________
Confidence Lower CP Upper CP Lower JP Upper JP
Value (%) Limit Limit Limit Limit
_______________________________________________________________________
50.000 0.17949 0.22259 0.18190 0.22001
75.000 0.16701 0.23693 0.16934 0.23429
90.000 0.15455 0.25225 0.15681 0.24956
95.000 0.14689 0.26223 0.14910 0.25951
99.000 0.13257 0.28218 0.13468 0.27940
99.900 0.11703 0.30601 0.11902 0.30318
99.990 0.10489 0.32652 0.10677 0.32366
99.999 0.09492 0.34485 0.09670 0.34197
___________________________________________
2-Sided Confidence Limits For Success Ratio
___________________________________________
Number of Observations = 2000
Number of successes = 400
Sample frequency of occurrence = 0.2000000
_______________________________________________________________________
Confidence Lower CP Upper CP Lower JP Upper JP
Value (%) Limit Limit Limit Limit
_______________________________________________________________________
50.000 0.19382 0.20638 0.19406 0.20613
75.000 0.18965 0.21072 0.18990 0.21047
90.000 0.18537 0.21528 0.18561 0.21503
95.000 0.18267 0.21821 0.18291 0.21796
99.000 0.17745 0.22400 0.17769 0.22374
99.900 0.17150 0.23079 0.17173 0.23053
99.990 0.16658 0.23657 0.16681 0.23631
99.999 0.16233 0.24169 0.16256 0.24143
*/
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