libs/math/example/binomial_confidence_limits.cpp
// Copyright John Maddock 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> #include <iomanip> #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; 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 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 */