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166 lines
7.2 KiB
C++
166 lines
7.2 KiB
C++
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// Copyright John Maddock 2006
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// Copyright Paul A. Bristow 2010
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// Use, modification and distribution are subject to the
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// Boost Software License, Version 1.0.
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// (See accompanying file LICENSE_1_0.txt
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// or copy at http://www.boost.org/LICENSE_1_0.txt)
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#ifdef _MSC_VER
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# pragma warning(disable: 4512) // assignment operator could not be generated.
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# pragma warning(disable: 4510) // default constructor could not be generated.
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# pragma warning(disable: 4610) // can never be instantiated - user defined constructor required.
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#endif
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#include <iostream>
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using std::cout; using std::endl;
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#include <iomanip>
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using std::fixed; using std::left; using std::right; using std::right; using std::setw;
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using std::setprecision;
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#include <boost/math/distributions/binomial.hpp>
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void confidence_limits_on_frequency(unsigned trials, unsigned successes)
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{
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//
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// trials = Total number of trials.
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// successes = Total number of observed successes.
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//
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// Calculate confidence limits for an observed
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// frequency of occurrence that follows a binomial distribution.
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//
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//using namespace std; // Avoid
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// using namespace boost::math; // potential name ambiguity with std <random>
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using boost::math::binomial_distribution;
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// Print out general info:
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cout <<
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"___________________________________________\n"
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"2-Sided Confidence Limits For Success Ratio\n"
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"___________________________________________\n\n";
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cout << setprecision(7);
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cout << setw(40) << left << "Number of Observations" << "= " << trials << "\n";
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cout << setw(40) << left << "Number of successes" << "= " << successes << "\n";
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cout << setw(40) << left << "Sample frequency of occurrence" << "= " << double(successes) / trials << "\n";
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//
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// Define a table of significance levels:
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//
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double alpha[] = { 0.5, 0.25, 0.1, 0.05, 0.01, 0.001, 0.0001, 0.00001 };
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//
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// Print table header:
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//
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cout << "\n\n"
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"_______________________________________________________________________\n"
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"Confidence Lower CP Upper CP Lower JP Upper JP\n"
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" Value (%) Limit Limit Limit Limit\n"
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"_______________________________________________________________________\n";
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//
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// Now print out the data for the table rows.
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//
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for(unsigned i = 0; i < sizeof(alpha)/sizeof(alpha[0]); ++i)
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{
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// Confidence value:
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cout << fixed << setprecision(3) << setw(10) << right << 100 * (1-alpha[i]);
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// Calculate Clopper Pearson bounds:
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double l = binomial_distribution<>::find_lower_bound_on_p(trials, successes, alpha[i]/2);
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double u = binomial_distribution<>::find_upper_bound_on_p(trials, successes, alpha[i]/2);
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// Print Clopper Pearson Limits:
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cout << fixed << setprecision(5) << setw(15) << right << l;
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cout << fixed << setprecision(5) << setw(15) << right << u;
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// Calculate Jeffreys Prior Bounds:
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l = binomial_distribution<>::find_lower_bound_on_p(trials, successes, alpha[i]/2, binomial_distribution<>::jeffreys_prior_interval);
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u = binomial_distribution<>::find_upper_bound_on_p(trials, successes, alpha[i]/2, binomial_distribution<>::jeffreys_prior_interval);
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// Print Jeffreys Prior Limits:
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cout << fixed << setprecision(5) << setw(15) << right << l;
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cout << fixed << setprecision(5) << setw(15) << right << u << std::endl;
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}
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cout << endl;
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} // void confidence_limits_on_frequency()
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int main()
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{
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confidence_limits_on_frequency(20, 4);
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confidence_limits_on_frequency(200, 40);
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confidence_limits_on_frequency(2000, 400);
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return 0;
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} // int main()
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/*
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------ Build started: Project: binomial_confidence_limits, Configuration: Debug Win32 ------
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Compiling...
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binomial_confidence_limits.cpp
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Linking...
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Autorun "i:\boost-06-05-03-1300\libs\math\test\Math_test\debug\binomial_confidence_limits.exe"
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___________________________________________
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2-Sided Confidence Limits For Success Ratio
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___________________________________________
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Number of Observations = 20
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Number of successes = 4
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Sample frequency of occurrence = 0.2
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_______________________________________________________________________
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Confidence Lower CP Upper CP Lower JP Upper JP
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Value (%) Limit Limit Limit Limit
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_______________________________________________________________________
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50.000 0.12840 0.29588 0.14974 0.26916
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75.000 0.09775 0.34633 0.11653 0.31861
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90.000 0.07135 0.40103 0.08734 0.37274
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95.000 0.05733 0.43661 0.07152 0.40823
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99.000 0.03576 0.50661 0.04655 0.47859
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99.900 0.01905 0.58632 0.02634 0.55960
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99.990 0.01042 0.64997 0.01530 0.62495
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99.999 0.00577 0.70216 0.00901 0.67897
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___________________________________________
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2-Sided Confidence Limits For Success Ratio
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___________________________________________
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Number of Observations = 200
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Number of successes = 40
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Sample frequency of occurrence = 0.2000000
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_______________________________________________________________________
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Confidence Lower CP Upper CP Lower JP Upper JP
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Value (%) Limit Limit Limit Limit
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_______________________________________________________________________
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50.000 0.17949 0.22259 0.18190 0.22001
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75.000 0.16701 0.23693 0.16934 0.23429
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90.000 0.15455 0.25225 0.15681 0.24956
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95.000 0.14689 0.26223 0.14910 0.25951
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99.000 0.13257 0.28218 0.13468 0.27940
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99.900 0.11703 0.30601 0.11902 0.30318
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99.990 0.10489 0.32652 0.10677 0.32366
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99.999 0.09492 0.34485 0.09670 0.34197
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___________________________________________
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2-Sided Confidence Limits For Success Ratio
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___________________________________________
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Number of Observations = 2000
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Number of successes = 400
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Sample frequency of occurrence = 0.2000000
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_______________________________________________________________________
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Confidence Lower CP Upper CP Lower JP Upper JP
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Value (%) Limit Limit Limit Limit
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_______________________________________________________________________
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50.000 0.19382 0.20638 0.19406 0.20613
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75.000 0.18965 0.21072 0.18990 0.21047
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90.000 0.18537 0.21528 0.18561 0.21503
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95.000 0.18267 0.21821 0.18291 0.21796
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99.000 0.17745 0.22400 0.17769 0.22374
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99.900 0.17150 0.23079 0.17173 0.23053
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99.990 0.16658 0.23657 0.16681 0.23631
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99.999 0.16233 0.24169 0.16256 0.24143
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*/
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