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179 lines
6.7 KiB
C++
179 lines
6.7 KiB
C++
// neg_binomial_confidence_limits.cpp
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// Copyright John Maddock 2006
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// Copyright Paul A. Bristow 2007, 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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// Caution: this file contains quickbook markup as well as code
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// and comments, don't change any of the special comment markups!
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//[neg_binomial_confidence_limits
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/*`
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First we need some includes to access the negative binomial distribution
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(and some basic std output of course).
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*/
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#include <boost/math/distributions/negative_binomial.hpp>
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using boost::math::negative_binomial;
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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::setprecision;
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using std::setw; using std::left; using std::fixed; using std::right;
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/*`
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First define a table of significance levels: these are the
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probabilities that the true occurrence frequency lies outside the calculated
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interval:
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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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Confidence value as % is (1 - alpha) * 100, so alpha 0.05 == 95% confidence
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that the true occurrence frequency lies *inside* the calculated interval.
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We need a function to calculate and print confidence limits
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for an observed frequency of occurrence
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that follows a negative binomial distribution.
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*/
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void confidence_limits_on_frequency(unsigned trials, unsigned successes)
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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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// failures = trials - successes.
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// success_fraction = successes /trials.
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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 Fraction\n"
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"______________________________________________\n\n";
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cout << setprecision(7);
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cout << setw(40) << left << "Number of trials" << " = " << trials << "\n";
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cout << setw(40) << left << "Number of successes" << " = " << successes << "\n";
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cout << setw(40) << left << "Number of failures" << " = " << trials - successes << "\n";
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cout << setw(40) << left << "Observed frequency of occurrence" << " = " << double(successes) / trials << "\n";
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// Print table header:
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cout << "\n\n"
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"___________________________________________\n"
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"Confidence Lower Upper\n"
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" Value (%) Limit Limit\n"
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"___________________________________________\n";
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/*`
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And now for the important part - the bounds themselves.
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For each value of /alpha/, we call `find_lower_bound_on_p` and
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`find_upper_bound_on_p` to obtain lower and upper bounds respectively.
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Note that since we are calculating a two-sided interval,
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we must divide the value of alpha in two. Had we been calculating a
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single-sided interval, for example: ['"Calculate a lower bound so that we are P%
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sure that the true occurrence frequency is greater than some value"]
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then we would *not* have divided by two.
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*/
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// Now print out the upper and lower limits for the alpha table values.
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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 bounds:
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double lower = negative_binomial::find_lower_bound_on_p(trials, successes, alpha[i]/2);
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double upper = negative_binomial::find_upper_bound_on_p(trials, successes, alpha[i]/2);
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// Print limits:
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cout << fixed << setprecision(5) << setw(15) << right << lower;
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cout << fixed << setprecision(5) << setw(15) << right << upper << endl;
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}
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cout << endl;
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} // void confidence_limits_on_frequency(unsigned trials, unsigned successes)
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/*`
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And then call confidence_limits_on_frequency with increasing numbers of trials,
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but always the same success fraction 0.1, or 1 in 10.
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*/
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int main()
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{
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confidence_limits_on_frequency(20, 2); // 20 trials, 2 successes, 2 in 20, = 1 in 10 = 0.1 success fraction.
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confidence_limits_on_frequency(200, 20); // More trials, but same 0.1 success fraction.
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confidence_limits_on_frequency(2000, 200); // Many more trials, but same 0.1 success fraction.
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return 0;
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} // int main()
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//] [/negative_binomial_confidence_limits_eg end of Quickbook in C++ markup]
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/*
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______________________________________________
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2-Sided Confidence Limits For Success Fraction
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______________________________________________
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Number of trials = 20
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Number of successes = 2
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Number of failures = 18
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Observed frequency of occurrence = 0.1
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___________________________________________
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Confidence Lower Upper
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Value (%) Limit Limit
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___________________________________________
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50.000 0.04812 0.13554
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75.000 0.03078 0.17727
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90.000 0.01807 0.22637
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95.000 0.01235 0.26028
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99.000 0.00530 0.33111
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99.900 0.00164 0.41802
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99.990 0.00051 0.49202
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99.999 0.00016 0.55574
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______________________________________________
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2-Sided Confidence Limits For Success Fraction
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______________________________________________
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Number of trials = 200
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Number of successes = 20
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Number of failures = 180
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Observed frequency of occurrence = 0.1000000
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___________________________________________
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Confidence Lower Upper
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Value (%) Limit Limit
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___________________________________________
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50.000 0.08462 0.11350
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75.000 0.07580 0.12469
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90.000 0.06726 0.13695
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95.000 0.06216 0.14508
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99.000 0.05293 0.16170
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99.900 0.04343 0.18212
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99.990 0.03641 0.20017
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99.999 0.03095 0.21664
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______________________________________________
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2-Sided Confidence Limits For Success Fraction
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______________________________________________
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Number of trials = 2000
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Number of successes = 200
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Number of failures = 1800
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Observed frequency of occurrence = 0.1000000
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___________________________________________
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Confidence Lower Upper
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Value (%) Limit Limit
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___________________________________________
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50.000 0.09536 0.10445
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75.000 0.09228 0.10776
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90.000 0.08916 0.11125
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95.000 0.08720 0.11352
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99.000 0.08344 0.11802
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99.900 0.07921 0.12336
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99.990 0.07577 0.12795
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99.999 0.07282 0.13206
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*/
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