| // neg_binomial_confidence_limits.cpp |
| |
| // Copyright John Maddock 2006 |
| // Copyright Paul A. Bristow 2007, 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) |
| |
| // Caution: this file contains quickbook markup as well as code |
| // and comments, don't change any of the special comment markups! |
| |
| //[neg_binomial_confidence_limits |
| |
| /*` |
| |
| First we need some includes to access the negative binomial distribution |
| (and some basic std output of course). |
| |
| */ |
| |
| #include <boost/math/distributions/negative_binomial.hpp> |
| using boost::math::negative_binomial; |
| |
| #include <iostream> |
| using std::cout; using std::endl; |
| #include <iomanip> |
| using std::setprecision; |
| using std::setw; using std::left; using std::fixed; using std::right; |
| |
| /*` |
| First define a table of significance levels: these are the |
| probabilities that the true occurrence frequency lies outside the calculated |
| interval: |
| */ |
| |
| double alpha[] = { 0.5, 0.25, 0.1, 0.05, 0.01, 0.001, 0.0001, 0.00001 }; |
| |
| /*` |
| |
| Confidence value as % is (1 - alpha) * 100, so alpha 0.05 == 95% confidence |
| that the true occurence frequency lies *inside* the calculated interval. |
| |
| We need a function to calculate and print confidence limits |
| for an observed frequency of occurrence |
| that follows a negative binomial distribution. |
| |
| */ |
| |
| void confidence_limits_on_frequency(unsigned trials, unsigned successes) |
| { |
| // trials = Total number of trials. |
| // successes = Total number of observed successes. |
| // failures = trials - successes. |
| // success_fraction = successes /trials. |
| // Print out general info: |
| cout << |
| "______________________________________________\n" |
| "2-Sided Confidence Limits For Success Fraction\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 frequency of occurrence" << " = " << double(successes) / trials << "\n"; |
| |
| // Print table header: |
| cout << "\n\n" |
| "___________________________________________\n" |
| "Confidence Lower Upper\n" |
| " Value (%) Limit Limit\n" |
| "___________________________________________\n"; |
| |
| |
| /*` |
| And now for the important part - the bounds themselves. |
| For each value of /alpha/, we call `find_lower_bound_on_p` and |
| `find_upper_bound_on_p` to obtain lower and upper bounds respectively. |
| Note that since we are calculating a two-sided interval, |
| we must divide the value of alpha in two. Had we been calculating a |
| single-sided interval, for example: ['"Calculate a lower bound so that we are P% |
| sure that the true occurrence frequency is greater than some value"] |
| then we would *not* have divided by two. |
| |
| */ |
| |
| // Now print out the upper and lower limits for the alpha table values. |
| 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 lower = negative_binomial::find_lower_bound_on_p(trials, successes, alpha[i]/2); |
| double upper = negative_binomial::find_upper_bound_on_p(trials, successes, alpha[i]/2); |
| // Print limits: |
| cout << fixed << setprecision(5) << setw(15) << right << lower; |
| cout << fixed << setprecision(5) << setw(15) << right << upper << endl; |
| } |
| cout << endl; |
| } // void confidence_limits_on_frequency(unsigned trials, unsigned successes) |
| |
| /*` |
| |
| And then call confidence_limits_on_frequency with increasing numbers of trials, |
| but always the same success fraction 0.1, or 1 in 10. |
| |
| */ |
| |
| int main() |
| { |
| confidence_limits_on_frequency(20, 2); // 20 trials, 2 successes, 2 in 20, = 1 in 10 = 0.1 success fraction. |
| confidence_limits_on_frequency(200, 20); // More trials, but same 0.1 success fraction. |
| confidence_limits_on_frequency(2000, 200); // Many more trials, but same 0.1 success fraction. |
| |
| return 0; |
| } // int main() |
| |
| //] [/negative_binomial_confidence_limits_eg end of Quickbook in C++ markup] |
| |
| /* |
| |
| ______________________________________________ |
| 2-Sided Confidence Limits For Success Fraction |
| ______________________________________________ |
| Number of trials = 20 |
| Number of successes = 2 |
| Number of failures = 18 |
| Observed frequency of occurrence = 0.1 |
| ___________________________________________ |
| Confidence Lower Upper |
| Value (%) Limit Limit |
| ___________________________________________ |
| 50.000 0.04812 0.13554 |
| 75.000 0.03078 0.17727 |
| 90.000 0.01807 0.22637 |
| 95.000 0.01235 0.26028 |
| 99.000 0.00530 0.33111 |
| 99.900 0.00164 0.41802 |
| 99.990 0.00051 0.49202 |
| 99.999 0.00016 0.55574 |
| ______________________________________________ |
| 2-Sided Confidence Limits For Success Fraction |
| ______________________________________________ |
| Number of trials = 200 |
| Number of successes = 20 |
| Number of failures = 180 |
| Observed frequency of occurrence = 0.1000000 |
| ___________________________________________ |
| Confidence Lower Upper |
| Value (%) Limit Limit |
| ___________________________________________ |
| 50.000 0.08462 0.11350 |
| 75.000 0.07580 0.12469 |
| 90.000 0.06726 0.13695 |
| 95.000 0.06216 0.14508 |
| 99.000 0.05293 0.16170 |
| 99.900 0.04343 0.18212 |
| 99.990 0.03641 0.20017 |
| 99.999 0.03095 0.21664 |
| ______________________________________________ |
| 2-Sided Confidence Limits For Success Fraction |
| ______________________________________________ |
| Number of trials = 2000 |
| Number of successes = 200 |
| Number of failures = 1800 |
| Observed frequency of occurrence = 0.1000000 |
| ___________________________________________ |
| Confidence Lower Upper |
| Value (%) Limit Limit |
| ___________________________________________ |
| 50.000 0.09536 0.10445 |
| 75.000 0.09228 0.10776 |
| 90.000 0.08916 0.11125 |
| 95.000 0.08720 0.11352 |
| 99.000 0.08344 0.11802 |
| 99.900 0.07921 0.12336 |
| 99.990 0.07577 0.12795 |
| 99.999 0.07282 0.13206 |
| */ |
| |
