ceph/src/boost/libs/math/example/neg_binom_confidence_limits.cpp

   1 // neg_binomial_confidence_limits.cpp
   2
   3 // Copyright John Maddock 2006
   4 // Copyright Paul A. Bristow 2007, 2010
   5 // Use, modification and distribution are subject to the
   6 // Boost Software License, Version 1.0.
   7 // (See accompanying file LICENSE_1_0.txt
   8 // or copy at http://www.boost.org/LICENSE_1_0.txt)
   9
  10 // Caution: this file contains quickbook markup as well as code
  11 // and comments, don't change any of the special comment markups!
  12
  13 //[neg_binomial_confidence_limits
  14
  15 /*`
  16
  17 First we need some includes to access the negative binomial distribution
  18 (and some basic std output of course).
  19
  20 */
  21
  22 #include <boost/math/distributions/negative_binomial.hpp>
  23 using boost::math::negative_binomial;
  24
  25 #include <iostream>
  26 using std::cout; using std::endl;
  27 #include <iomanip>
  28 using std::setprecision;
  29 using std::setw; using std::left; using std::fixed; using std::right;
  30
  31 /*`
  32 First define a table of significance levels: these are the
  33 probabilities that the true occurrence frequency lies outside the calculated
  34 interval:
  35 */
  36
  37   double alpha[] = { 0.5, 0.25, 0.1, 0.05, 0.01, 0.001, 0.0001, 0.00001 };
  38
  39 /*`
  40 Confidence value as % is (1 - alpha) * 100, so alpha 0.05 == 95% confidence
  41 that the true occurrence frequency lies *inside* the calculated interval.
  42
  43 We need a function to calculate and print confidence limits
  44 for an observed frequency of occurrence
  45 that follows a negative binomial distribution.
  46
  47 */
  48
  49 void confidence_limits_on_frequency(unsigned trials, unsigned successes)
  50 {
  51    // trials = Total number of trials.
  52    // successes = Total number of observed successes.
  53    // failures = trials - successes.
  54    // success_fraction = successes /trials.
  55    // Print out general info:
  56    cout <<
  57       "______________________________________________\n"
  58       "2-Sided Confidence Limits For Success Fraction\n"
  59       "______________________________________________\n\n";
  60    cout << setprecision(7);
  61    cout << setw(40) << left << "Number of trials" << " =  " << trials << "\n";
  62    cout << setw(40) << left << "Number of successes" << " =  " << successes << "\n";
  63    cout << setw(40) << left << "Number of failures" << " =  " << trials - successes << "\n";
  64    cout << setw(40) << left << "Observed frequency of occurrence" << " =  " << double(successes) / trials << "\n";
  65
  66    // Print table header:
  67    cout << "\n\n"
  68            "___________________________________________\n"
  69            "Confidence        Lower          Upper\n"
  70            " Value (%)        Limit          Limit\n"
  71            "___________________________________________\n";
  72
  73
  74 /*`
  75 And now for the important part - the bounds themselves.
  76 For each value of /alpha/, we call `find_lower_bound_on_p` and
  77 `find_upper_bound_on_p` to obtain lower and upper bounds respectively.
  78 Note that since we are calculating a two-sided interval,
  79 we must divide the value of alpha in two.  Had we been calculating a
  80 single-sided interval, for example: ['"Calculate a lower bound so that we are P%
  81 sure that the true occurrence frequency is greater than some value"]
  82 then we would *not* have divided by two.
  83 */
  84
  85    // Now print out the upper and lower limits for the alpha table values.
  86    for(unsigned i = 0; i < sizeof(alpha)/sizeof(alpha[0]); ++i)
  87    {
  88       // Confidence value:
  89       cout << fixed << setprecision(3) << setw(10) << right << 100 * (1-alpha[i]);
  90       // Calculate bounds:
  91       double lower = negative_binomial::find_lower_bound_on_p(trials, successes, alpha[i]/2);
  92       double upper = negative_binomial::find_upper_bound_on_p(trials, successes, alpha[i]/2);
  93       // Print limits:
  94       cout << fixed << setprecision(5) << setw(15) << right << lower;
  95       cout << fixed << setprecision(5) << setw(15) << right << upper << endl;
  96    }
  97    cout << endl;
  98 } // void confidence_limits_on_frequency(unsigned trials, unsigned successes)
  99
 100 /*`
 101
 102 And then call confidence_limits_on_frequency with increasing numbers of trials,
 103 but always the same success fraction 0.1, or 1 in 10.
 104
 105 */
 106
 107 int main()
 108 {
 109   confidence_limits_on_frequency(20, 2); // 20 trials, 2 successes, 2 in 20, = 1 in 10 = 0.1 success fraction.
 110   confidence_limits_on_frequency(200, 20); // More trials, but same 0.1 success fraction.
 111   confidence_limits_on_frequency(2000, 200); // Many more trials, but same 0.1 success fraction.
 112
 113   return 0;
 114 } // int main()
 115
 116 //] [/negative_binomial_confidence_limits_eg end of Quickbook in C++ markup]
 117
 118 /*
 119
 120 ______________________________________________
 121 2-Sided Confidence Limits For Success Fraction
 122 ______________________________________________
 123 Number of trials                         =  20
 124 Number of successes                      =  2
 125 Number of failures                       =  18
 126 Observed frequency of occurrence         =  0.1
 127 ___________________________________________
 128 Confidence        Lower          Upper
 129  Value (%)        Limit          Limit
 130 ___________________________________________
 131     50.000        0.04812        0.13554
 132     75.000        0.03078        0.17727
 133     90.000        0.01807        0.22637
 134     95.000        0.01235        0.26028
 135     99.000        0.00530        0.33111
 136     99.900        0.00164        0.41802
 137     99.990        0.00051        0.49202
 138     99.999        0.00016        0.55574
 139 ______________________________________________
 140 2-Sided Confidence Limits For Success Fraction
 141 ______________________________________________
 142 Number of trials                         =  200
 143 Number of successes                      =  20
 144 Number of failures                       =  180
 145 Observed frequency of occurrence         =  0.1000000
 146 ___________________________________________
 147 Confidence        Lower          Upper
 148  Value (%)        Limit          Limit
 149 ___________________________________________
 150     50.000        0.08462        0.11350
 151     75.000        0.07580        0.12469
 152     90.000        0.06726        0.13695
 153     95.000        0.06216        0.14508
 154     99.000        0.05293        0.16170
 155     99.900        0.04343        0.18212
 156     99.990        0.03641        0.20017
 157     99.999        0.03095        0.21664
 158 ______________________________________________
 159 2-Sided Confidence Limits For Success Fraction
 160 ______________________________________________
 161 Number of trials                         =  2000
 162 Number of successes                      =  200
 163 Number of failures                       =  1800
 164 Observed frequency of occurrence         =  0.1000000
 165 ___________________________________________
 166 Confidence        Lower          Upper
 167  Value (%)        Limit          Limit
 168 ___________________________________________
 169     50.000        0.09536        0.10445
 170     75.000        0.09228        0.10776
 171     90.000        0.08916        0.11125
 172     95.000        0.08720        0.11352
 173     99.000        0.08344        0.11802
 174     99.900        0.07921        0.12336
 175     99.990        0.07577        0.12795
 176     99.999        0.07282        0.13206
 177 */
 178