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

   1 // Copyright Paul A. 2007, 2010
   2 // Copyright John Maddock 2007
   3 // Use, modification and distribution are subject to the
   4 // Boost Software License, Version 1.0.
   5 // (See accompanying file LICENSE_1_0.txt
   6 // or copy at http://www.boost.org/LICENSE_1_0.txt)
   7
   8 // Simple example of computing probabilities for a binomial random variable.
   9 // Replication of source nag_binomial_dist (g01bjc).
  10
  11 // Shows how to replace NAG C library calls by Boost Math Toolkit C++ calls.
  12 // Note that the default policy does not replicate the way that NAG
  13 // library calls handle 'bad' arguments, but you can define policies that do,
  14 // as well as other policies that may suit your application even better.
  15 // See the examples of changing default policies for details.
  16
  17 #include <boost/math/distributions/binomial.hpp>
  18
  19 #include <iostream>
  20   using std::cout; using std::endl; using std::ios; using std::showpoint;
  21 #include <iomanip>
  22   using std::fixed; using std::setw;
  23
  24 int main()
  25 {
  26   cout << "Using the binomial distribution to replicate a NAG library call." << endl;
  27   using boost::math::binomial_distribution;
  28
  29   // This replicates the computation of the examples of using nag-binomial_dist
  30   // using g01bjc in section g01 Somple Calculations on Statistical Data.
  31   // http://www.nag.co.uk/numeric/cl/manual/pdf/G01/g01bjc.pdf
  32   // Program results section 8.3 page 3.g01bjc.3
  33     //8.2. Program Data
  34     //g01bjc Example Program Data
  35     //4 0.50 2 : n, p, k
  36     //19 0.44 13
  37     //100 0.75 67
  38     //2000 0.33 700
  39     //8.3. Program Results
  40     //g01bjc Example Program Results
  41     //n p k plek pgtk peqk
  42     //4 0.500 2 0.68750 0.31250 0.37500
  43     //19 0.440 13 0.99138 0.00862 0.01939
  44     //100 0.750 67 0.04460 0.95540 0.01700
  45     //2000 0.330 700 0.97251 0.02749 0.00312
  46
  47   cout.setf(ios::showpoint); // Trailing zeros to show significant decimal digits.
  48   cout.precision(5); // Might calculate this from trials in distribution?
  49   cout << fixed;
  50   //  Binomial distribution.
  51
  52   // Note  that  cdf(dist, k) is equivalent to NAG library plek probability of <= k
  53   // cdf(complement(dist, k)) is equivalent to NAG library pgtk probability of > k
  54   //             pdf(dist, k) is equivalent to NAG library peqk probability of == k
  55
  56   cout << " n        p     k     plek     pgtk     peqk " << endl;
  57   binomial_distribution<>my_dist(4, 0.5);
  58   cout << setw(4) << (int)my_dist.trials() << "  " << my_dist.success_fraction()
  59   << "   " << 2 << "  " << cdf(my_dist, 2) << "  "
  60   << cdf(complement(my_dist, 2)) << "  " << pdf(my_dist, 2) << endl;
  61
  62   binomial_distribution<>two(19, 0.440);
  63   cout << setw(4) << (int)two.trials() <<  "  "  << two.success_fraction()
  64     << "  " << 13 << "  " << cdf(two, 13) << "  "
  65     << cdf(complement(two, 13)) << "  " << pdf(two, 13) << endl;
  66
  67   binomial_distribution<>three(100, 0.750);
  68   cout << setw(4) << (int)three.trials() << "  " << three.success_fraction()
  69     << "  " << 67 << "  " << cdf(three, 67) << "  " << cdf(complement(three, 67))
  70     << "  " << pdf(three, 67) << endl;
  71   binomial_distribution<>four(2000, 0.330);
  72   cout << setw(4) << (int)four.trials() <<  "  "  << four.success_fraction()
  73   << " " << 700 << "  "
  74     << cdf(four, 700) << "  " << cdf(complement(four, 700))
  75     << "  " << pdf(four, 700) << endl;
  76
  77   return 0;
  78 } // int main()
  79
  80 /*
  81
  82 Example of using the binomial distribution to replicate a NAG library call.
  83  n        p     k     plek     pgtk     peqk
  84    4  0.50000   2  0.68750  0.31250  0.37500
  85   19  0.44000  13  0.99138  0.00862  0.01939
  86  100  0.75000  67  0.04460  0.95540  0.01700
  87 2000  0.33000 700  0.97251  0.02749  0.00312
  88
  89
  90  */
  91