// Copyright Paul A. 2006 // Copyright John Maddock 2006 // 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) // Simple example of computing probabilities for a binomial random variable. // Replication of source nag_binomial_dist (g01bjc). // Shows how to replace NAG C library calls by Boost Math Toolkit C++ calls. #ifdef _MSC_VER # pragma warning(disable: 4512) // assignment operator could not be generated. # pragma warning(disable: 4510) // default constructor could not be generated. # pragma warning(disable: 4610) // can never be instantiated - user defined constructor required. #endif #include <iostream> using std::cout; using std::endl; using std::ios; using std::showpoint; #include <iomanip> using std::fixed; using std::setw; #include <boost/math/distributions/binomial.hpp> int main() { cout << "Example 3 of using the binomial distribution to replicate a NAG library call." << endl; using boost::math::binomial_distribution; // This replicates the computation of the examples of using nag-binomial_dist // using g01bjc in section g01 Sample Calculations on Statistical Data. // http://www.nag.co.uk/numeric/cl/manual/pdf/G01/g01bjc.pdf // Program results section 8.3 page 3.g01bjc.3 //8.2. Program Data //g01bjc Example Program Data //4 0.50 2 : n, p, k //19 0.44 13 //100 0.75 67 //2000 0.33 700 //8.3. Program Results //g01bjc Example Program Results //n p k plek pgtk peqk //4 0.500 2 0.68750 0.31250 0.37500 //19 0.440 13 0.99138 0.00862 0.01939 //100 0.750 67 0.04460 0.95540 0.01700 //2000 0.330 700 0.97251 0.02749 0.00312 cout.setf(ios::showpoint); // Trailing zeros to show significant decimal digits. cout.precision(5); // Should be able to calculate this? cout << fixed; // Binomial distribution. // Note that cdf(dist, k) is equivalent to NAG library plek probability of <= k // cdf(complement(dist, k)) is equivalent to NAG library pgtk probability of > k // pdf(dist, k) is equivalent to NAG library peqk probability of == k cout << " n p k plek pgtk peqk " << endl; binomial_distribution<>my_dist(4, 0.5); cout << setw(4) << (int)my_dist.trials() << " " << my_dist.success_fraction() << " "<< 2 << " " << cdf(my_dist, 2) << " " << cdf(complement(my_dist, 2)) << " " << pdf(my_dist, 2) << endl; binomial_distribution<>two(19, 0.440); cout << setw(4) << (int)two.trials() << " " << two.success_fraction() << " " << 13 << " " << cdf(two, 13) << " " << cdf(complement(two, 13)) << " " << pdf(two, 13) << endl; binomial_distribution<>three(100, 0.750); cout << setw(4) << (int)three.trials() << " " << three.success_fraction() << " " << 67 << " " << cdf(three, 67) << " " << cdf(complement(three, 67)) << " " << pdf(three, 67) << endl; binomial_distribution<>four(2000, 0.330); cout << setw(4) << (int)four.trials() << " " << four.success_fraction() << " " << 700 << " " << cdf(four, 700) << " " << cdf(complement(four, 700)) << " " << pdf(four, 700) << endl; return 0; } // int main() /* Autorun "i:\boost-sandbox\math_toolkit\libs\math\test\msvc80\debug\binomial_example3.exe" Example 3 of using the binomial distribution. n p k plek pgtk peqk 4 0.50000 2 0.68750 0.31250 0.37500 19 0.44000 13 0.99138 0.00862 0.01939 100 0.75000 67 0.04460 0.95540 0.01700 2000 0.33000 700 0.97251 0.02749 0.00312 */