92 lines
3.5 KiB
C++
92 lines
3.5 KiB
C++
// Copyright Paul A. 2007, 2010
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// Copyright John Maddock 2007
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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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// Simple example of computing probabilities for a binomial random variable.
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// Replication of source nag_binomial_dist (g01bjc).
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// Shows how to replace NAG C library calls by Boost Math Toolkit C++ calls.
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// Note that the default policy does not replicate the way that NAG
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// library calls handle 'bad' arguments, but you can define policies that do,
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// as well as other policies that may suit your application even better.
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// See the examples of changing default policies for details.
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#include <boost/math/distributions/binomial.hpp>
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#include <iostream>
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using std::cout; using std::endl; using std::ios; using std::showpoint;
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#include <iomanip>
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using std::fixed; using std::setw;
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int main()
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{
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cout << "Using the binomial distribution to replicate a NAG library call." << endl;
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using boost::math::binomial_distribution;
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// This replicates the computation of the examples of using nag-binomial_dist
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// using g01bjc in section g01 Somple Calculations on Statistical Data.
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// http://www.nag.co.uk/numeric/cl/manual/pdf/G01/g01bjc.pdf
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// Program results section 8.3 page 3.g01bjc.3
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//8.2. Program Data
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//g01bjc Example Program Data
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//4 0.50 2 : n, p, k
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//19 0.44 13
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//100 0.75 67
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//2000 0.33 700
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//8.3. Program Results
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//g01bjc Example Program Results
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//n p k plek pgtk peqk
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//4 0.500 2 0.68750 0.31250 0.37500
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//19 0.440 13 0.99138 0.00862 0.01939
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//100 0.750 67 0.04460 0.95540 0.01700
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//2000 0.330 700 0.97251 0.02749 0.00312
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cout.setf(ios::showpoint); // Trailing zeros to show significant decimal digits.
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cout.precision(5); // Might calculate this from trials in distribution?
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cout << fixed;
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// Binomial distribution.
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// Note that cdf(dist, k) is equivalent to NAG library plek probability of <= k
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// cdf(complement(dist, k)) is equivalent to NAG library pgtk probability of > k
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// pdf(dist, k) is equivalent to NAG library peqk probability of == k
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cout << " n p k plek pgtk peqk " << endl;
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binomial_distribution<>my_dist(4, 0.5);
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cout << setw(4) << (int)my_dist.trials() << " " << my_dist.success_fraction()
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<< " " << 2 << " " << cdf(my_dist, 2) << " "
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<< cdf(complement(my_dist, 2)) << " " << pdf(my_dist, 2) << endl;
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binomial_distribution<>two(19, 0.440);
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cout << setw(4) << (int)two.trials() << " " << two.success_fraction()
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<< " " << 13 << " " << cdf(two, 13) << " "
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<< cdf(complement(two, 13)) << " " << pdf(two, 13) << endl;
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binomial_distribution<>three(100, 0.750);
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cout << setw(4) << (int)three.trials() << " " << three.success_fraction()
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<< " " << 67 << " " << cdf(three, 67) << " " << cdf(complement(three, 67))
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<< " " << pdf(three, 67) << endl;
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binomial_distribution<>four(2000, 0.330);
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cout << setw(4) << (int)four.trials() << " " << four.success_fraction()
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<< " " << 700 << " "
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<< cdf(four, 700) << " " << cdf(complement(four, 700))
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<< " " << pdf(four, 700) << endl;
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return 0;
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} // int main()
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/*
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Example of using the binomial distribution to replicate a NAG library call.
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n p k plek pgtk peqk
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4 0.50000 2 0.68750 0.31250 0.37500
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19 0.44000 13 0.99138 0.00862 0.01939
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100 0.75000 67 0.04460 0.95540 0.01700
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2000 0.33000 700 0.97251 0.02749 0.00312
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*/
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