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
main()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 Simple 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
92