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Some very simple examples of usage.
[SVN r3432]
This commit is contained in:
Paul A. Bristow
@@ -7,18 +7,19 @@
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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 examples for Negative Binomial Distribution.
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// Simple examples demonstrating use of the Negative Binomial Distribution.
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// (See other examples for practical applications).
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#define BOOST_MATH_THROW_ON_DOMAIN_ERROR
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#ifdef _MSC_VER
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# pragma warning(disable: 4127) // conditional expression is constant.
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# pragma warning(disable: 4100) // unreferenced formal parameter.
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# pragma warning(disable: 4512) // assignment operator could not be generated.
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#endif
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#include <boost/math/distributions/negative_binomial.hpp> // for negative_binomial_distribution
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using boost::math::negative_binomial_distribution;
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#include <boost/math/distributions/negative_binomial.hpp>
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using boost::math::negative_binomial_distribution;
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using boost::math::negative_binomial; // typedef
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// In a sequence of trials or events
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// (Bernoulli, independent, yes or no, succeed or fail)
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@@ -26,15 +27,6 @@ using boost::math::negative_binomial_distribution;
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// negative_binomial is the probability that k or fewer failures
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// preceed the r th trial's success.
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#include <boost/math/special_functions/gamma.hpp>
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using boost::math::lgamma; // log gamma
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//#include <boost/math/concepts/real_concept.hpp> // for real_concept
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//using ::boost::math::concepts::real_concept;
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//#include <boost/test/included/test_exec_monitor.hpp> // for test_main
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//#include <boost/test/floating_point_comparison.hpp> // for BOOST_CHECK_CLOSE
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#include <iostream>
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using std::cout;
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using std::endl;
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@@ -42,40 +34,40 @@ using std::setprecision;
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using std::showpoint;
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using std::setw;
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using std::left;
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using std::right;
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#include <limits>
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using std::numeric_limits;
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int main(int, char* [])
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int main()
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{
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#ifdef BOOST_MATH_THROW_ON_DOMAIN_ERROR
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cout << "BOOST_MATH_THROW_ON_DOMAIN_ERROR" << " is defined to throw on domain error." << endl;
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#else
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cout << "BOOST_MATH_THROW_ON_DOMAIN_ERROR" << " is NOT defined, so NO throw on domain error." << endl;
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#endif
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cout << "negative_binomial distribution - simples examples" << endl;
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using namespace boost::math;
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cout << setprecision(17) << showpoint << endl; // max_digits10 precision including trailing zeros.
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cout << "negative_binomial distribution - simples example 2" << endl;
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negative_binomial_distribution<double> my8dist(8., 0.25);
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// 8 successes (r), 0.25 success fraction = 25% or 1 in 4 successes.
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// Note: double values (matching the distribution definition) avoid the need for any casting.
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// Construct distribution: 8 successes (r), 0.25 success fraction = 25% or 1 in 4 successes.
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// negative_binomial_distribution<double> my8dist(8, 0.25);
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negative_binomial my8dist(8, 0.25); // Shorter method using typedef.
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cout << "mean(my8dist) = " << mean(my8dist) << endl; //
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cout.precision(17); // max_digits10 precision
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cout << "mean(my8dist) = " << mean(my8dist) << endl; // 24
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cout << "my8dist.successes() = " << my8dist.successes() << endl;
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// r th trial is successful, after r-1 = k failures.
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cout << "my8dist.success_fraction() = " << my8dist.success_fraction() << endl;
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// failures/successes.
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cout << "cdf(my8dist, 2.) = " << cdf(my8dist, 2.) << endl; // 4.1580200195313E-4
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cout << "cdf(my8dist, 8.) = " << cdf(my8dist, 8.) << endl;
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cout << "cdf(complement(my8dist, 8.)) = " << cdf(complement(my8dist, 8.)) << endl;
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cout << "cdf + complement = " << cdf(my8dist, 8.) + cdf(complement(my8dist, 8.)) << endl;
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// Expect unity.
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// cout << "cdf(complement(my8dist, 8.)) = " << pdf(complement(my8dist, 8.)) << endl;
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// r th successful trial, after k failures, is r + k th trial.
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cout << "my8dist.success_fraction() = " << my8dist.success_fraction() << endl;
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// success_fraction = failures/successes or k/r = 0.25 or 25%.
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cout << "my8dist.percent success = " << my8dist.success_fraction() * 100 << "%" << endl;
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cout << "cdf(my8dist, 2.) = " << cdf(my8dist, 2.) << endl; // 0.000415802001953125
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cout << "cdf(my8dist, 8.) = " << cdf(my8dist, 8.) << endl; // 0.027129956288263202
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cout << "cdf(complement(my8dist, 8.)) = " << cdf(complement(my8dist, 8.)) << endl; // 0.9728700437117368
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// Check that cdf plus its complement is unity.
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cout << "cdf + complement = " << cdf(my8dist, 8.) + cdf(complement(my8dist, 8.)) << endl; // 1
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// Note: No complement for pdf!
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double sum = 0.;
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int k = 20;
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// Compare cdf with sum of pdfs.
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double sum = 0.; // of pdfs
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int k = 20;
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for(signed i = 0; i <= k; ++i)
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{
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sum += pdf(my8dist, double(i));
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@@ -84,35 +76,34 @@ int main(int, char* [])
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double cdf8 = cdf(my8dist, static_cast<double>(k));
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double diff = sum - cdf8;
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cout << setprecision(17) << showpoint << "Sum pdfs = " << sum <<' ' // 0.40025683281803714
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<< ", cdf = " << cdf(my8dist, static_cast<double>(k))
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cout << setprecision(17) << "Sum pdfs = " << sum << ' ' // 0.40025683281803698
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<< ", cdf = " << cdf(my8dist, static_cast<double>(k)) // cdf = 0.40025683281803687
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<< ", difference = "
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<< diff/ std::numeric_limits<double>::epsilon()
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<< diff/ std::numeric_limits<double>::epsilon() // difference = 0.50000000000000000
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<< " in epsilon units." << endl;
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// 0.40025683281803681
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//double tol = boost::math::tools::epsilon<double>() * 100 * 10; // 100 for %, so 10 eps
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// Use boost::math::tools::epsilon rather than std::numeric_limits to cover
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// RealTypes that do not specialize numeric_limits.
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//BOOST_CHECK_CLOSE(sum, cdf(my8dist, static_cast<double>(20)), tol);
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// Note: Use boost::math::tools::epsilon rather than std::numeric_limits to cover
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// RealTypes that do not specialize numeric_limits.
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// Print a list of values that can be used to plot
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// using Excel, or some superior graphical display tool.
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// using Excel, or some other superior graphical display tool.
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cout << setprecision(17) << showpoint << endl; // max_digits10 precision, including trailing zeros.
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int maxk = static_cast<int>(2. * my8dist.successes() / my8dist.success_fraction());
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// This shows most of the range of interest.
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// This maxk shows most of the range of interest, probability about 0.0001 to 0.9999.
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cout << " k pdf cdf""\n" << endl;
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for (int k = 0; k < maxk; k++)
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{
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cout << setprecision(17) << showpoint
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<< left << setw(3) << k << ", "
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<< left << setw(23) << pdf(my8dist, static_cast<double>(k)) << ", "
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<< left << setw(23) << cdf(my8dist, static_cast<double>(k))
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cout << right << setprecision(17) << showpoint
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<< right << setw(3) << k << ", "
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<< left << setw(25) << pdf(my8dist, static_cast<double>(k)) << ", "
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<< left << setw(25) << cdf(my8dist, static_cast<double>(k))
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<< endl;
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}
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cout << endl;
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return 0;
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} // int main(int, char* [])
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} // int main()
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/*
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@@ -124,79 +115,81 @@ negative_binomial_example2.cpp
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Linking...
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Autorun "i:\boost-06-05-03-1300\libs\math\test\Math_test\debug\negative_binomial_example2.exe"
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BOOST_MATH_THROW_ON_DOMAIN_ERROR is defined to throw on domain error.
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negative_binomial distribution - simples examples
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mean(my8dist) = 24.000000000000000
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my8dist.successes() = 8.0000000000000000
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my8dist.success_fraction() = 0.25000000000000000
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cdf(my8dist, 2.) = 0.00041580200195312495
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cdf(my8dist, 8.) = 0.027129956288263198
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cdf(complement(my8dist, 8.)) = 0.97287004371173680
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cdf + complement = 1.0000000000000000
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Sum pdfs = 0.40025683281803714 , cdf = 0.40025683281803681, difference = 1.5000000000000000 in epsilon units.
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0 , 1.5258789062499998e-005, 1.5258789062500003e-005
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1 , 9.1552734374999959e-005, 0.00010681152343750000
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2 , 0.00030899047851562522 , 0.00041580200195312495
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3 , 0.00077247619628906239 , 0.0011882781982421873
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4 , 0.0015932321548461931 , 0.0027815103530883785
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5 , 0.0028678178787231463 , 0.0056493282318115226
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6 , 0.0046602040529251142 , 0.010309532284736632
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7 , 0.0069903060793876605 , 0.017299838364124295
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8 , 0.0098301179241389071 , 0.027129956288263198
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9 , 0.013106823898851858 , 0.040236780187115066
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10 , 0.016711200471036133 , 0.056947980658151202
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11 , 0.020509200578089803 , 0.077457181236240999
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12 , 0.024354675686481628 , 0.10181185692272264
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13 , 0.028101548869017345 , 0.12991340579173991
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14 , 0.031614242477644432 , 0.16152764826938434
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15 , 0.034775666725408945 , 0.19630331499479323
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16 , 0.037492515688331500 , 0.23379583068312468
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17 , 0.039697957787645122 , 0.27349378847076972
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18 , 0.041352039362130291 , 0.31484582783289999
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19 , 0.042440250924291600 , 0.35728607875719159
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20 , 0.042970754060845266 , 0.40025683281803681
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21 , 0.042970754060845252 , 0.44322758687888208
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22 , 0.042482450037426567 , 0.48571003691630860
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23 , 0.041558918514873790 , 0.52726895543118235
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24 , 0.040260202311284035 , 0.56752915774246648
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25 , 0.038649794218832613 , 0.60617895196129901
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26 , 0.036791631035234952 , 0.64297058299653465
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27 , 0.034747651533277447 , 0.67771823452981150
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28 , 0.032575923312447616 , 0.71029415784225836
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29 , 0.030329307911589130 , 0.74062346575384863
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30 , 0.028054609818219937 , 0.76867807557206813
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31 , 0.025792141284492535 , 0.79447021685656094
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32 , 0.023575629142856481 , 0.81804584599941688
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33 , 0.021432390129869510 , 0.83947823612928674
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34 , 0.019383705779220179 , 0.85886194190850684
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35 , 0.017445335201298227 , 0.87630727710980472
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36 , 0.015628112784496315 , 0.89193538989430132
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37 , 0.013938587078064250 , 0.90587397697236538
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38 , 0.012379666154859706 , 0.91825364312722502
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39 , 0.010951243136991251 , 0.92920488626421649
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40 , 0.0096507830144735348 , 0.93885566927868991
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41 , 0.0084738582566109191 , 0.94732952753530109
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42 , 0.0074146259745345999 , 0.95474415350983566
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43 , 0.0064662435824429246 , 0.96121039709227840
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44 , 0.0056212231142827853 , 0.96683162020656122
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45 , 0.0048717266990450708 , 0.97170334690560634
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46 , 0.0042098073105878457 , 0.97591315421619418
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47 , 0.0036275999165703964 , 0.97954075413276454
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48 , 0.0031174686783026818 , 0.98265822281106729
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49 , 0.0026721160099737293 , 0.98533033882104104
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50 , 0.0022846591885275322 , 0.98761499800956853
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51 , 0.0019486798960970076 , 0.98956367790566557
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52 , 0.0016582516423517852 , 0.99122192954801736
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53 , 0.0014079495076571762 , 0.99262987905567457
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54 , 0.0011928461106539983 , 0.99382272516632852
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55 , 0.0010084971662801955 , 0.99483122233260879
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56 , 0.00085091948404891532 , 0.99568214181665760
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57 , 0.00071656377604119553 , 0.99639870559269883
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58 , 0.00060228420831048911 , 0.99700098980100937
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59 , 0.00050530624256557902 , 0.99750629604357488
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60 , 0.00042319397814867321 , 0.99792949002172360
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61 , 0.00035381791615708398 , 0.99828330793788067
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62 , 0.00029532382517950264 , 0.99857863176306016
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63 , 0.00024610318764958615 , 0.99882473495070978
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negative_binomial distribution - simples example 2
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mean(my8dist) = 24
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my8dist.successes() = 8
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my8dist.success_fraction() = 0.25
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my8dist.percent success = 25%
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cdf(my8dist, 2.) = 0.000415802001953125
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cdf(my8dist, 8.) = 0.027129956288263202
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cdf(complement(my8dist, 8.)) = 0.9728700437117368
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cdf + complement = 1
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Sum pdfs = 0.40025683281803698 , cdf = 0.40025683281803687, difference = 0.5 in epsilon units.
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k pdf cdf
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0, 1.5258789062499998e-005 , 1.5258789062499998e-005
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1, 9.1552734374999959e-005 , 0.00010681152343750000
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2, 0.00030899047851562522 , 0.00041580200195312500
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3, 0.00077247619628906239 , 0.0011882781982421875
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4, 0.0015932321548461931 , 0.0027815103530883789
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5, 0.0028678178787231463 , 0.0056493282318115234
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6, 0.0046602040529251142 , 0.010309532284736633
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7, 0.0069903060793876605 , 0.017299838364124298
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8, 0.0098301179241388984 , 0.027129956288263202
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9, 0.013106823898851870 , 0.040236780187115073
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10, 0.016711200471036133 , 0.056947980658151209
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11, 0.020509200578089803 , 0.077457181236241013
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12, 0.024354675686481628 , 0.10181185692272265
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13, 0.028101548869017230 , 0.12991340579173993
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14, 0.031614242477644432 , 0.16152764826938440
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15, 0.034775666725408917 , 0.19630331499479325
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16, 0.037492515688331465 , 0.23379583068312471
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17, 0.039697957787645122 , 0.27349378847076977
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18, 0.041352039362130291 , 0.31484582783290005
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19, 0.042440250924291587 , 0.35728607875719176
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20, 0.042970754060845266 , 0.40025683281803687
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21, 0.042970754060845245 , 0.44322758687888220
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22, 0.042482450037426567 , 0.48571003691630876
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23, 0.041558918514873776 , 0.52726895543118257
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24, 0.040260202311284021 , 0.56752915774246648
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25, 0.038649794218832613 , 0.60617895196129912
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26, 0.036791631035234945 , 0.64297058299653398
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27, 0.034747651533277434 , 0.67771823452981139
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28, 0.032575923312447595 , 0.71029415784225891
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29, 0.030329307911589130 , 0.74062346575384819
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30, 0.028054609818219924 , 0.76867807557206813
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31, 0.025792141284492545 , 0.79447021685656061
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32, 0.023575629142856457 , 0.81804584599941710
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33, 0.021432390129869489 , 0.83947823612928651
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34, 0.019383705779220179 , 0.85886194190850684
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35, 0.017445335201298224 , 0.87630727710980494
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36, 0.015628112784496322 , 0.89193538989430121
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37, 0.013938587078064250 , 0.90587397697236549
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38, 0.012379666154859706 , 0.91825364312722524
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39, 0.010951243136991251 , 0.92920488626421649
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40, 0.0096507830144735539 , 0.93885566927869002
|
||||
41, 0.0084738582566109364 , 0.94732952753530097
|
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42, 0.0074146259745345557 , 0.95474415350983555
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43, 0.0064662435824429246 , 0.96121039709227851
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44, 0.0056212231142827853 , 0.96683162020656122
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45, 0.0048717266990450708 , 0.97170334690560634
|
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46, 0.0042098073105878604 , 0.97591315421619418
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47, 0.0036275999165703964 , 0.97954075413276465
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48, 0.0031174686783026818 , 0.98265822281106729
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49, 0.0026721160099737293 , 0.98533033882104104
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50, 0.0022846591885275322 , 0.98761499800956853
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51, 0.0019486798960970148 , 0.98956367790566557
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52, 0.0016582516423517925 , 0.99122192954801736
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53, 0.0014079495076571762 , 0.99262987905567457
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54, 0.0011928461106539983 , 0.99382272516632852
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55, 0.0010084971662802015 , 0.99483122233260868
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56, 0.00085091948404891532 , 0.99568214181665760
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57, 0.00071656377604119553 , 0.99639870559269883
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58, 0.00060228420831048650 , 0.99700098980100937
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59, 0.00050530624256557675 , 0.99750629604357488
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60, 0.00042319397814867180 , 0.99792949002172360
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61, 0.00035381791615708398 , 0.99828330793788067
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62, 0.00029532382517950324 , 0.99857863176306016
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63, 0.00024610318764958566 , 0.99882473495070978
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Build Time 0:03
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Build log was saved at "file://i:\boost-06-05-03-1300\libs\math\test\Math_test\neative_binomial_example2\Debug\BuildLog.htm"
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negative_binomial_example2 - 0 error(s), 0 warning(s)
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