diff options
Diffstat (limited to 'src/boost/libs/math/example/negative_binomial_example2.cpp')
| -rw-r--r-- | src/boost/libs/math/example/negative_binomial_example2.cpp | 182 |
1 files changed, 182 insertions, 0 deletions
diff --git a/src/boost/libs/math/example/negative_binomial_example2.cpp b/src/boost/libs/math/example/negative_binomial_example2.cpp new file mode 100644 index 00000000..601180c3 --- /dev/null +++ b/src/boost/libs/math/example/negative_binomial_example2.cpp @@ -0,0 +1,182 @@ +// negative_binomial_example2.cpp + +// Copyright Paul A. Bristow 2007, 2010. + +// 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 demonstrating use of the Negative Binomial Distribution. + +#include <boost/math/distributions/negative_binomial.hpp> + using boost::math::negative_binomial_distribution; + using boost::math::negative_binomial; // typedef + +// In a sequence of trials or events +// (Bernoulli, independent, yes or no, succeed or fail) +// with success_fraction probability p, +// negative_binomial is the probability that k or fewer failures +// preceed the r th trial's success. + +#include <iostream> +using std::cout; +using std::endl; +using std::setprecision; +using std::showpoint; +using std::setw; +using std::left; +using std::right; +#include <limits> +using std::numeric_limits; + +int main() +{ + cout << "Negative_binomial distribution - simple example 2" << endl; + // Construct a negative binomial distribution with: + // 8 successes (r), success fraction (p) 0.25 = 25% or 1 in 4 successes. + negative_binomial mynbdist(8, 0.25); // Shorter method using typedef. + + // Display (to check) properties of the distribution just constructed. + cout << "mean(mynbdist) = " << mean(mynbdist) << endl; // 24 + cout << "mynbdist.successes() = " << mynbdist.successes() << endl; // 8 + // r th successful trial, after k failures, is r + k th trial. + cout << "mynbdist.success_fraction() = " << mynbdist.success_fraction() << endl; + // success_fraction = failures/successes or k/r = 0.25 or 25%. + cout << "mynbdist.percent success = " << mynbdist.success_fraction() * 100 << "%" << endl; + // Show as % too. + // Show some cumulative distribution function values for failures k = 2 and 8 + cout << "cdf(mynbdist, 2.) = " << cdf(mynbdist, 2.) << endl; // 0.000415802001953125 + cout << "cdf(mynbdist, 8.) = " << cdf(mynbdist, 8.) << endl; // 0.027129956288263202 + cout << "cdf(complement(mynbdist, 8.)) = " << cdf(complement(mynbdist, 8.)) << endl; // 0.9728700437117368 + // Check that cdf plus its complement is unity. + cout << "cdf + complement = " << cdf(mynbdist, 8.) + cdf(complement(mynbdist, 8.)) << endl; // 1 + // Note: No complement for pdf! + + // Compare cdf with sum of pdfs. + double sum = 0.; // Calculate the sum of all the pdfs, + int k = 20; // for 20 failures + for(signed i = 0; i <= k; ++i) + { + sum += pdf(mynbdist, double(i)); + } + // Compare with the cdf + double cdf8 = cdf(mynbdist, static_cast<double>(k)); + double diff = sum - cdf8; // Expect the diference to be very small. + cout << setprecision(17) << "Sum pdfs = " << sum << ' ' // sum = 0.40025683281803698 + << ", cdf = " << cdf(mynbdist, static_cast<double>(k)) // cdf = 0.40025683281803687 + << ", difference = " // difference = 0.50000000000000000 + << setprecision(1) << diff/ (std::numeric_limits<double>::epsilon() * sum) + << " in epsilon units." << endl; + + // Note: Use boost::math::tools::epsilon rather than std::numeric_limits + // to cover RealTypes that do not specialize numeric_limits. + +//[neg_binomial_example2 + + // Print a table of values that can be used to plot + // using Excel, or some other superior graphical display tool. + + cout.precision(17); // Use max_digits10 precision, the maximum available for a reference table. + cout << showpoint << endl; // include trailing zeros. + // This is a maximum possible precision for the type (here double) to suit a reference table. + int maxk = static_cast<int>(2. * mynbdist.successes() / mynbdist.success_fraction()); + // This maxk shows most of the range of interest, probability about 0.0001 to 0.999. + cout << "\n"" k pdf cdf""\n" << endl; + for (int k = 0; k < maxk; k++) + { + cout << right << setprecision(17) << showpoint + << right << setw(3) << k << ", " + << left << setw(25) << pdf(mynbdist, static_cast<double>(k)) + << left << setw(25) << cdf(mynbdist, static_cast<double>(k)) + << endl; + } + cout << endl; +//] [/ neg_binomial_example2] + return 0; +} // int main() + +/* + +Output is: + +negative_binomial distribution - simple example 2 +mean(mynbdist) = 24 +mynbdist.successes() = 8 +mynbdist.success_fraction() = 0.25 +mynbdist.percent success = 25% +cdf(mynbdist, 2.) = 0.000415802001953125 +cdf(mynbdist, 8.) = 0.027129956288263202 +cdf(complement(mynbdist, 8.)) = 0.9728700437117368 +cdf + complement = 1 +Sum pdfs = 0.40025683281803692 , cdf = 0.40025683281803687, difference = 0.25 in epsilon units. + +//[neg_binomial_example2_1 + k pdf cdf + 0, 1.5258789062500000e-005 1.5258789062500003e-005 + 1, 9.1552734375000000e-005 0.00010681152343750000 + 2, 0.00030899047851562522 0.00041580200195312500 + 3, 0.00077247619628906272 0.0011882781982421875 + 4, 0.0015932321548461918 0.0027815103530883789 + 5, 0.0028678178787231476 0.0056493282318115234 + 6, 0.0046602040529251142 0.010309532284736633 + 7, 0.0069903060793876605 0.017299838364124298 + 8, 0.0098301179241389001 0.027129956288263202 + 9, 0.013106823898851871 0.040236780187115073 + 10, 0.016711200471036140 0.056947980658151209 + 11, 0.020509200578089786 0.077457181236241013 + 12, 0.024354675686481652 0.10181185692272265 + 13, 0.028101548869017230 0.12991340579173993 + 14, 0.031614242477644432 0.16152764826938440 + 15, 0.034775666725408917 0.19630331499479325 + 16, 0.037492515688331451 0.23379583068312471 + 17, 0.039697957787645101 0.27349378847076977 + 18, 0.041352039362130305 0.31484582783290005 + 19, 0.042440250924291580 0.35728607875719176 + 20, 0.042970754060845245 0.40025683281803687 + 21, 0.042970754060845225 0.44322758687888220 + 22, 0.042482450037426581 0.48571003691630876 + 23, 0.041558918514873783 0.52726895543118257 + 24, 0.040260202311284021 0.56752915774246648 + 25, 0.038649794218832620 0.60617895196129912 + 26, 0.036791631035234917 0.64297058299653398 + 27, 0.034747651533277427 0.67771823452981139 + 28, 0.032575923312447595 0.71029415784225891 + 29, 0.030329307911589130 0.74062346575384819 + 30, 0.028054609818219924 0.76867807557206813 + 31, 0.025792141284492545 0.79447021685656061 + 32, 0.023575629142856460 0.81804584599941710 + 33, 0.021432390129869489 0.83947823612928651 + 34, 0.019383705779220189 0.85886194190850684 + 35, 0.017445335201298231 0.87630727710980494 + 36, 0.015628112784496322 0.89193538989430121 + 37, 0.013938587078064250 0.90587397697236549 + 38, 0.012379666154859701 0.91825364312722524 + 39, 0.010951243136991251 0.92920488626421649 + 40, 0.0096507830144735539 0.93885566927869002 + 41, 0.0084738582566109364 0.94732952753530097 + 42, 0.0074146259745345548 0.95474415350983555 + 43, 0.0064662435824429246 0.96121039709227851 + 44, 0.0056212231142827853 0.96683162020656122 + 45, 0.0048717266990450708 0.97170334690560634 + 46, 0.0042098073105878630 0.97591315421619418 + 47, 0.0036275999165703964 0.97954075413276465 + 48, 0.0031174686783026818 0.98265822281106729 + 49, 0.0026721160099737302 0.98533033882104104 + 50, 0.0022846591885275322 0.98761499800956853 + 51, 0.0019486798960970148 0.98956367790566557 + 52, 0.0016582516423517923 0.99122192954801736 + 53, 0.0014079495076571762 0.99262987905567457 + 54, 0.0011928461106539983 0.99382272516632852 + 55, 0.0010084971662802015 0.99483122233260868 + 56, 0.00085091948404891532 0.99568214181665760 + 57, 0.00071656377604119542 0.99639870559269883 + 58, 0.00060228420831048650 0.99700098980100937 + 59, 0.00050530624256557675 0.99750629604357488 + 60, 0.00042319397814867202 0.99792949002172360 + 61, 0.00035381791615708398 0.99828330793788067 + 62, 0.00029532382517950324 0.99857863176306016 + 63, 0.00024610318764958566 0.99882473495070978 +//] [neg_binomial_example2_1 end of Quickbook] + +*/ |