| // 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] |
| |
| */ |