libs/math/example/neg_binomial_sample_sizes.cpp
// neg_binomial_sample_sizes.cpp // Copyright John Maddock 2006 // 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) #include <boost/math/distributions/negative_binomial.hpp> using boost::math::negative_binomial; // Default RealType is double so this permits use of: double find_minimum_number_of_trials( double k, // number of failures (events), k >= 0. double p, // fraction of trails for which event occurs, 0 <= p <= 1. double probability); // probability threshold, 0 <= probability <= 1. #include <iostream> using std::cout; using std::endl; using std::fixed; using std::right; #include <iomanip> using std::setprecision; using std::setw; //[neg_binomial_sample_sizes /*` It centres around a routine that prints out a table of minimum sample sizes (number of trials) for various probability thresholds: */ void find_number_of_trials(double failures, double p); /*` First define a table of significance levels: these are the maximum acceptable probability that /failure/ or fewer events will be observed. */ double alpha[] = { 0.5, 0.25, 0.1, 0.05, 0.01, 0.001, 0.0001, 0.00001 }; /*` Confidence value as % is (1 - alpha) * 100, so alpha 0.05 == 95% confidence that the desired number of failures will be observed. The values range from a very low 0.5 or 50% confidence up to an extremely high confidence of 99.999. Much of the rest of the program is pretty-printing, the important part is in the calculation of minimum number of trials required for each value of alpha using: (int)ceil(negative_binomial::find_minimum_number_of_trials(failures, p, alpha[i]); find_minimum_number_of_trials returns a double, so `ceil` rounds this up to ensure we have an integral minimum number of trials. */ void find_number_of_trials(double failures, double p) { // trials = number of trials // failures = number of failures before achieving required success(es). // p = success fraction (0 <= p <= 1.). // // Calculate how many trials we need to ensure the // required number of failures DOES exceed "failures". cout << "\n""Target number of failures = " << (int)failures; cout << ", Success fraction = " << fixed << setprecision(1) << 100 * p << "%" << endl; // Print table header: cout << "____________________________\n" "Confidence Min Number\n" " Value (%) Of Trials \n" "____________________________\n"; // Now print out the data for the alpha table values. for(unsigned i = 0; i < sizeof(alpha)/sizeof(alpha[0]); ++i) { // Confidence values %: cout << fixed << setprecision(3) << setw(10) << right << 100 * (1-alpha[i]) << " " // find_minimum_number_of_trials << setw(6) << right << (int)ceil(negative_binomial::find_minimum_number_of_trials(failures, p, alpha[i])) << endl; } cout << endl; } // void find_number_of_trials(double failures, double p) /*` finally we can produce some tables of minimum trials for the chosen confidence levels: */ int main() { find_number_of_trials(5, 0.5); find_number_of_trials(50, 0.5); find_number_of_trials(500, 0.5); find_number_of_trials(50, 0.1); find_number_of_trials(500, 0.1); find_number_of_trials(5, 0.9); return 0; } // int main() //] [/neg_binomial_sample_sizes.cpp end of Quickbook in C++ markup] /* Output is: Target number of failures = 5, Success fraction = 50.0% ____________________________ Confidence Min Number Value (%) Of Trials ____________________________ 50.000 11 75.000 14 90.000 17 95.000 18 99.000 22 99.900 27 99.990 31 99.999 36 Target number of failures = 50, Success fraction = 50.0% ____________________________ Confidence Min Number Value (%) Of Trials ____________________________ 50.000 101 75.000 109 90.000 115 95.000 119 99.000 128 99.900 137 99.990 146 99.999 154 Target number of failures = 500, Success fraction = 50.0% ____________________________ Confidence Min Number Value (%) Of Trials ____________________________ 50.000 1001 75.000 1023 90.000 1043 95.000 1055 99.000 1078 99.900 1104 99.990 1126 99.999 1146 Target number of failures = 50, Success fraction = 10.0% ____________________________ Confidence Min Number Value (%) Of Trials ____________________________ 50.000 56 75.000 58 90.000 60 95.000 61 99.000 63 99.900 66 99.990 68 99.999 71 Target number of failures = 500, Success fraction = 10.0% ____________________________ Confidence Min Number Value (%) Of Trials ____________________________ 50.000 556 75.000 562 90.000 567 95.000 570 99.000 576 99.900 583 99.990 588 99.999 594 Target number of failures = 5, Success fraction = 90.0% ____________________________ Confidence Min Number Value (%) Of Trials ____________________________ 50.000 57 75.000 73 90.000 91 95.000 103 99.000 127 99.900 159 99.990 189 99.999 217 Target number of failures = 5, Success fraction = 95.0% ____________________________ Confidence Min Number Value (%) Of Trials ____________________________ 50.000 114 75.000 148 90.000 184 95.000 208 99.000 259 99.900 324 99.990 384 99.999 442 */