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// Copyright John Maddock 2006
// Copyright Paul A. Bristow 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)
#ifdef _MSC_VER
# pragma warning(disable: 4512) // assignment operator could not be generated.
# pragma warning(disable: 4510) // default constructor could not be generated.
# pragma warning(disable: 4610) // can never be instantiated - user defined constructor required.
#endif
#include <iostream>
using std::cout; using std::endl;
#include <iomanip>
using std::fixed; using std::left; using std::right; using std::right; using std::setw;
using std::setprecision;
#include <boost/math/distributions/binomial.hpp>
void find_max_sample_size(double p, unsigned successes)
{
//
// p = success ratio.
// successes = Total number of observed successes.
//
// Calculate how many trials we can have to ensure the
// maximum number of successes does not exceed "successes".
// A typical use would be failure analysis, where you want
// zero or fewer "successes" with some probability.
//
// using namespace boost::math;
// Avoid potential binomial_distribution name ambiguity with std <random>
using boost::math::binomial_distribution;
// Print out general info:
cout <<
"________________________\n"
"Maximum Number of Trials\n"
"________________________\n\n";
cout << setprecision(7);
cout << setw(40) << left << "Success ratio" << "= " << p << "\n";
cout << setw(40) << left << "Maximum Number of \"successes\" permitted" << "= " << successes << "\n";
//
// Define a table of confidence intervals:
//
double alpha[] = { 0.5, 0.25, 0.1, 0.05, 0.01, 0.001, 0.0001, 0.00001 };
//
// Print table header:
//
cout << "\n\n"
"____________________________\n"
"Confidence Max Number\n"
" Value (%) Of Trials \n"
"____________________________\n";
//
// Now print out the data for the table rows.
//
for(unsigned i = 0; i < sizeof(alpha)/sizeof(alpha[0]); ++i)
{
// Confidence value:
cout << fixed << setprecision(3) << setw(10) << right << 100 * (1-alpha[i]);
// calculate trials:
double t = binomial_distribution<>::find_maximum_number_of_trials(successes, p, alpha[i]);
t = floor(t);
// Print Trials:
cout << fixed << setprecision(0) << setw(15) << right << t << endl;
}
cout << endl;
}
int main()
{
find_max_sample_size(1.0/1000, 0);
find_max_sample_size(1.0/10000, 0);
find_max_sample_size(1.0/100000, 0);
find_max_sample_size(1.0/1000000, 0);
return 0;
}
/*
Output:
binomial_sample_sizes.cpp
binomial_sample_sizes_example.vcxproj -> J:\Cpp\MathToolkit\test\Math_test\Debug\binomial_sample_sizes_example.exe
________________________
Maximum Number of Trials
________________________
Success ratio = 0.001
Maximum Number of "successes" permitted = 0
____________________________
Confidence Max Number
Value (%) Of Trials
____________________________
50.000 692
75.000 287
90.000 105
95.000 51
99.000 10
99.900 0
99.990 0
99.999 0
________________________
Maximum Number of Trials
________________________
Success ratio = 0.0001000
Maximum Number of "successes" permitted = 0
____________________________
Confidence Max Number
Value (%) Of Trials
____________________________
50.000 6931
75.000 2876
90.000 1053
95.000 512
99.000 100
99.900 10
99.990 0
99.999 0
________________________
Maximum Number of Trials
________________________
Success ratio = 0.0000100
Maximum Number of "successes" permitted = 0
____________________________
Confidence Max Number
Value (%) Of Trials
____________________________
50.000 69314
75.000 28768
90.000 10535
95.000 5129
99.000 1005
99.900 100
99.990 10
99.999 1
________________________
Maximum Number of Trials
________________________
Success ratio = 0.0000010
Maximum Number of "successes" permitted = 0
____________________________
Confidence Max Number
Value (%) Of Trials
____________________________
50.000 693146
75.000 287681
90.000 105360
95.000 51293
99.000 10050
99.900 1000
99.990 100
99.999 10
*/
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