{

//

// trials = Total number of trials.

// successes = Total number of observed successes.

//

// Calculate confidence limits for an observed

// frequency of occurrence that follows a binomial distribution.

//

//using namespace std; // Avoid

// using namespace boost::math; // potential name ambiguity with std <random>

using boost::math::binomial_distribution;

// Print out general info:

cout <<

"___________________________________________\n"

"2-Sided Confidence Limits For Success Ratio\n"

"___________________________________________\n\n";

cout << setprecision(7);

cout << setw(40) << left << "Number of Observations" << "= " << trials << "\n";

cout << setw(40) << left << "Number of successes" << "= " << successes << "\n";

cout << setw(40) << left << "Sample frequency of occurrence" << "= " << double(successes) / trials << "\n";

//

// Define a table of significance levels:

//

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 Lower CP Upper CP Lower JP Upper JP\n"

" Value (%) Limit Limit Limit Limit\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 Clopper Pearson bounds:

double l = binomial_distribution<>::find_lower_bound_on_p(trials, successes, alpha[i]/2);

double u = binomial_distribution<>::find_upper_bound_on_p(trials, successes, alpha[i]/2);

// Print Clopper Pearson Limits:

cout << fixed << setprecision(5) << setw(15) << right << l;

cout << fixed << setprecision(5) << setw(15) << right << u;

// Calculate Jeffreys Prior Bounds:

l = binomial_distribution<>::find_lower_bound_on_p(trials, successes, alpha[i]/2, binomial_distribution<>::jeffreys_prior_interval);

u = binomial_distribution<>::find_upper_bound_on_p(trials, successes, alpha[i]/2, binomial_distribution<>::jeffreys_prior_interval);

// Print Jeffreys Prior Limits:

cout << fixed << setprecision(5) << setw(15) << right << l;

cout << fixed << setprecision(5) << setw(15) << right << u << std::endl;

}

cout << endl;

{

confidence_limits_on_frequency(20, 4);

confidence_limits_on_frequency(200, 40);

confidence_limits_on_frequency(2000, 400);

return 0;