179 lines
6.7 KiB
C++
179 lines
6.7 KiB
C++
// neg_binomial_confidence_limits.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)
|
|
|
|
// Caution: this file contains quickbook markup as well as code
|
|
// and comments, don't change any of the special comment markups!
|
|
|
|
//[neg_binomial_confidence_limits
|
|
|
|
/*`
|
|
|
|
First we need some includes to access the negative binomial distribution
|
|
(and some basic std output of course).
|
|
|
|
*/
|
|
|
|
#include <boost/math/distributions/negative_binomial.hpp>
|
|
using boost::math::negative_binomial;
|
|
|
|
#include <iostream>
|
|
using std::cout; using std::endl;
|
|
#include <iomanip>
|
|
using std::setprecision;
|
|
using std::setw; using std::left; using std::fixed; using std::right;
|
|
|
|
/*`
|
|
First define a table of significance levels: these are the
|
|
probabilities that the true occurrence frequency lies outside the calculated
|
|
interval:
|
|
*/
|
|
|
|
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 true occurrence frequency lies *inside* the calculated interval.
|
|
|
|
We need a function to calculate and print confidence limits
|
|
for an observed frequency of occurrence
|
|
that follows a negative binomial distribution.
|
|
|
|
*/
|
|
|
|
void confidence_limits_on_frequency(unsigned trials, unsigned successes)
|
|
{
|
|
// trials = Total number of trials.
|
|
// successes = Total number of observed successes.
|
|
// failures = trials - successes.
|
|
// success_fraction = successes /trials.
|
|
// Print out general info:
|
|
cout <<
|
|
"______________________________________________\n"
|
|
"2-Sided Confidence Limits For Success Fraction\n"
|
|
"______________________________________________\n\n";
|
|
cout << setprecision(7);
|
|
cout << setw(40) << left << "Number of trials" << " = " << trials << "\n";
|
|
cout << setw(40) << left << "Number of successes" << " = " << successes << "\n";
|
|
cout << setw(40) << left << "Number of failures" << " = " << trials - successes << "\n";
|
|
cout << setw(40) << left << "Observed frequency of occurrence" << " = " << double(successes) / trials << "\n";
|
|
|
|
// Print table header:
|
|
cout << "\n\n"
|
|
"___________________________________________\n"
|
|
"Confidence Lower Upper\n"
|
|
" Value (%) Limit Limit\n"
|
|
"___________________________________________\n";
|
|
|
|
|
|
/*`
|
|
And now for the important part - the bounds themselves.
|
|
For each value of /alpha/, we call `find_lower_bound_on_p` and
|
|
`find_upper_bound_on_p` to obtain lower and upper bounds respectively.
|
|
Note that since we are calculating a two-sided interval,
|
|
we must divide the value of alpha in two. Had we been calculating a
|
|
single-sided interval, for example: ['"Calculate a lower bound so that we are P%
|
|
sure that the true occurrence frequency is greater than some value"]
|
|
then we would *not* have divided by two.
|
|
*/
|
|
|
|
// Now print out the upper and lower limits for the alpha table values.
|
|
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 bounds:
|
|
double lower = negative_binomial::find_lower_bound_on_p(trials, successes, alpha[i]/2);
|
|
double upper = negative_binomial::find_upper_bound_on_p(trials, successes, alpha[i]/2);
|
|
// Print limits:
|
|
cout << fixed << setprecision(5) << setw(15) << right << lower;
|
|
cout << fixed << setprecision(5) << setw(15) << right << upper << endl;
|
|
}
|
|
cout << endl;
|
|
} // void confidence_limits_on_frequency(unsigned trials, unsigned successes)
|
|
|
|
/*`
|
|
|
|
And then call confidence_limits_on_frequency with increasing numbers of trials,
|
|
but always the same success fraction 0.1, or 1 in 10.
|
|
|
|
*/
|
|
|
|
int main()
|
|
{
|
|
confidence_limits_on_frequency(20, 2); // 20 trials, 2 successes, 2 in 20, = 1 in 10 = 0.1 success fraction.
|
|
confidence_limits_on_frequency(200, 20); // More trials, but same 0.1 success fraction.
|
|
confidence_limits_on_frequency(2000, 200); // Many more trials, but same 0.1 success fraction.
|
|
|
|
return 0;
|
|
} // int main()
|
|
|
|
//] [/negative_binomial_confidence_limits_eg end of Quickbook in C++ markup]
|
|
|
|
/*
|
|
|
|
______________________________________________
|
|
2-Sided Confidence Limits For Success Fraction
|
|
______________________________________________
|
|
Number of trials = 20
|
|
Number of successes = 2
|
|
Number of failures = 18
|
|
Observed frequency of occurrence = 0.1
|
|
___________________________________________
|
|
Confidence Lower Upper
|
|
Value (%) Limit Limit
|
|
___________________________________________
|
|
50.000 0.04812 0.13554
|
|
75.000 0.03078 0.17727
|
|
90.000 0.01807 0.22637
|
|
95.000 0.01235 0.26028
|
|
99.000 0.00530 0.33111
|
|
99.900 0.00164 0.41802
|
|
99.990 0.00051 0.49202
|
|
99.999 0.00016 0.55574
|
|
______________________________________________
|
|
2-Sided Confidence Limits For Success Fraction
|
|
______________________________________________
|
|
Number of trials = 200
|
|
Number of successes = 20
|
|
Number of failures = 180
|
|
Observed frequency of occurrence = 0.1000000
|
|
___________________________________________
|
|
Confidence Lower Upper
|
|
Value (%) Limit Limit
|
|
___________________________________________
|
|
50.000 0.08462 0.11350
|
|
75.000 0.07580 0.12469
|
|
90.000 0.06726 0.13695
|
|
95.000 0.06216 0.14508
|
|
99.000 0.05293 0.16170
|
|
99.900 0.04343 0.18212
|
|
99.990 0.03641 0.20017
|
|
99.999 0.03095 0.21664
|
|
______________________________________________
|
|
2-Sided Confidence Limits For Success Fraction
|
|
______________________________________________
|
|
Number of trials = 2000
|
|
Number of successes = 200
|
|
Number of failures = 1800
|
|
Observed frequency of occurrence = 0.1000000
|
|
___________________________________________
|
|
Confidence Lower Upper
|
|
Value (%) Limit Limit
|
|
___________________________________________
|
|
50.000 0.09536 0.10445
|
|
75.000 0.09228 0.10776
|
|
90.000 0.08916 0.11125
|
|
95.000 0.08720 0.11352
|
|
99.000 0.08344 0.11802
|
|
99.900 0.07921 0.12336
|
|
99.990 0.07577 0.12795
|
|
99.999 0.07282 0.13206
|
|
*/
|
|
|