210 lines
6.1 KiB
C++
210 lines
6.1 KiB
C++
// neg_binomial_sample_sizes.cpp
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// Copyright John Maddock 2006
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// Copyright Paul A. Bristow 2007, 2010
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// Use, modification and distribution are subject to the
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// Boost Software License, Version 1.0.
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// (See accompanying file LICENSE_1_0.txt
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// or copy at http://www.boost.org/LICENSE_1_0.txt)
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#include <boost/math/distributions/negative_binomial.hpp>
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using boost::math::negative_binomial;
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// Default RealType is double so this permits use of:
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double find_minimum_number_of_trials(
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double k, // number of failures (events), k >= 0.
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double p, // fraction of trails for which event occurs, 0 <= p <= 1.
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double probability); // probability threshold, 0 <= probability <= 1.
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#include <iostream>
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using std::cout;
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using std::endl;
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using std::fixed;
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using std::right;
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#include <iomanip>
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using std::setprecision;
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using std::setw;
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//[neg_binomial_sample_sizes
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/*`
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It centres around a routine that prints out a table of
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minimum sample sizes (number of trials) for various probability thresholds:
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*/
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void find_number_of_trials(double failures, double p);
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/*`
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First define a table of significance levels: these are the maximum
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acceptable probability that /failure/ or fewer events will be observed.
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*/
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double alpha[] = { 0.5, 0.25, 0.1, 0.05, 0.01, 0.001, 0.0001, 0.00001 };
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/*`
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Confidence value as % is (1 - alpha) * 100, so alpha 0.05 == 95% confidence
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that the desired number of failures will be observed.
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The values range from a very low 0.5 or 50% confidence up to an extremely high
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confidence of 99.999.
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Much of the rest of the program is pretty-printing, the important part
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is in the calculation of minimum number of trials required for each
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value of alpha using:
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(int)ceil(negative_binomial::find_minimum_number_of_trials(failures, p, alpha[i]);
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find_minimum_number_of_trials returns a double,
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so `ceil` rounds this up to ensure we have an integral minimum number of trials.
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*/
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void find_number_of_trials(double failures, double p)
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{
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// trials = number of trials
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// failures = number of failures before achieving required success(es).
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// p = success fraction (0 <= p <= 1.).
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//
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// Calculate how many trials we need to ensure the
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// required number of failures DOES exceed "failures".
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cout << "\n""Target number of failures = " << (int)failures;
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cout << ", Success fraction = " << fixed << setprecision(1) << 100 * p << "%" << endl;
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// Print table header:
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cout << "____________________________\n"
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"Confidence Min Number\n"
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" Value (%) Of Trials \n"
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"____________________________\n";
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// Now print out the data for the alpha table values.
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for(unsigned i = 0; i < sizeof(alpha)/sizeof(alpha[0]); ++i)
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{ // Confidence values %:
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cout << fixed << setprecision(3) << setw(10) << right << 100 * (1-alpha[i]) << " "
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// find_minimum_number_of_trials
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<< setw(6) << right
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<< (int)ceil(negative_binomial::find_minimum_number_of_trials(failures, p, alpha[i]))
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<< endl;
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}
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cout << endl;
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} // void find_number_of_trials(double failures, double p)
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/*` finally we can produce some tables of minimum trials for the chosen confidence levels:
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*/
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int main()
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{
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find_number_of_trials(5, 0.5);
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find_number_of_trials(50, 0.5);
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find_number_of_trials(500, 0.5);
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find_number_of_trials(50, 0.1);
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find_number_of_trials(500, 0.1);
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find_number_of_trials(5, 0.9);
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return 0;
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} // int main()
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//] [/neg_binomial_sample_sizes.cpp end of Quickbook in C++ markup]
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/*
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Output is:
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Target number of failures = 5, Success fraction = 50.0%
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____________________________
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Confidence Min Number
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Value (%) Of Trials
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____________________________
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50.000 11
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75.000 14
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90.000 17
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95.000 18
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99.000 22
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99.900 27
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99.990 31
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99.999 36
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Target number of failures = 50, Success fraction = 50.0%
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____________________________
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Confidence Min Number
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Value (%) Of Trials
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____________________________
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50.000 101
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75.000 109
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90.000 115
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95.000 119
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99.000 128
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99.900 137
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99.990 146
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99.999 154
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Target number of failures = 500, Success fraction = 50.0%
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____________________________
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Confidence Min Number
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Value (%) Of Trials
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____________________________
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50.000 1001
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75.000 1023
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90.000 1043
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95.000 1055
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99.000 1078
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99.900 1104
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99.990 1126
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99.999 1146
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Target number of failures = 50, Success fraction = 10.0%
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____________________________
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Confidence Min Number
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Value (%) Of Trials
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____________________________
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50.000 56
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75.000 58
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90.000 60
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95.000 61
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99.000 63
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99.900 66
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99.990 68
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99.999 71
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Target number of failures = 500, Success fraction = 10.0%
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____________________________
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Confidence Min Number
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Value (%) Of Trials
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____________________________
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50.000 556
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75.000 562
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90.000 567
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95.000 570
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99.000 576
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99.900 583
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99.990 588
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99.999 594
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Target number of failures = 5, Success fraction = 90.0%
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____________________________
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Confidence Min Number
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Value (%) Of Trials
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____________________________
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50.000 57
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75.000 73
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90.000 91
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95.000 103
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99.000 127
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99.900 159
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99.990 189
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99.999 217
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Target number of failures = 5, Success fraction = 95.0%
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____________________________
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Confidence Min Number
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Value (%) Of Trials
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____________________________
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50.000 114
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75.000 148
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90.000 184
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95.000 208
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99.000 259
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99.900 324
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99.990 384
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99.999 442
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*/
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