Merge commit '4ebe6417a5fce5f0994fc0c31bebf732be96a07c' as 'boost'

boost/libs/math/example/binomial_sample_sizes.cpp

@@ -0,0 +1,176 @@
+// 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
+  
+
+*/