Adding upstream version 14.2.21.upstream/14.2.21upstream

Signed-off-by: Daniel Baumann <daniel.baumann@progress-linux.org>

1 files changed, 120 insertions, 0 deletions

diff --git a/src/boost/libs/math/example/students_t_example3.cpp b/src/boost/libs/math/example/students_t_example3.cpp
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+// students_t_example3.cpp
+// Copyright Paul A. Bristow 2006, 2007.
+
+// 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)
+
+// Example 3 of using Student's t.
+
+// A general guide to Student's t is at
+// http://en.wikipedia.org/wiki/Student's_t-test
+// (and many other elementary and advanced statistics texts).
+// It says:
+// The t statistic was invented by William Sealy Gosset
+// for cheaply monitoring the quality of beer brews.
+// "Student" was his pen name.
+// Gosset was statistician for Guinness brewery in Dublin, Ireland,
+// hired due to Claude Guinness's innovative policy of recruiting the
+// best graduates from Oxford and Cambridge for applying biochemistry
+// and statistics to Guinness's industrial processes.
+// Gosset published the t test in Biometrika in 1908,
+// but was forced to use a pen name by his employer who regarded the fact
+// that they were using statistics as a trade secret.
+// In fact, Gosset's identity was unknown not only to fellow statisticians
+// but to his employer - the company insisted on the pseudonym
+// so that it could turn a blind eye to the breach of its rules.
+
+// The Students't distribution function is described at
+// http://en.wikipedia.org/wiki/Student%27s_t_distribution
+
+#include <boost/math/distributions/students_t.hpp>
+   using boost::math::students_t;  // Probability of students_t(df, t).
+
+#include <iostream>
+   using std::cout;    using std::endl;
+#include <iomanip>
+   using std::setprecision;    using std::setw;
+#include <cmath>
+   using std::sqrt;
+
+// This example of a two-sided test is from:
+// B. M. Smith & M. B. Griffiths, Analyst, 1982, 107, 253,
+// from Statistics for Analytical Chemistry, 3rd ed. (1994), pp 58-59
+// J. C. Miller and J. N. Miller, Ellis Horwood ISBN 0 13 0309907
+
+// Concentrations of lead (ug/l) determined by two different methods
+// for each of four test portions,
+// the concentration of each portion is significantly different,
+// the values may NOT be pooled.
+// (Called a 'paired test' by Miller and Miller
+// because each portion analysed has a different concentration.)
+
+// Portion  Wet oxidation Direct Extraction
+//   1           71            76
+//   2           61            68
+//   3           50            48
+//   4           60            57
+
+const int portions = 4;
+const int methods = 2;
+float data [portions][methods] = {{71, 76}, {61,68}, {50, 48}, {60, 57}};
+float diffs[portions];
+
+int main()
+{
+   cout << "Example3 using Student's t function. " << endl;
+   float mean_diff = 0.f;
+   cout << "\n""Portion  wet_oxidation  Direct_extraction  difference" << endl;
+   for (int portion = 0; portion < portions; portion++)
+   { // Echo data and differences.
+      diffs[portion] = data[portion][0] - data[portion][1];
+      mean_diff += diffs[portion];
+      cout << setw(4) << portion << ' ' << setw(14) << data[portion][0] << ' ' << setw(18)<< data[portion][1] << ' ' << setw(9) << diffs[portion] << endl;
+   }
+   mean_diff /= portions;
+   cout << "Mean difference = " << mean_diff << endl; // -1.75
+
+   float sd_diffs = 0.f;
+   for (int portion = 0; portion < portions; portion++)
+   { // Calculate standard deviation of differences.
+      sd_diffs +=(diffs[portion] - mean_diff) * (diffs[portion] - mean_diff);
+   }
+   int degrees_of_freedom = portions-1; // Use the n-1 formula.
+   sd_diffs /= degrees_of_freedom;
+   sd_diffs = sqrt(sd_diffs);
+   cout << "Standard deviation of differences = " << sd_diffs << endl; // 4.99166
+   // Standard deviation of differences = 4.99166
+   double t = mean_diff * sqrt(static_cast<double>(portions))/ sd_diffs; // -0.70117
+   cout << "Student's t = " << t << ", if " << degrees_of_freedom << " degrees of freedom." << endl;
+   // Student's t = -0.70117, if 3 degrees of freedom.
+   cout << "Probability of the means being different is "
+    << 2.F * cdf(students_t(degrees_of_freedom), t) << "."<< endl; // 0.266846 * 2 = 0.533692
+   // Double the probability because using a 'two-sided test' because
+   // mean for 'Wet oxidation' could be either
+   // greater OR LESS THAN for 'Direct extraction'.
+
+   return 0;
+}  // int main()
+
+/*
+
+Output is:
+
+Example3 using Student's t function. 
+Portion  wet_oxidation  Direct_extraction  difference
+   0             71                 76        -5
+   1             61                 68        -7
+   2             50                 48         2
+   3             60                 57         3
+Mean difference = -1.75
+Standard deviation of differences = 4.99166
+Student's t = -0.70117, if 3 degrees of freedom.
+Probability of the means being different is 0.533692.
+
+*/
+
+
+
+