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+
+// normal_misc_examples.cpp
+
+// Copyright Paul A. Bristow 2007, 2010, 2014, 2016.
+
+// 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 of using normal distribution.
+
+// Note that this file contains Quickbook mark-up as well as code
+// and comments, don't change any of the special comment mark-ups!
+
+/*`
+First we need some includes to access the normal distribution
+(and some std output of course).
+*/
+
+#include <boost/cstdfloat.hpp> // MUST be first include!!!
+// See Implementation of Float128 type, Overloading template functions with float128_t.
+
+#include <boost/math/distributions/normal.hpp> // for normal_distribution.
+ using boost::math::normal; // typedef provides default type of double.
+
+#include <iostream>
+ //using std::cout; using std::endl;
+ //using std::left; using std::showpoint; using std::noshowpoint;
+#include <iomanip>
+ //using std::setw; using std::setprecision;
+#include <limits>
+ //using std::numeric_limits;
+
+ /*!
+Function max_digits10
+Returns maximum number of possibly significant decimal digits for a floating-point type FPT,
+even for older compilers/standard libraries that
+lack support for std::std::numeric_limits<FPT>::max_digits10,
+when the Kahan formula 2 + binary_digits * 0.3010 is used instead.
+Also provides the correct result for Visual Studio 2010 where the max_digits10 provided for float is wrong.
+*/
+namespace boost
+{
+namespace math
+{
+template <typename FPT>
+int max_digits10()
+{
+// Since max_digits10 is not defined (or wrong) on older systems, define a local max_digits10.
+
+ // Usage: int m = max_digits10<boost::float64_t>();
+ const int m =
+#if (defined BOOST_NO_CXX11_NUMERIC_LIMITS) || (_MSC_VER == 1600) // is wrongly 8 not 9 for VS2010.
+ 2 + std::numeric_limits<FPT>::digits * 3010/10000;
+#else
+ std::numeric_limits<FPT>::max_digits10;
+#endif
+ return m;
+}
+} // namespace math
+} // namespace boost
+
+template <typename FPT>
+void normal_table()
+{
+ using namespace boost::math;
+
+ FPT step = static_cast<FPT>(1.); // step in z.
+ FPT range = static_cast<FPT>(10.); // min and max z = -range to +range.
+
+ // Traditional tables are only computed to much lower precision.
+ // but @c std::std::numeric_limits<double>::max_digits10;
+ // on new Standard Libraries gives 17,
+ // the maximum number of digits from 64-bit double that can possibly be significant.
+ // @c std::std::numeric_limits<double>::digits10; == 15
+ // is number of @b guaranteed digits, the other two digits being 'noisy'.
+ // Here we use a custom version of max_digits10 which deals with those platforms
+ // where @c std::numeric_limits is not specialized,
+ // or @c std::numeric_limits<>::max_digits10 not implemented, or wrong.
+ int precision = boost::math::max_digits10<FPT>();
+
+// std::cout << typeid(FPT).name() << std::endl;
+// demo_normal.cpp:85: undefined reference to `typeinfo for __float128'
+// [@http://gcc.gnu.org/bugzilla/show_bug.cgi?id=43622 GCC 43622]
+// typeinfo for __float128 was missing GCC 4.9 Mar 2014, but OK for GCC 6.1.1.
+
+ // Construct a standard normal distribution s, with
+ // (default mean = zero, and standard deviation = unity)
+ normal s;
+ std::cout << "\nStandard normal distribution, mean = "<< s.mean()
+ << ", standard deviation = " << s.standard_deviation() << std::endl;
+
+ std::cout << "maxdigits_10 is " << precision
+ << ", digits10 is " << std::numeric_limits<FPT>::digits10 << std::endl;
+
+ std::cout << "Probability distribution function values" << std::endl;
+
+ std::cout << " z " " PDF " << std::endl;
+ for (FPT z = -range; z < range + step; z += step)
+ {
+ std::cout << std::left << std::setprecision(3) << std::setw(6) << z << " "
+ << std::setprecision(precision) << std::setw(12) << pdf(s, z) << std::endl;
+ }
+ std::cout.precision(6); // Restore to default precision.
+
+/*`And the area under the normal curve from -[infin] up to z,
+ the cumulative distribution function (CDF).
+*/
+ // For a standard normal distribution:
+ std::cout << "Standard normal mean = "<< s.mean()
+ << ", standard deviation = " << s.standard_deviation() << std::endl;
+ std::cout << "Integral (area under the curve) from - infinity up to z." << std::endl;
+ std::cout << " z " " CDF " << std::endl;
+ for (FPT z = -range; z < range + step; z += step)
+ {
+ std::cout << std::left << std::setprecision(3) << std::setw(6) << z << " "
+ << std::setprecision(precision) << std::setw(12) << cdf(s, z) << std::endl;
+ }
+ std::cout.precision(6); // Reset to default precision.
+} // template <typename FPT> void normal_table()
+
+int main()
+{
+ std::cout << "\nExample: Normal distribution tables." << std::endl;
+
+ using namespace boost::math;
+
+ try
+ {// Tip - always use try'n'catch blocks to ensure that messages from thrown exceptions are shown.
+
+//[normal_table_1
+#ifdef BOOST_FLOAT32_C
+ normal_table<boost::float32_t>(); // Usually type float
+#endif
+ normal_table<boost::float64_t>(); // Usually type double. Assume that float64_t is always available.
+#ifdef BOOST_FLOAT80_C
+ normal_table<boost::float80_t>(); // Type long double on some X86 platforms.
+#endif
+#ifdef BOOST_FLOAT128_C
+ normal_table<boost::float128_t>(); // Type _Quad on some Intel and __float128 on some GCC platforms.
+#endif
+ normal_table<boost::floatmax_t>();
+//] [/normal_table_1 ]
+ }
+ catch(std::exception ex)
+ {
+ std::cout << "exception thrown " << ex.what() << std::endl;
+ }
+
+ return 0;
+} // int main()
+
+
+/*
+
+GCC 4.8.1 with quadmath
+
+Example: Normal distribution tables.
+
+Standard normal distribution, mean = 0, standard deviation = 1
+maxdigits_10 is 9, digits10 is 6
+Probability distribution function values
+ z PDF
+-10 7.69459863e-023
+-9 1.02797736e-018
+-8 5.05227108e-015
+-7 9.13472041e-012
+-6 6.07588285e-009
+-5 1.48671951e-006
+-4 0.000133830226
+-3 0.00443184841
+-2 0.0539909665
+-1 0.241970725
+0 0.39894228
+1 0.241970725
+2 0.0539909665
+3 0.00443184841
+4 0.000133830226
+5 1.48671951e-006
+6 6.07588285e-009
+7 9.13472041e-012
+8 5.05227108e-015
+9 1.02797736e-018
+10 7.69459863e-023
+Standard normal mean = 0, standard deviation = 1
+Integral (area under the curve) from - infinity up to z.
+ z CDF
+-10 7.61985302e-024
+-9 1.12858841e-019
+-8 6.22096057e-016
+-7 1.27981254e-012
+-6 9.86587645e-010
+-5 2.86651572e-007
+-4 3.16712418e-005
+-3 0.00134989803
+-2 0.0227501319
+-1 0.158655254
+0 0.5
+1 0.841344746
+2 0.977249868
+3 0.998650102
+4 0.999968329
+5 0.999999713
+6 0.999999999
+7 1
+8 1
+9 1
+10 1
+
+Standard normal distribution, mean = 0, standard deviation = 1
+maxdigits_10 is 17, digits10 is 15
+Probability distribution function values
+ z PDF
+-10 7.6945986267064199e-023
+-9 1.0279773571668917e-018
+-8 5.0522710835368927e-015
+-7 9.1347204083645953e-012
+-6 6.0758828498232861e-009
+-5 1.4867195147342979e-006
+-4 0.00013383022576488537
+-3 0.0044318484119380075
+-2 0.053990966513188063
+-1 0.24197072451914337
+0 0.3989422804014327
+1 0.24197072451914337
+2 0.053990966513188063
+3 0.0044318484119380075
+4 0.00013383022576488537
+5 1.4867195147342979e-006
+6 6.0758828498232861e-009
+7 9.1347204083645953e-012
+8 5.0522710835368927e-015
+9 1.0279773571668917e-018
+10 7.6945986267064199e-023
+Standard normal mean = 0, standard deviation = 1
+Integral (area under the curve) from - infinity up to z.
+ z CDF
+-10 7.6198530241605945e-024
+-9 1.1285884059538422e-019
+-8 6.2209605742718204e-016
+-7 1.279812543885835e-012
+-6 9.865876450377014e-010
+-5 2.8665157187919455e-007
+-4 3.1671241833119972e-005
+-3 0.0013498980316300957
+-2 0.022750131948179216
+-1 0.15865525393145705
+0 0.5
+1 0.84134474606854293
+2 0.97724986805182079
+3 0.9986501019683699
+4 0.99996832875816688
+5 0.99999971334842808
+6 0.9999999990134123
+7 0.99999999999872013
+8 0.99999999999999933
+9 1
+10 1
+
+Standard normal distribution, mean = 0, standard deviation = 1
+maxdigits_10 is 21, digits10 is 18
+Probability distribution function values
+ z PDF
+-10 7.69459862670641993759e-023
+-9 1.0279773571668916523e-018
+-8 5.05227108353689273243e-015
+-7 9.13472040836459525705e-012
+-6 6.07588284982328608733e-009
+-5 1.48671951473429788965e-006
+-4 0.00013383022576488536764
+-3 0.00443184841193800752729
+-2 0.0539909665131880628364
+-1 0.241970724519143365328
+0 0.398942280401432702863
+1 0.241970724519143365328
+2 0.0539909665131880628364
+3 0.00443184841193800752729
+4 0.00013383022576488536764
+5 1.48671951473429788965e-006
+6 6.07588284982328608733e-009
+7 9.13472040836459525705e-012
+8 5.05227108353689273243e-015
+9 1.0279773571668916523e-018
+10 7.69459862670641993759e-023
+Standard normal mean = 0, standard deviation = 1
+Integral (area under the curve) from - infinity up to z.
+ z CDF
+-10 7.61985302416059451083e-024
+-9 1.12858840595384222719e-019
+-8 6.22096057427182035917e-016
+-7 1.279812543885834962e-012
+-6 9.86587645037701399241e-010
+-5 2.86651571879194547129e-007
+-4 3.16712418331199717608e-005
+-3 0.00134989803163009566139
+-2 0.0227501319481792155242
+-1 0.158655253931457046468
+0 0.5
+1 0.841344746068542925777
+2 0.977249868051820791415
+3 0.998650101968369896532
+4 0.999968328758166880021
+5 0.999999713348428076465
+6 0.999999999013412299576
+7 0.999999999998720134897
+8 0.999999999999999333866
+9 1
+10 1
+
+Standard normal distribution, mean = 0, standard deviation = 1
+maxdigits_10 is 36, digits10 is 34
+Probability distribution function values
+ z PDF
+-10 7.69459862670641993759264402330435296e-023
+-9 1.02797735716689165230378750485667109e-018
+-8 5.0522710835368927324337437844893081e-015
+-7 9.13472040836459525705208369548147081e-012
+-6 6.07588284982328608733411870229841611e-009
+-5 1.48671951473429788965346931561839483e-006
+-4 0.00013383022576488536764006964663309418
+-3 0.00443184841193800752728870762098267733
+-2 0.0539909665131880628363703067407186609
+-1 0.241970724519143365327522587904240936
+0 0.398942280401432702863218082711682655
+1 0.241970724519143365327522587904240936
+2 0.0539909665131880628363703067407186609
+3 0.00443184841193800752728870762098267733
+4 0.00013383022576488536764006964663309418
+5 1.48671951473429788965346931561839483e-006
+6 6.07588284982328608733411870229841611e-009
+7 9.13472040836459525705208369548147081e-012
+8 5.0522710835368927324337437844893081e-015
+9 1.02797735716689165230378750485667109e-018
+10 7.69459862670641993759264402330435296e-023
+Standard normal mean = 0, standard deviation = 1
+Integral (area under the curve) from - infinity up to z.
+ z CDF
+-10 7.61985302416059451083278826816793623e-024
+-9 1.1285884059538422271881384555435713e-019
+-8 6.22096057427182035917417257601387863e-016
+-7 1.27981254388583496200054074948511201e-012
+-6 9.86587645037701399241244820583623953e-010
+-5 2.86651571879194547128505464808623238e-007
+-4 3.16712418331199717608064048146587766e-005
+-3 0.001349898031630095661392854111682027
+-2 0.0227501319481792155241528519127314212
+-1 0.158655253931457046467912164189328905
+0 0.5
+1 0.841344746068542925776512220181757584
+2 0.977249868051820791414741051994496956
+3 0.998650101968369896532351503992686048
+4 0.999968328758166880021462930017150939
+5 0.999999713348428076464813329948810861
+6 0.999999999013412299575520592043176293
+7 0.999999999998720134897212119540199637
+8 0.999999999999999333866185224906075746
+9 1
+10 1
+
+Standard normal distribution, mean = 0, standard deviation = 1
+maxdigits_10 is 36, digits10 is 34
+Probability distribution function values
+ z PDF
+-10 7.69459862670641993759264402330435296e-023
+-9 1.02797735716689165230378750485667109e-018
+-8 5.0522710835368927324337437844893081e-015
+-7 9.13472040836459525705208369548147081e-012
+-6 6.07588284982328608733411870229841611e-009
+-5 1.48671951473429788965346931561839483e-006
+-4 0.00013383022576488536764006964663309418
+-3 0.00443184841193800752728870762098267733
+-2 0.0539909665131880628363703067407186609
+-1 0.241970724519143365327522587904240936
+0 0.398942280401432702863218082711682655
+1 0.241970724519143365327522587904240936
+2 0.0539909665131880628363703067407186609
+3 0.00443184841193800752728870762098267733
+4 0.00013383022576488536764006964663309418
+5 1.48671951473429788965346931561839483e-006
+6 6.07588284982328608733411870229841611e-009
+7 9.13472040836459525705208369548147081e-012
+8 5.0522710835368927324337437844893081e-015
+9 1.02797735716689165230378750485667109e-018
+10 7.69459862670641993759264402330435296e-023
+Standard normal mean = 0, standard deviation = 1
+Integral (area under the curve) from - infinity up to z.
+ z CDF
+-10 7.61985302416059451083278826816793623e-024
+-9 1.1285884059538422271881384555435713e-019
+-8 6.22096057427182035917417257601387863e-016
+-7 1.27981254388583496200054074948511201e-012
+-6 9.86587645037701399241244820583623953e-010
+-5 2.86651571879194547128505464808623238e-007
+-4 3.16712418331199717608064048146587766e-005
+-3 0.001349898031630095661392854111682027
+-2 0.0227501319481792155241528519127314212
+-1 0.158655253931457046467912164189328905
+0 0.5
+1 0.841344746068542925776512220181757584
+2 0.977249868051820791414741051994496956
+3 0.998650101968369896532351503992686048
+4 0.999968328758166880021462930017150939
+5 0.999999713348428076464813329948810861
+6 0.999999999013412299575520592043176293
+7 0.999999999998720134897212119540199637
+8 0.999999999999999333866185224906075746
+9 1
+10 1
+
+MSVC 2013 64-bit
+1>
+1> Example: Normal distribution tables.
+1>
+1> Standard normal distribution, mean = 0, standard deviation = 1
+1> maxdigits_10 is 9, digits10 is 6
+1> Probability distribution function values
+1> z PDF
+1> -10 7.69459863e-023
+1> -9 1.02797736e-018
+1> -8 5.05227108e-015
+1> -7 9.13472041e-012
+1> -6 6.07588285e-009
+1> -5 1.48671951e-006
+1> -4 0.000133830226
+1> -3 0.00443184841
+1> -2 0.0539909665
+1> -1 0.241970725
+1> 0 0.39894228
+1> 1 0.241970725
+1> 2 0.0539909665
+1> 3 0.00443184841
+1> 4 0.000133830226
+1> 5 1.48671951e-006
+1> 6 6.07588285e-009
+1> 7 9.13472041e-012
+1> 8 5.05227108e-015
+1> 9 1.02797736e-018
+1> 10 7.69459863e-023
+1> Standard normal mean = 0, standard deviation = 1
+1> Integral (area under the curve) from - infinity up to z.
+1> z CDF
+1> -10 7.61985302e-024
+1> -9 1.12858841e-019
+1> -8 6.22096057e-016
+1> -7 1.27981254e-012
+1> -6 9.86587645e-010
+1> -5 2.86651572e-007
+1> -4 3.16712418e-005
+1> -3 0.00134989803
+1> -2 0.0227501319
+1> -1 0.158655254
+1> 0 0.5
+1> 1 0.841344746
+1> 2 0.977249868
+1> 3 0.998650102
+1> 4 0.999968329
+1> 5 0.999999713
+1> 6 0.999999999
+1> 7 1
+1> 8 1
+1> 9 1
+1> 10 1
+1>
+1> Standard normal distribution, mean = 0, standard deviation = 1
+1> maxdigits_10 is 17, digits10 is 15
+1> Probability distribution function values
+1> z PDF
+1> -10 7.6945986267064199e-023
+1> -9 1.0279773571668917e-018
+1> -8 5.0522710835368927e-015
+1> -7 9.1347204083645953e-012
+1> -6 6.0758828498232861e-009
+1> -5 1.4867195147342979e-006
+1> -4 0.00013383022576488537
+1> -3 0.0044318484119380075
+1> -2 0.053990966513188063
+1> -1 0.24197072451914337
+1> 0 0.3989422804014327
+1> 1 0.24197072451914337
+1> 2 0.053990966513188063
+1> 3 0.0044318484119380075
+1> 4 0.00013383022576488537
+1> 5 1.4867195147342979e-006
+1> 6 6.0758828498232861e-009
+1> 7 9.1347204083645953e-012
+1> 8 5.0522710835368927e-015
+1> 9 1.0279773571668917e-018
+1> 10 7.6945986267064199e-023
+1> Standard normal mean = 0, standard deviation = 1
+1> Integral (area under the curve) from - infinity up to z.
+1> z CDF
+1> -10 7.6198530241605813e-024
+1> -9 1.1285884059538408e-019
+1> -8 6.2209605742718292e-016
+1> -7 1.2798125438858352e-012
+1> -6 9.8658764503770161e-010
+1> -5 2.8665157187919439e-007
+1> -4 3.1671241833119979e-005
+1> -3 0.0013498980316300957
+1> -2 0.022750131948179219
+1> -1 0.15865525393145707
+1> 0 0.5
+1> 1 0.84134474606854293
+1> 2 0.97724986805182079
+1> 3 0.9986501019683699
+1> 4 0.99996832875816688
+1> 5 0.99999971334842808
+1> 6 0.9999999990134123
+1> 7 0.99999999999872013
+1> 8 0.99999999999999933
+1> 9 1
+1> 10 1
+1>
+1> Standard normal distribution, mean = 0, standard deviation = 1
+1> maxdigits_10 is 17, digits10 is 15
+1> Probability distribution function values
+1> z PDF
+1> -10 7.6945986267064199e-023
+1> -9 1.0279773571668917e-018
+1> -8 5.0522710835368927e-015
+1> -7 9.1347204083645953e-012
+1> -6 6.0758828498232861e-009
+1> -5 1.4867195147342979e-006
+1> -4 0.00013383022576488537
+1> -3 0.0044318484119380075
+1> -2 0.053990966513188063
+1> -1 0.24197072451914337
+1> 0 0.3989422804014327
+1> 1 0.24197072451914337
+1> 2 0.053990966513188063
+1> 3 0.0044318484119380075
+1> 4 0.00013383022576488537
+1> 5 1.4867195147342979e-006
+1> 6 6.0758828498232861e-009
+1> 7 9.1347204083645953e-012
+1> 8 5.0522710835368927e-015
+1> 9 1.0279773571668917e-018
+1> 10 7.6945986267064199e-023
+1> Standard normal mean = 0, standard deviation = 1
+1> Integral (area under the curve) from - infinity up to z.
+1> z CDF
+1> -10 7.6198530241605813e-024
+1> -9 1.1285884059538408e-019
+1> -8 6.2209605742718292e-016
+1> -7 1.2798125438858352e-012
+1> -6 9.8658764503770161e-010
+1> -5 2.8665157187919439e-007
+1> -4 3.1671241833119979e-005
+1> -3 0.0013498980316300957
+1> -2 0.022750131948179219
+1> -1 0.15865525393145707
+1> 0 0.5
+1> 1 0.84134474606854293
+1> 2 0.97724986805182079
+1> 3 0.9986501019683699
+1> 4 0.99996832875816688
+1> 5 0.99999971334842808
+1> 6 0.9999999990134123
+1> 7 0.99999999999872013
+1> 8 0.99999999999999933
+1> 9 1
+1> 10 1
+
+
+*/
generated by cgit v1.2.3 (git 2.39.1) at 2024-12-21 11:35:25 +0000