boost_1_45_0/libs/math/example/laplace_example.cpp - nest-learning-thermostat/5.0/boost - Git at Google

 // laplace_example.cpp

 // Copyright Paul A. Bristow 2008, 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)

 // Example of using laplace (& comparing with 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!

 //[laplace_example1
 /*`
 First we need some includes to access the laplace & normal distributions
 (and some std output of course).
 */

 #include <boost/math/distributions/laplace.hpp> // for laplace_distribution
   using boost::math::laplace; // typedef provides default type is double.
 #include <boost/math/distributions/normal.hpp> // for normal_distribution
   using boost::math::normal; // typedef provides default type is 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;

 int main()
 {
   cout << "Example: Laplace distribution." << endl;

   try
   {
     { // Traditional tables and values.
 /*`Let's start by printing some traditional tables.
 */
       double step = 1.; // in z
       double range = 4; // min and max z = -range to +range.
       //int precision = 17; // traditional tables are only computed to much lower precision.
       int precision = 4; // traditional table at much lower precision.
       int width = 10; // for use with setw.

       // Construct standard laplace & normal distributions l & s
         normal s; // (default location or mean = zero, and scale or standard deviation = unity)
         cout << "Standard normal distribution, mean or location = "<< s.location()
           << ", standard deviation or scale = " << s.scale() << endl;
         laplace l; // (default mean = zero, and standard deviation = unity)
         cout << "Laplace normal distribution, location = "<< l.location()
           << ", scale = " << l.scale() << endl;

 /*` First the probability distribution function (pdf).
 */
       cout << "Probability distribution function values" << endl;
       cout << " z  PDF  normal     laplace    (difference)" << endl;
       cout.precision(5);
       for (double z = -range; z < range + step; z += step)
       {
         cout << left << setprecision(3) << setw(6) << z << " "
           << setprecision(precision) << setw(width) << pdf(s, z) << "  "
           << setprecision(precision) << setw(width) << pdf(l, z)<<  "  ("
           << setprecision(precision) << setw(width) << pdf(l, z) - pdf(s, z) // difference.
           << ")" << endl;
       }
       cout.precision(6); // default
 /*`Notice how the laplace is less at z = 1 , but has 'fatter' tails at 2 and 3.

    And the area under the normal curve from -[infin] up to z,
    the cumulative distribution function (cdf).
 */
       // For a standard distribution
       cout << "Standard location = "<< s.location()
         << ", scale = " << s.scale() << endl;
       cout << "Integral (area under the curve) from - infinity up to z " << endl;
       cout << " z  CDF  normal     laplace    (difference)" << endl;
       for (double z = -range; z < range + step; z += step)
       {
         cout << left << setprecision(3) << setw(6) << z << " "
           << setprecision(precision) << setw(width) << cdf(s, z) << "  "
           << setprecision(precision) << setw(width) << cdf(l, z) <<  "  ("
           << setprecision(precision) << setw(width) << cdf(l, z) - cdf(s, z) // difference.
           << ")" << endl;
       }
       cout.precision(6); // default

 /*`
 Pretty-printing a traditional 2-dimensional table is left as an exercise for the student,
 but why bother now that the Boost Math Toolkit lets you write
 */
     double z = 2.;
     cout << "Area for gaussian z = " << z << " is " << cdf(s, z) << endl; // to get the area for z.
     cout << "Area for laplace z = " << z << " is " << cdf(l, z) << endl; //
 /*`
 Correspondingly, we can obtain the traditional 'critical' values for significance levels.
 For the 95% confidence level, the significance level usually called alpha,
 is 0.05 = 1 - 0.95 (for a one-sided test), so we can write
 */
      cout << "95% of gaussian area has a z below " << quantile(s, 0.95) << endl;
      cout << "95% of laplace area has a z below " << quantile(l, 0.95) << endl;
    // 95% of area has a z below 1.64485
    // 95% of laplace area has a z below 2.30259
 /*`and a two-sided test (a comparison between two levels, rather than a one-sided test)

 */
      cout << "95% of gaussian area has a z between " << quantile(s, 0.975)
        << " and " << -quantile(s, 0.975) << endl;
      cout << "95% of laplace area has a z between " << quantile(l, 0.975)
        << " and " << -quantile(l, 0.975) << endl;
    // 95% of area has a z between 1.95996 and -1.95996
    // 95% of laplace area has a z between 2.99573 and -2.99573
 /*`Notice how much wider z has to be to enclose 95% of the area.
 */
   }
 //] [/[laplace_example1]
   }
   catch(const std::exception& e)
   { // Always useful to include try & catch blocks because default policies
     // are to throw exceptions on arguments that cause errors like underflow, overflow.
     // Lacking try & catch blocks, the program will abort without a message below,
     // which may give some helpful clues as to the cause of the exception.
     std::cout <<
       "\n""Message from thrown exception was:\n   " << e.what() << std::endl;
   }
   return 0;
 }  // int main()

 /*

 Output is:

 Example: Laplace distribution.
 Standard normal distribution, mean or location = 0, standard deviation or scale = 1
 Laplace normal distribution, location = 0, scale = 1
 Probability distribution function values
  z  PDF  normal     laplace    (difference)
 -4     0.0001338   0.009158    (0.009024  )
 -3     0.004432    0.02489     (0.02046   )
 -2     0.05399     0.06767     (0.01368   )
 -1     0.242       0.1839      (-0.05803  )
 0      0.3989      0.5         (0.1011    )
 1      0.242       0.1839      (-0.05803  )
 2      0.05399     0.06767     (0.01368   )
 3      0.004432    0.02489     (0.02046   )
 4      0.0001338   0.009158    (0.009024  )
 Standard location = 0, scale = 1
 Integral (area under the curve) from - infinity up to z
  z  CDF  normal     laplace    (difference)
 -4     3.167e-005  0.009158    (0.009126  )
 -3     0.00135     0.02489     (0.02354   )
 -2     0.02275     0.06767     (0.04492   )
 -1     0.1587      0.1839      (0.02528   )
 0      0.5         0.5         (0         )
 1      0.8413      0.8161      (-0.02528  )
 2      0.9772      0.9323      (-0.04492  )
 3      0.9987      0.9751      (-0.02354  )
 4      1           0.9908      (-0.009126 )
 Area for gaussian z = 2 is 0.97725
 Area for laplace z = 2 is 0.932332
 95% of gaussian area has a z below 1.64485
 95% of laplace area has a z below 2.30259
 95% of gaussian area has a z between 1.95996 and -1.95996
 95% of laplace area has a z between 2.99573 and -2.99573

 */
	// laplace_example.cpp

	// Copyright Paul A. Bristow 2008, 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)

	// Example of using laplace (& comparing with 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!

	//[laplace_example1
	/*`
	First we need some includes to access the laplace & normal distributions
	(and some std output of course).
	*/

	#include <boost/math/distributions/laplace.hpp> // for laplace_distribution
	using boost::math::laplace; // typedef provides default type is double.
	#include <boost/math/distributions/normal.hpp> // for normal_distribution
	using boost::math::normal; // typedef provides default type is 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;

	int main()
	{
	cout << "Example: Laplace distribution." << endl;

	try
	{
	{ // Traditional tables and values.
	/*`Let's start by printing some traditional tables.
	*/
	double step = 1.; // in z
	double range = 4; // min and max z = -range to +range.
	//int precision = 17; // traditional tables are only computed to much lower precision.
	int precision = 4; // traditional table at much lower precision.
	int width = 10; // for use with setw.

	// Construct standard laplace & normal distributions l & s
	normal s; // (default location or mean = zero, and scale or standard deviation = unity)
	cout << "Standard normal distribution, mean or location = "<< s.location()
	<< ", standard deviation or scale = " << s.scale() << endl;
	laplace l; // (default mean = zero, and standard deviation = unity)
	cout << "Laplace normal distribution, location = "<< l.location()
	<< ", scale = " << l.scale() << endl;

	/*` First the probability distribution function (pdf).
	*/
	cout << "Probability distribution function values" << endl;
	cout << " z PDF normal laplace (difference)" << endl;
	cout.precision(5);
	for (double z = -range; z < range + step; z += step)
	{
	cout << left << setprecision(3) << setw(6) << z << " "
	<< setprecision(precision) << setw(width) << pdf(s, z) << " "
	<< setprecision(precision) << setw(width) << pdf(l, z)<< " ("
	<< setprecision(precision) << setw(width) << pdf(l, z) - pdf(s, z) // difference.
	<< ")" << endl;
	}
	cout.precision(6); // default
	/*`Notice how the laplace is less at z = 1 , but has 'fatter' tails at 2 and 3.

	And the area under the normal curve from -[infin] up to z,
	the cumulative distribution function (cdf).
	*/
	// For a standard distribution
	cout << "Standard location = "<< s.location()
	<< ", scale = " << s.scale() << endl;
	cout << "Integral (area under the curve) from - infinity up to z " << endl;
	cout << " z CDF normal laplace (difference)" << endl;
	for (double z = -range; z < range + step; z += step)
	{
	cout << left << setprecision(3) << setw(6) << z << " "
	<< setprecision(precision) << setw(width) << cdf(s, z) << " "
	<< setprecision(precision) << setw(width) << cdf(l, z) << " ("
	<< setprecision(precision) << setw(width) << cdf(l, z) - cdf(s, z) // difference.
	<< ")" << endl;
	}
	cout.precision(6); // default

	/*`
	Pretty-printing a traditional 2-dimensional table is left as an exercise for the student,
	but why bother now that the Boost Math Toolkit lets you write
	*/
	double z = 2.;
	cout << "Area for gaussian z = " << z << " is " << cdf(s, z) << endl; // to get the area for z.
	cout << "Area for laplace z = " << z << " is " << cdf(l, z) << endl; //
	/*`
	Correspondingly, we can obtain the traditional 'critical' values for significance levels.
	For the 95% confidence level, the significance level usually called alpha,
	is 0.05 = 1 - 0.95 (for a one-sided test), so we can write
	*/
	cout << "95% of gaussian area has a z below " << quantile(s, 0.95) << endl;
	cout << "95% of laplace area has a z below " << quantile(l, 0.95) << endl;
	// 95% of area has a z below 1.64485
	// 95% of laplace area has a z below 2.30259
	/*`and a two-sided test (a comparison between two levels, rather than a one-sided test)

	*/
	cout << "95% of gaussian area has a z between " << quantile(s, 0.975)
	<< " and " << -quantile(s, 0.975) << endl;
	cout << "95% of laplace area has a z between " << quantile(l, 0.975)
	<< " and " << -quantile(l, 0.975) << endl;
	// 95% of area has a z between 1.95996 and -1.95996
	// 95% of laplace area has a z between 2.99573 and -2.99573
	/*`Notice how much wider z has to be to enclose 95% of the area.
	*/
	}
	//] [/[laplace_example1]
	}
	catch(const std::exception& e)
	{ // Always useful to include try & catch blocks because default policies
	// are to throw exceptions on arguments that cause errors like underflow, overflow.
	// Lacking try & catch blocks, the program will abort without a message below,
	// which may give some helpful clues as to the cause of the exception.
	std::cout <<
	"\n""Message from thrown exception was:\n " << e.what() << std::endl;
	}
	return 0;
	} // int main()

	/*

	Output is:

	Example: Laplace distribution.
	Standard normal distribution, mean or location = 0, standard deviation or scale = 1
	Laplace normal distribution, location = 0, scale = 1
	Probability distribution function values
	z PDF normal laplace (difference)
	-4 0.0001338 0.009158 (0.009024 )
	-3 0.004432 0.02489 (0.02046 )
	-2 0.05399 0.06767 (0.01368 )
	-1 0.242 0.1839 (-0.05803 )
	0 0.3989 0.5 (0.1011 )
	1 0.242 0.1839 (-0.05803 )
	2 0.05399 0.06767 (0.01368 )
	3 0.004432 0.02489 (0.02046 )
	4 0.0001338 0.009158 (0.009024 )
	Standard location = 0, scale = 1
	Integral (area under the curve) from - infinity up to z
	z CDF normal laplace (difference)
	-4 3.167e-005 0.009158 (0.009126 )
	-3 0.00135 0.02489 (0.02354 )
	-2 0.02275 0.06767 (0.04492 )
	-1 0.1587 0.1839 (0.02528 )
	0 0.5 0.5 (0 )
	1 0.8413 0.8161 (-0.02528 )
	2 0.9772 0.9323 (-0.04492 )
	3 0.9987 0.9751 (-0.02354 )
	4 1 0.9908 (-0.009126 )
	Area for gaussian z = 2 is 0.97725
	Area for laplace z = 2 is 0.932332
	95% of gaussian area has a z below 1.64485
	95% of laplace area has a z below 2.30259
	95% of gaussian area has a z between 1.95996 and -1.95996
	95% of laplace area has a z between 2.99573 and -2.99573

	*/