mirror of
https://github.com/saitohirga/WSJT-X.git
synced 2024-11-26 06:08:42 -05:00
170 lines
6.9 KiB
C++
170 lines
6.9 KiB
C++
// 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
|
|
|
|
*/
|
|
|