WSJT-X/boost/libs/math/example/inverse_gamma_distribution_example.cpp

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// inverse_gamma_distribution_example.cpp
// Copyright Paul A. Bristow 2010.
// Copyright Thomas Mang 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 1 of using inverse gamma
#include <boost/math/distributions/inverse_gamma.hpp>
using boost::math::inverse_gamma_distribution; // inverse_gamma_distribution.
using boost::math::inverse_gamma;
#include <boost/math/special_functions/gamma.hpp>
using boost::math::tgamma; // Used for naive pdf as a comparison.
#include <boost/math/distributions/gamma.hpp>
using boost::math::inverse_gamma_distribution;
#include <iostream>
using std::cout; using std::endl;
#include <iomanip>
using std::setprecision;
#include <cmath>
using std::sqrt;
int main()
{
cout << "Example using Inverse Gamma distribution. " << endl;
// TODO - awaiting a real example using Bayesian statistics.
#ifdef BOOST_NO_CXX11_NUMERIC_LIMITS
int max_digits10 = 2 + (boost::math::policies::digits<double, boost::math::policies::policy<> >() * 30103UL) / 100000UL;
cout << "BOOST_NO_CXX11_NUMERIC_LIMITS is defined" << endl;
#else
int max_digits10 = std::numeric_limits<double>::max_digits10;
#endif
cout << "Show all potentially significant decimal digits std::numeric_limits<double>::max_digits10 = "
<< max_digits10 << endl;
cout.precision(max_digits10); //
double shape = 1.;
double scale = 1.;
double x = 0.5;
// Construction using default RealType double, and default shape and scale..
inverse_gamma_distribution<> my_inverse_gamma(shape, scale); // (alpha, beta)
cout << "my_inverse_gamma.shape() = " << my_inverse_gamma.shape()
<< ", scale = "<< my_inverse_gamma.scale() << endl;
cout << "x = " << x << ", pdf = " << pdf(my_inverse_gamma, x)
<< ", cdf = " << cdf(my_inverse_gamma, x) << endl;
// Construct using typedef and default shape and scale parameters.
inverse_gamma my_ig;
inverse_gamma my_ig23(2, 3);
cout << "my_inverse_gamma.shape() = " << my_ig23.shape()
<< ", scale = "<< my_ig23.scale() << endl;
cout << "x = " << x << ", pdf = " << pdf(my_ig23, x)
<< ", cdf = " << cdf(my_ig23, x) << endl;
// Example of providing an 'out of domain' or 'bad' parameter,
// here a shape < 1, for which mean is not defined.
// Try block is essential to catch the exception message.
// (Uses the default policy which is to throw on all errors).
try
{
inverse_gamma if051(0.5, 1);
//inverse_gamma if051(0.5, 1);
cout << "mean(if051) = " << mean(if051) << endl;
}
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 using Inverse Gamma distribution.
std::numeric_limits<double>::max_digits10 = 17
my_inverse_gamma.shape() = 1, scale = 1
x = 0.5, pdf = 0.54134113294645081, cdf = 0.1353352832366127
my_inverse_gamma.shape() = 2, scale = 3
x = 0.5, pdf = 0.17847015671997774, cdf = 0.017351265236664509
Message from thrown exception was:
Error in function boost::math::mean(const inverse_gamma_distribution<double>&): Shape parameter is 0.5, but for a defined mean it must be > 1
*/