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172 lines
6.9 KiB
C++
172 lines
6.9 KiB
C++
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// inverse_chi_squared_distribution_example.cpp
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// Copyright Paul A. Bristow 2010.
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// Copyright Thomas Mang 2010.
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// Use, modification and distribution are subject to the
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// Boost Software License, Version 1.0.
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// (See accompanying file LICENSE_1_0.txt
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// or copy at http://www.boost.org/LICENSE_1_0.txt)
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// Example 1 of using inverse chi squared distribution
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#include <boost/math/distributions/inverse_chi_squared.hpp>
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using boost::math::inverse_chi_squared_distribution; // inverse_chi_squared_distribution.
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using boost::math::inverse_chi_squared; //typedef for nverse_chi_squared_distribution double.
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#include <iostream>
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using std::cout; using std::endl;
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#include <iomanip>
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using std::setprecision;
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using std::setw;
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#include <cmath>
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using std::sqrt;
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template <class RealType>
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RealType naive_pdf1(RealType df, RealType x)
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{ // Formula from Wikipedia http://en.wikipedia.org/wiki/Inverse-chi-square_distribution
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// definition 1 using tgamma for simplicity as a check.
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using namespace std; // For ADL of std functions.
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using boost::math::tgamma;
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RealType df2 = df / 2;
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RealType result = (pow(2., -df2) * pow(x, (-df2 -1)) * exp(-1/(2 * x) ) )
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/ tgamma(df2); //
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return result;
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}
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template <class RealType>
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RealType naive_pdf2(RealType df, RealType x)
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{ // Formula from Wikipedia http://en.wikipedia.org/wiki/Inverse-chi-square_distribution
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// Definition 2, using tgamma for simplicity as a check.
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// Not scaled, so assumes scale = 1 and only uses nu aka df.
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using namespace std; // For ADL of std functions.
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using boost::math::tgamma;
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RealType df2 = df / 2;
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RealType result = (pow(df2, df2) * pow(x, (-df2 -1)) * exp(-df/(2*x) ) )
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/ tgamma(df2);
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return result;
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}
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template <class RealType>
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RealType naive_pdf3(RealType df, RealType scale, RealType x)
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{ // Formula from Wikipedia http://en.wikipedia.org/wiki/Scaled-inverse-chi-square_distribution
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// *Scaled* version, definition 3, df aka nu, scale aka sigma^2
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// using tgamma for simplicity as a check.
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using namespace std; // For ADL of std functions.
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using boost::math::tgamma;
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RealType df2 = df / 2;
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RealType result = (pow(scale * df2, df2) * exp(-df2 * scale/x) )
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/ (tgamma(df2) * pow(x, 1+df2));
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return result;
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}
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template <class RealType>
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RealType naive_pdf4(RealType df, RealType scale, RealType x)
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{ // Formula from http://mathworld.wolfram.com/InverseChi-SquaredDistribution.html
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// Weisstein, Eric W. "Inverse Chi-Squared Distribution." From MathWorld--A Wolfram Web Resource.
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// *Scaled* version, definition 3, df aka nu, scale aka sigma^2
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// using tgamma for simplicity as a check.
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using namespace std; // For ADL of std functions.
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using boost::math::tgamma;
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RealType nu = df; // Wolfram uses greek symbols nu,
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RealType xi = scale; // and xi.
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RealType result =
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pow(2, -nu/2) * exp(- (nu * xi)/(2 * x)) * pow(x, -1-nu/2) * pow((nu * xi), nu/2)
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/ tgamma(nu/2);
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return result;
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}
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int main()
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{
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cout << "Example (basic) using Inverse chi squared distribution. " << endl;
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// TODO find a more practical/useful example. Suggestions welcome?
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#ifdef BOOST_NO_CXX11_NUMERIC_LIMITS
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int max_digits10 = 2 + (boost::math::policies::digits<double, boost::math::policies::policy<> >() * 30103UL) / 100000UL;
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cout << "BOOST_NO_CXX11_NUMERIC_LIMITS is defined" << endl;
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#else
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int max_digits10 = std::numeric_limits<double>::max_digits10;
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#endif
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cout << "Show all potentially significant decimal digits std::numeric_limits<double>::max_digits10 = "
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<< max_digits10 << endl;
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cout.precision(max_digits10); //
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inverse_chi_squared ichsqdef; // All defaults - not very useful!
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cout << "default df = " << ichsqdef.degrees_of_freedom()
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<< ", default scale = " << ichsqdef.scale() << endl; // default df = 1, default scale = 0.5
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inverse_chi_squared ichsqdef4(4); // Unscaled version, default scale = 1 / degrees_of_freedom
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cout << "default df = " << ichsqdef4.degrees_of_freedom()
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<< ", default scale = " << ichsqdef4.scale() << endl; // default df = 4, default scale = 2
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inverse_chi_squared ichsqdef32(3, 2); // Scaled version, both degrees_of_freedom and scale specified.
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cout << "default df = " << ichsqdef32.degrees_of_freedom()
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<< ", default scale = " << ichsqdef32.scale() << endl; // default df = 3, default scale = 2
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{
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cout.precision(3);
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double nu = 5.;
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//double scale1 = 1./ nu; // 1st definition sigma^2 = 1/df;
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//double scale2 = 1.; // 2nd definition sigma^2 = 1
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inverse_chi_squared ichsq(nu, 1/nu); // Not scaled
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inverse_chi_squared sichsq(nu, 1/nu); // scaled
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cout << "nu = " << ichsq.degrees_of_freedom() << ", scale = " << ichsq.scale() << endl;
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int width = 8;
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cout << " x pdf pdf1 pdf2 pdf(scaled) pdf pdf cdf cdf" << endl;
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for (double x = 0.0; x < 1.; x += 0.1)
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{
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cout
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<< setw(width) << x
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<< ' ' << setw(width) << pdf(ichsq, x) // unscaled
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<< ' ' << setw(width) << naive_pdf1(nu, x) // Wiki def 1 unscaled matches graph
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<< ' ' << setw(width) << naive_pdf2(nu, x) // scale = 1 - 2nd definition.
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<< ' ' << setw(width) << naive_pdf3(nu, 1/nu, x) // scaled
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<< ' ' << setw(width) << naive_pdf4(nu, 1/nu, x) // scaled
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<< ' ' << setw(width) << pdf(sichsq, x) // scaled
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<< ' ' << setw(width) << cdf(sichsq, x) // scaled
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<< ' ' << setw(width) << cdf(ichsq, x) // unscaled
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<< endl;
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}
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}
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cout.precision(max_digits10);
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inverse_chi_squared ichisq(2., 0.5);
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cout << "pdf(ichisq, 1.) = " << pdf(ichisq, 1.) << endl;
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cout << "cdf(ichisq, 1.) = " << cdf(ichisq, 1.) << endl;
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return 0;
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} // int main()
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/*
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Output is:
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Example (basic) using Inverse chi squared distribution.
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Show all potentially significant decimal digits std::numeric_limits<double>::max_digits10 = 17
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default df = 1, default scale = 1
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default df = 4, default scale = 0.25
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default df = 3, default scale = 2
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nu = 5, scale = 0.2
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x pdf pdf1 pdf2 pdf(scaled) pdf pdf cdf cdf
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0 0 -1.#J -1.#J -1.#J -1.#J 0 0 0
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0.1 2.83 2.83 3.26e-007 2.83 2.83 2.83 0.0752 0.0752
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0.2 3.05 3.05 0.00774 3.05 3.05 3.05 0.416 0.416
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0.3 1.7 1.7 0.121 1.7 1.7 1.7 0.649 0.649
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0.4 0.941 0.941 0.355 0.941 0.941 0.941 0.776 0.776
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0.5 0.553 0.553 0.567 0.553 0.553 0.553 0.849 0.849
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0.6 0.345 0.345 0.689 0.345 0.345 0.345 0.893 0.893
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0.7 0.227 0.227 0.728 0.227 0.227 0.227 0.921 0.921
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0.8 0.155 0.155 0.713 0.155 0.155 0.155 0.94 0.94
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0.9 0.11 0.11 0.668 0.11 0.11 0.11 0.953 0.953
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1 0.0807 0.0807 0.61 0.0807 0.0807 0.0807 0.963 0.963
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pdf(ichisq, 1.) = 0.30326532985631671
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cdf(ichisq, 1.) = 0.60653065971263365
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*/
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