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// inverse_chi_squared_distribution_find_df_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)
//#define BOOST_MATH_INSTRUMENT
// Example 1 of using inverse chi squared distribution
#include <boost/math/distributions/inverse_chi_squared.hpp>
using boost::math::inverse_chi_squared_distribution; // inverse_chi_squared_distribution.
using boost::math::inverse_chi_squared; //typedef for nverse_chi_squared_distribution double.
#include <iostream>
using std::cout; using std::endl;
#include <iomanip>
using std::setprecision;
using std::setw;
#include <cmath>
using std::sqrt;
int main()
{
cout << "Example using Inverse chi squared distribution to find df. " << endl;
try
{
cout.precision(std::numeric_limits<double>::max_digits10); //
int i = std::numeric_limits<double>::max_digits10;
cout << "Show all potentially significant decimal digits std::numeric_limits<double>::max_digits10 = " << i << endl;
cout.precision(3);
double nu = 10.;
double scale1 = 1./ nu; // 1st definition sigma^2 = 1/df;
double scale2 = 1.; // 2nd definition sigma^2 = 1
inverse_chi_squared sichsq(nu, 1/nu); // Explicitly scaled to default scale = 1/df.
inverse_chi_squared ichsq(nu); // Implicitly scaled to default scale = 1/df.
// Try degrees of freedom estimator
//double df = chi_squared::find_degrees_of_freedom(-diff, alpha[i], alpha[i], variance);
cout << "ichsq.degrees_of_freedom() = " << ichsq.degrees_of_freedom() << endl;
double diff = 0.5; // difference from variance to detect (delta).
double variance = 1.; // true variance
double alpha = 0.9;
double beta = 0.9;
cout << "diff = " << diff
<< ", variance = " << variance << ", ratio = " << diff/variance
<< ", alpha = " << alpha << ", beta = " << beta << endl;
/* inverse_chi_square_df_estimator is not in the code base anymore?
using boost::math::detail::inverse_chi_square_df_estimator;
using boost::math::policies::default_policy;
inverse_chi_square_df_estimator<> a_df(alpha, beta, variance, diff);
cout << "df est" << endl;
for (double df = 1; df < 3; df += 0.1)
{
double est_df = a_df(1);
cout << df << " " << a_df(df) << endl;
}
*/
//template <class F, class T, class Tol, class Policy>std::pair<T, T>
// bracket_and_solve_root(F f, const T& guess, T factor, bool rising, Tol tol, std::uintmax_t& max_iter, const Policy& pol)
// TODO: Not implemented
//double df = inverse_chi_squared_distribution<>::find_degrees_of_freedom(diff, alpha, beta, variance, 0);
//cout << df << 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 chi squared distribution to find df.
Show all potentially significant decimal digits std::numeric_limits<double>::max_digits10 = 17
10
Message from thrown exception was:
Error in function boost::math::inverse_chi_squared_distribution<double>::inverse_chi_squared_distribution: Degrees of freedom argument is 1.#INF, but must be > 0 !
diff = 0.5, variance = 1, ratio = 0.5, alpha = 0.1, beta = 0.1
df est
1 1
ratio+1 = 1.5, quantile(0.1) = 0.00618, cdf = 6.5e-037, result = -0.1
1.1 -0.1
ratio+1 = 1.5, quantile(0.1) = 0.00903, cdf = 1.2e-025, result = -0.1
1.2 -0.1
ratio+1 = 1.5, quantile(0.1) = 0.0125, cdf = 8.25e-019, result = -0.1
1.3 -0.1
ratio+1 = 1.5, quantile(0.1) = 0.0166, cdf = 2.17e-014, result = -0.1
1.4 -0.1
ratio+1 = 1.5, quantile(0.1) = 0.0212, cdf = 2.2e-011, result = -0.1
1.5 -0.1
ratio+1 = 1.5, quantile(0.1) = 0.0265, cdf = 3e-009, result = -0.1
1.6 -0.1
ratio+1 = 1.5, quantile(0.1) = 0.0323, cdf = 1.11e-007, result = -0.1
1.7 -0.1
ratio+1 = 1.5, quantile(0.1) = 0.0386, cdf = 1.7e-006, result = -0.1
1.8 -0.1
ratio+1 = 1.5, quantile(0.1) = 0.0454, cdf = 1.41e-005, result = -0.1
1.9 -0.1
ratio+1 = 1.5, quantile(0.1) = 0.0527, cdf = 7.55e-005, result = -0.1
2 -0.1
ratio+1 = 1.5, quantile(0.1) = 0.0604, cdf = 0.000291, result = -0.1
2.1 -0.1
ratio+1 = 1.5, quantile(0.1) = 0.0685, cdf = 0.00088, result = -0.1
2.2 -0.1
ratio+1 = 1.5, quantile(0.1) = 0.0771, cdf = 0.0022, result = -0.0999
2.3 -0.0999
ratio+1 = 1.5, quantile(0.1) = 0.0859, cdf = 0.00475, result = -0.0997
2.4 -0.0997
ratio+1 = 1.5, quantile(0.1) = 0.0952, cdf = 0.00911, result = -0.0993
2.5 -0.0993
ratio+1 = 1.5, quantile(0.1) = 0.105, cdf = 0.0159, result = -0.0984
2.6 -0.0984
ratio+1 = 1.5, quantile(0.1) = 0.115, cdf = 0.0257, result = -0.0967
2.7 -0.0967
ratio+1 = 1.5, quantile(0.1) = 0.125, cdf = 0.039, result = -0.094
2.8 -0.094
ratio+1 = 1.5, quantile(0.1) = 0.135, cdf = 0.056, result = -0.0897
2.9 -0.0897
ratio+1 = 1.5, quantile(0.1) = 20.6, cdf = 1, result = 0.9
ichsq.degrees_of_freedom() = 10
diff = 0.5, variance = 1, ratio = 0.5, alpha = 0.9, beta = 0.9
df est
1 1
ratio+1 = 1.5, quantile(0.9) = 0.729, cdf = 0.269, result = -0.729
1.1 -0.729
ratio+1 = 1.5, quantile(0.9) = 0.78, cdf = 0.314, result = -0.693
1.2 -0.693
ratio+1 = 1.5, quantile(0.9) = 0.83, cdf = 0.36, result = -0.655
1.3 -0.655
ratio+1 = 1.5, quantile(0.9) = 0.879, cdf = 0.405, result = -0.615
1.4 -0.615
ratio+1 = 1.5, quantile(0.9) = 0.926, cdf = 0.449, result = -0.575
1.5 -0.575
ratio+1 = 1.5, quantile(0.9) = 0.973, cdf = 0.492, result = -0.535
1.6 -0.535
ratio+1 = 1.5, quantile(0.9) = 1.02, cdf = 0.534, result = -0.495
1.7 -0.495
ratio+1 = 1.5, quantile(0.9) = 1.06, cdf = 0.574, result = -0.455
1.8 -0.455
ratio+1 = 1.5, quantile(0.9) = 1.11, cdf = 0.612, result = -0.417
1.9 -0.417
ratio+1 = 1.5, quantile(0.9) = 1.15, cdf = 0.648, result = -0.379
2 -0.379
ratio+1 = 1.5, quantile(0.9) = 1.19, cdf = 0.681, result = -0.342
2.1 -0.342
ratio+1 = 1.5, quantile(0.9) = 1.24, cdf = 0.713, result = -0.307
2.2 -0.307
ratio+1 = 1.5, quantile(0.9) = 1.28, cdf = 0.742, result = -0.274
2.3 -0.274
ratio+1 = 1.5, quantile(0.9) = 1.32, cdf = 0.769, result = -0.242
2.4 -0.242
ratio+1 = 1.5, quantile(0.9) = 1.36, cdf = 0.793, result = -0.212
2.5 -0.212
ratio+1 = 1.5, quantile(0.9) = 1.4, cdf = 0.816, result = -0.184
2.6 -0.184
ratio+1 = 1.5, quantile(0.9) = 1.44, cdf = 0.836, result = -0.157
2.7 -0.157
ratio+1 = 1.5, quantile(0.9) = 1.48, cdf = 0.855, result = -0.133
2.8 -0.133
ratio+1 = 1.5, quantile(0.9) = 1.52, cdf = 0.872, result = -0.11
2.9 -0.11
ratio+1 = 1.5, quantile(0.9) = 29.6, cdf = 1, result = 0.1
*/
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