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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;
- 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, boost::uintmax_t& max_iter, const Policy& pol)
- //double df = inverse_chi_squared_distribution<>::find_degrees_of_freedom(diff, alpha, beta, variance, 0);
-
- double df = inverse_chi_squared::find_degrees_of_freedom(diff, alpha, beta, variance, 100);
- 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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