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269 lines
9.7 KiB
C++
269 lines
9.7 KiB
C++
// Copyright John Maddock 2006.
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// Copyright Paul A. Bristow 2007, 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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// test_gamma_dist.cpp
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// http://en.wikipedia.org/wiki/Gamma_distribution
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// http://www.itl.nist.gov/div898/handbook/eda/section3/eda366b.htm
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// Also:
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// Weisstein, Eric W. "Gamma Distribution."
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// From MathWorld--A Wolfram Web Resource.
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// http://mathworld.wolfram.com/GammaDistribution.html
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#include <pch.hpp> // include directory libs/math/src/tr1/ is needed.
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#include <boost/math/concepts/real_concept.hpp> // for real_concept
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#define BOOST_TEST_MAIN
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#include <boost/test/unit_test.hpp> // Boost.Test
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#include <boost/test/floating_point_comparison.hpp>
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#include <boost/math/distributions/gamma.hpp>
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using boost::math::gamma_distribution;
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#include <boost/math/tools/test.hpp>
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#include "test_out_of_range.hpp"
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#include <iostream>
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#include <iomanip>
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using std::cout;
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using std::endl;
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using std::setprecision;
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#include <limits>
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using std::numeric_limits;
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template <class RealType>
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RealType NaivePDF(RealType shape, RealType scale, RealType x)
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{
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// Deliberately naive PDF calculator again which
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// we'll compare our pdf function. However some
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// published values to compare against would be better....
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using namespace std;
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RealType result = log(x) * (shape - 1) - x / scale - boost::math::lgamma(shape) - log(scale) * shape;
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return exp(result);
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}
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template <class RealType>
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void check_gamma(RealType shape, RealType scale, RealType x, RealType p, RealType q, RealType tol)
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{
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BOOST_CHECK_CLOSE(
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::boost::math::cdf(
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gamma_distribution<RealType>(shape, scale), // distribution.
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x), // random variable.
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p, // probability.
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tol); // %tolerance.
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BOOST_CHECK_CLOSE(
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::boost::math::cdf(
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complement(
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gamma_distribution<RealType>(shape, scale), // distribution.
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x)), // random variable.
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q, // probability complement.
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tol); // %tolerance.
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if(p < 0.999)
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{
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BOOST_CHECK_CLOSE(
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::boost::math::quantile(
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gamma_distribution<RealType>(shape, scale), // distribution.
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p), // probability.
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x, // random variable.
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tol); // %tolerance.
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}
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if(q < 0.999)
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{
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BOOST_CHECK_CLOSE(
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::boost::math::quantile(
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complement(
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gamma_distribution<RealType>(shape, scale), // distribution.
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q)), // probability complement.
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x, // random variable.
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tol); // %tolerance.
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}
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// PDF:
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BOOST_CHECK_CLOSE(
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boost::math::pdf(
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gamma_distribution<RealType>(shape, scale), // distribution.
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x), // random variable.
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NaivePDF(shape, scale, x), // PDF
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tol); // %tolerance.
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}
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template <class RealType>
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void test_spots(RealType)
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{
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// Basic sanity checks
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//
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// 15 decimal places expressed as a persentage.
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// The first tests use values generated by MathCAD,
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// and should be accurate to around double precision.
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//
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RealType tolerance = (std::max)(RealType(5e-14f), std::numeric_limits<RealType>::epsilon() * 20) * 100;
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cout << "Tolerance for type " << typeid(RealType).name() << " is " << tolerance << " %" << endl;
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check_gamma(
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static_cast<RealType>(0.5),
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static_cast<RealType>(1),
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static_cast<RealType>(0.5),
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static_cast<RealType>(0.682689492137085),
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static_cast<RealType>(1-0.682689492137085),
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tolerance);
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check_gamma(
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static_cast<RealType>(2),
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static_cast<RealType>(1),
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static_cast<RealType>(0.5),
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static_cast<RealType>(0.090204010431050),
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static_cast<RealType>(1-0.090204010431050),
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tolerance);
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check_gamma(
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static_cast<RealType>(40),
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static_cast<RealType>(1),
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static_cast<RealType>(10),
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static_cast<RealType>(7.34163631456064E-13),
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static_cast<RealType>(1-7.34163631456064E-13),
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tolerance);
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//
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// Some more test data generated by the online
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// calculator at http://espse.ed.psu.edu/edpsych/faculty/rhale/hale/507Mat/statlets/free/pdist.htm
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// This has the advantage of supporting the scale parameter as well
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// as shape, but has only a few digits accuracy, and produces
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// some deeply suspect values if the shape parameter is < 1
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// (it doesn't agree with MathCAD or this implementation).
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// To be fair the incomplete gamma is tricky to get right in this area...
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//
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tolerance = 1e-5f * 100; // 5 decimal places as a persentage
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cout << "Tolerance for type " << typeid(RealType).name() << " is " << tolerance << " %" << endl;
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check_gamma(
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static_cast<RealType>(2),
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static_cast<RealType>(1)/5,
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static_cast<RealType>(0.1),
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static_cast<RealType>(0.090204),
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static_cast<RealType>(1-0.090204),
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tolerance);
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check_gamma(
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static_cast<RealType>(2),
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static_cast<RealType>(1)/5,
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static_cast<RealType>(0.5),
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static_cast<RealType>(1-0.287298),
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static_cast<RealType>(0.287298),
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tolerance);
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check_gamma(
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static_cast<RealType>(3),
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static_cast<RealType>(2),
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static_cast<RealType>(1),
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static_cast<RealType>(0.014388),
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static_cast<RealType>(1-0.014388),
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tolerance * 10); // one less decimal place in the test value
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check_gamma(
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static_cast<RealType>(3),
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static_cast<RealType>(2),
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static_cast<RealType>(5),
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static_cast<RealType>(0.456187),
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static_cast<RealType>(1-0.456187),
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tolerance);
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RealType tol2 = boost::math::tools::epsilon<RealType>() * 5 * 100; // 5 eps as a persentage
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gamma_distribution<RealType> dist(8, 3);
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RealType x = static_cast<RealType>(0.125);
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using namespace std; // ADL of std names.
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// mean:
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BOOST_CHECK_CLOSE(
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mean(dist)
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, static_cast<RealType>(8*3), tol2);
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// variance:
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BOOST_CHECK_CLOSE(
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variance(dist)
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, static_cast<RealType>(8*3*3), tol2);
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// std deviation:
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BOOST_CHECK_CLOSE(
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standard_deviation(dist)
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, sqrt(static_cast<RealType>(8*3*3)), tol2);
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// hazard:
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BOOST_CHECK_CLOSE(
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hazard(dist, x)
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, pdf(dist, x) / cdf(complement(dist, x)), tol2);
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// cumulative hazard:
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BOOST_CHECK_CLOSE(
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chf(dist, x)
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, -log(cdf(complement(dist, x))), tol2);
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// coefficient_of_variation:
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BOOST_CHECK_CLOSE(
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coefficient_of_variation(dist)
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, standard_deviation(dist) / mean(dist), tol2);
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// mode:
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BOOST_CHECK_CLOSE(
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mode(dist)
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, static_cast<RealType>(7 * 3), tol2);
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// skewness:
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BOOST_CHECK_CLOSE(
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skewness(dist)
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, 2 / sqrt(static_cast<RealType>(8)), tol2);
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// kertosis:
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BOOST_CHECK_CLOSE(
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kurtosis(dist)
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, 3 + 6 / static_cast<RealType>(8), tol2);
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// kertosis excess:
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BOOST_CHECK_CLOSE(
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kurtosis_excess(dist)
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, 6 / static_cast<RealType>(8), tol2);
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BOOST_CHECK_CLOSE(
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median(dist), static_cast<RealType>(23.007748327502412), // double precision test value
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(std::max)(tol2, static_cast<RealType>(std::numeric_limits<double>::epsilon() * 2 * 100))); // 2 eps as persent
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// Rely on default definition in derived accessors.
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// error tests
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check_out_of_range<boost::math::gamma_distribution<RealType> >(1, 1);
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BOOST_MATH_CHECK_THROW(boost::math::gamma_distribution<RealType>(0, 1), std::domain_error);
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BOOST_MATH_CHECK_THROW(boost::math::gamma_distribution<RealType>(-1, 1), std::domain_error);
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BOOST_MATH_CHECK_THROW(boost::math::gamma_distribution<RealType>(1, 0), std::domain_error);
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BOOST_MATH_CHECK_THROW(boost::math::gamma_distribution<RealType>(1, -1), std::domain_error);
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} // template <class RealType>void test_spots(RealType)
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BOOST_AUTO_TEST_CASE( test_main )
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{
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// Basic sanity-check spot values.
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// (Parameter value, arbitrarily zero, only communicates the floating point type).
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test_spots(0.0F); // Test float. OK at decdigits = 0 tolerance = 0.0001 %
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test_spots(0.0); // Test double. OK at decdigits 7, tolerance = 1e07 %
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#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
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test_spots(0.0L); // Test long double.
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#ifndef BOOST_MATH_NO_REAL_CONCEPT_TESTS
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test_spots(boost::math::concepts::real_concept(0.)); // Test real concept.
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#endif
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#else
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std::cout << "<note>The long double tests have been disabled on this platform "
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"either because the long double overloads of the usual math functions are "
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"not available at all, or because they are too inaccurate for these tests "
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"to pass.</note>" << std::endl;
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#endif
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} // BOOST_AUTO_TEST_CASE( test_main )
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/*
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Output:
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Autorun "i:\boost-06-05-03-1300\libs\math\test\Math_test\debug\test_gamma_dist.exe"
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Running 1 test case...
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Tolerance for type float is 0.000238419 %
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Tolerance for type float is 0.001 %
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Tolerance for type double is 5e-012 %
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Tolerance for type double is 0.001 %
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Tolerance for type long double is 5e-012 %
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Tolerance for type long double is 0.001 %
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Tolerance for type class boost::math::concepts::real_concept is 5e-012 %
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Tolerance for type class boost::math::concepts::real_concept is 0.001 %
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*** No errors detected
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*/
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