| // Copyright John Maddock 2006, 2007. |
| // Copyright Paul A. Bristow 2007 |
| |
| // 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) |
| |
| // test_cauchy.cpp Test Cauchy distribution |
| |
| #ifdef _MSC_VER |
| # pragma warning(disable: 4100) // unreferenced formal parameter. |
| // Seems an entirely spurious warning - formal parameter T IS used - get error if /* T */ |
| //# pragma warning(disable: 4535) // calling _set_se_translator() requires /EHa (in Boost.test) |
| // Enable C++ Exceptions Yes With SEH Exceptions (/EHa) prevents warning 4535. |
| # pragma warning(disable: 4127) // conditional expression is constant |
| #endif |
| |
| // #define BOOST_MATH_ASSERT_UNDEFINED_POLICY false |
| // To compile even if Cauchy mean is used. |
| |
| #include <boost/math/concepts/real_concept.hpp> // for real_concept |
| #include <boost/math/distributions/cauchy.hpp> |
| using boost::math::cauchy_distribution; |
| |
| #include <boost/test/test_exec_monitor.hpp> // Boost.Test |
| #include <boost/test/floating_point_comparison.hpp> |
| |
| #include <iostream> |
| using std::cout; |
| using std::endl; |
| |
| template <class RealType> |
| void test_spots(RealType T) |
| { |
| // Check some bad parameters to the distribution, |
| BOOST_CHECK_THROW(boost::math::cauchy_distribution<RealType> nbad1(0, 0), std::domain_error); // zero sd |
| BOOST_CHECK_THROW(boost::math::cauchy_distribution<RealType> nbad1(0, -1), std::domain_error); // negative scale (shape) |
| cauchy_distribution<RealType> C01; |
| |
| BOOST_CHECK_EQUAL(C01.location(), 0); // Check standard values. |
| BOOST_CHECK_EQUAL(C01.scale(), 1); |
| |
| // Tests on extreme values of random variate x, if has numeric_limit infinity etc. |
| if(std::numeric_limits<RealType>::has_infinity) |
| { |
| BOOST_CHECK_EQUAL(pdf(C01, +std::numeric_limits<RealType>::infinity()), 0); // x = + infinity, pdf = 0 |
| BOOST_CHECK_EQUAL(pdf(C01, -std::numeric_limits<RealType>::infinity()), 0); // x = - infinity, pdf = 0 |
| BOOST_CHECK_EQUAL(cdf(C01, +std::numeric_limits<RealType>::infinity()), 1); // x = + infinity, cdf = 1 |
| BOOST_CHECK_EQUAL(cdf(C01, -std::numeric_limits<RealType>::infinity()), 0); // x = - infinity, cdf = 0 |
| BOOST_CHECK_EQUAL(cdf(complement(C01, +std::numeric_limits<RealType>::infinity())), 0); // x = + infinity, cdf = 0 |
| BOOST_CHECK_EQUAL(cdf(complement(C01, -std::numeric_limits<RealType>::infinity())), 1); // x = - infinity, cdf = 1 |
| BOOST_CHECK_THROW(boost::math::cauchy_distribution<RealType> nbad1(std::numeric_limits<RealType>::infinity(), static_cast<RealType>(1)), std::domain_error); // +infinite mean |
| BOOST_CHECK_THROW(boost::math::cauchy_distribution<RealType> nbad1(-std::numeric_limits<RealType>::infinity(), static_cast<RealType>(1)), std::domain_error); // -infinite mean |
| BOOST_CHECK_THROW(boost::math::cauchy_distribution<RealType> nbad1(static_cast<RealType>(0), std::numeric_limits<RealType>::infinity()), std::domain_error); // infinite sd |
| } |
| |
| if (std::numeric_limits<RealType>::has_quiet_NaN) |
| { // No longer allow x to be NaN, so these tests should throw. |
| BOOST_CHECK_THROW(pdf(C01, +std::numeric_limits<RealType>::quiet_NaN()), std::domain_error); // x = NaN |
| BOOST_CHECK_THROW(cdf(C01, +std::numeric_limits<RealType>::quiet_NaN()), std::domain_error); // x = NaN |
| BOOST_CHECK_THROW(cdf(complement(C01, +std::numeric_limits<RealType>::quiet_NaN())), std::domain_error); // x = + infinity |
| BOOST_CHECK_THROW(quantile(C01, +std::numeric_limits<RealType>::quiet_NaN()), std::domain_error); // p = + infinity |
| BOOST_CHECK_THROW(quantile(complement(C01, +std::numeric_limits<RealType>::quiet_NaN())), std::domain_error); // p = + infinity |
| } |
| |
| // Basic sanity checks. |
| // 50eps as a percentage, up to a maximum of double precision |
| // (that's the limit of our test data). |
| RealType tolerance = (std::max)( |
| static_cast<RealType>(boost::math::tools::epsilon<double>()), |
| boost::math::tools::epsilon<RealType>()); |
| tolerance *= 50 * 100; |
| |
| cout << "Tolerance for type " << typeid(T).name() << " is " << tolerance << " %" << endl; |
| |
| // These first sets of test values were calculated by punching numbers |
| // into a calculator, and using the formulas on the Mathworld website: |
| // http://mathworld.wolfram.com/CauchyDistribution.html |
| // and values from MathCAD 200 Professional, |
| // CDF: |
| // |
| BOOST_CHECK_CLOSE( |
| ::boost::math::cdf( |
| cauchy_distribution<RealType>(), |
| static_cast<RealType>(0.125)), // x |
| static_cast<RealType>(0.53958342416056554201085167134004L), // probability. |
| tolerance); // % |
| BOOST_CHECK_CLOSE( |
| ::boost::math::cdf( |
| cauchy_distribution<RealType>(), |
| static_cast<RealType>(-0.125)), // x |
| static_cast<RealType>(0.46041657583943445798914832865996L), // probability. |
| tolerance); // % |
| BOOST_CHECK_CLOSE( |
| ::boost::math::cdf( |
| cauchy_distribution<RealType>(), |
| static_cast<RealType>(0.5)), // x |
| static_cast<RealType>(0.64758361765043327417540107622474L), // probability. |
| tolerance); // % |
| BOOST_CHECK_CLOSE( |
| ::boost::math::cdf( |
| cauchy_distribution<RealType>(), |
| static_cast<RealType>(-0.5)), // x |
| static_cast<RealType>(0.35241638234956672582459892377526L), // probability. |
| tolerance); // % |
| BOOST_CHECK_CLOSE( |
| ::boost::math::cdf( |
| cauchy_distribution<RealType>(), |
| static_cast<RealType>(1.0)), // x |
| static_cast<RealType>(0.75), // probability. |
| tolerance); // % |
| BOOST_CHECK_CLOSE( |
| ::boost::math::cdf( |
| cauchy_distribution<RealType>(), |
| static_cast<RealType>(-1.0)), // x |
| static_cast<RealType>(0.25), // probability. |
| tolerance); // % |
| BOOST_CHECK_CLOSE( |
| ::boost::math::cdf( |
| cauchy_distribution<RealType>(), |
| static_cast<RealType>(2.0)), // x |
| static_cast<RealType>(0.85241638234956672582459892377526L), // probability. |
| tolerance); // % |
| BOOST_CHECK_CLOSE( |
| ::boost::math::cdf( |
| cauchy_distribution<RealType>(), |
| static_cast<RealType>(-2.0)), // x |
| static_cast<RealType>(0.14758361765043327417540107622474L), // probability. |
| tolerance); // % |
| BOOST_CHECK_CLOSE( |
| ::boost::math::cdf( |
| cauchy_distribution<RealType>(), |
| static_cast<RealType>(10.0)), // x |
| static_cast<RealType>(0.9682744825694464304850228813987L), // probability. |
| tolerance); // % |
| BOOST_CHECK_CLOSE( |
| ::boost::math::cdf( |
| cauchy_distribution<RealType>(), |
| static_cast<RealType>(-10.0)), // x |
| static_cast<RealType>(0.031725517430553569514977118601302L), // probability. |
| tolerance); // % |
| |
| // |
| // Complements: |
| // |
| BOOST_CHECK_CLOSE( |
| ::boost::math::cdf( |
| complement(cauchy_distribution<RealType>(), |
| static_cast<RealType>(0.125))), // x |
| static_cast<RealType>(0.46041657583943445798914832865996L), // probability. |
| tolerance); // % |
| BOOST_CHECK_CLOSE( |
| ::boost::math::cdf( |
| complement(cauchy_distribution<RealType>(), |
| static_cast<RealType>(-0.125))), // x |
| static_cast<RealType>(0.53958342416056554201085167134004L), // probability. |
| tolerance); // % |
| BOOST_CHECK_CLOSE( |
| ::boost::math::cdf( |
| complement(cauchy_distribution<RealType>(), |
| static_cast<RealType>(0.5))), // x |
| static_cast<RealType>(0.35241638234956672582459892377526L), // probability. |
| tolerance); // % |
| BOOST_CHECK_CLOSE( |
| ::boost::math::cdf( |
| complement(cauchy_distribution<RealType>(), |
| static_cast<RealType>(-0.5))), // x |
| static_cast<RealType>(0.64758361765043327417540107622474L), // probability. |
| tolerance); // % |
| BOOST_CHECK_CLOSE( |
| ::boost::math::cdf( |
| complement(cauchy_distribution<RealType>(), |
| static_cast<RealType>(1.0))), // x |
| static_cast<RealType>(0.25), // probability. |
| tolerance); // % |
| BOOST_CHECK_CLOSE( |
| ::boost::math::cdf( |
| complement(cauchy_distribution<RealType>(), |
| static_cast<RealType>(-1.0))), // x |
| static_cast<RealType>(0.75), // probability. |
| tolerance); // % |
| BOOST_CHECK_CLOSE( |
| ::boost::math::cdf( |
| complement(cauchy_distribution<RealType>(), |
| static_cast<RealType>(2.0))), // x |
| static_cast<RealType>(0.14758361765043327417540107622474L), // probability. |
| tolerance); // % |
| BOOST_CHECK_CLOSE( |
| ::boost::math::cdf( |
| complement(cauchy_distribution<RealType>(), |
| static_cast<RealType>(-2.0))), // x |
| static_cast<RealType>(0.85241638234956672582459892377526L), // probability. |
| tolerance); // % |
| BOOST_CHECK_CLOSE( |
| ::boost::math::cdf( |
| complement(cauchy_distribution<RealType>(), |
| static_cast<RealType>(10.0))), // x |
| static_cast<RealType>(0.031725517430553569514977118601302L), // probability. |
| tolerance); // % |
| BOOST_CHECK_CLOSE( |
| ::boost::math::cdf( |
| complement(cauchy_distribution<RealType>(), |
| static_cast<RealType>(-10.0))), // x |
| static_cast<RealType>(0.9682744825694464304850228813987L), // probability. |
| tolerance); // % |
| |
| // |
| // Quantiles: |
| // |
| BOOST_CHECK_CLOSE( |
| ::boost::math::quantile( |
| cauchy_distribution<RealType>(), |
| static_cast<RealType>(0.53958342416056554201085167134004L)), |
| static_cast<RealType>(0.125), |
| tolerance); // % |
| BOOST_CHECK_CLOSE( |
| ::boost::math::quantile( |
| cauchy_distribution<RealType>(), |
| static_cast<RealType>(0.46041657583943445798914832865996L)), |
| static_cast<RealType>(-0.125), |
| tolerance); // % |
| BOOST_CHECK_CLOSE( |
| ::boost::math::quantile( |
| cauchy_distribution<RealType>(), |
| static_cast<RealType>(0.64758361765043327417540107622474L)), |
| static_cast<RealType>(0.5), |
| tolerance); // % |
| BOOST_CHECK_CLOSE( |
| ::boost::math::quantile( |
| cauchy_distribution<RealType>(), |
| static_cast<RealType>(0.35241638234956672582459892377526)), |
| static_cast<RealType>(-0.5), |
| tolerance); // % |
| BOOST_CHECK_CLOSE( |
| ::boost::math::quantile( |
| cauchy_distribution<RealType>(), |
| static_cast<RealType>(0.75)), |
| static_cast<RealType>(1.0), |
| tolerance); // % |
| BOOST_CHECK_CLOSE( |
| ::boost::math::quantile( |
| cauchy_distribution<RealType>(), |
| static_cast<RealType>(0.25)), |
| static_cast<RealType>(-1.0), |
| tolerance); // % |
| BOOST_CHECK_CLOSE( |
| ::boost::math::quantile( |
| cauchy_distribution<RealType>(), |
| static_cast<RealType>(0.85241638234956672582459892377526L)), |
| static_cast<RealType>(2.0), |
| tolerance); // % |
| BOOST_CHECK_CLOSE( |
| ::boost::math::quantile( |
| cauchy_distribution<RealType>(), |
| static_cast<RealType>(0.14758361765043327417540107622474L)), |
| static_cast<RealType>(-2.0), |
| tolerance); // % |
| BOOST_CHECK_CLOSE( |
| ::boost::math::quantile( |
| cauchy_distribution<RealType>(), |
| static_cast<RealType>(0.9682744825694464304850228813987L)), |
| static_cast<RealType>(10.0), |
| tolerance); // % |
| BOOST_CHECK_CLOSE( |
| ::boost::math::quantile( |
| cauchy_distribution<RealType>(), |
| static_cast<RealType>(0.031725517430553569514977118601302L)), |
| static_cast<RealType>(-10.0), |
| tolerance); // % |
| |
| // |
| // Quantile from complement: |
| // |
| BOOST_CHECK_CLOSE( |
| ::boost::math::quantile( |
| complement(cauchy_distribution<RealType>(), |
| static_cast<RealType>(0.46041657583943445798914832865996L))), |
| static_cast<RealType>(0.125), |
| tolerance); // % |
| BOOST_CHECK_CLOSE( |
| ::boost::math::quantile( |
| complement(cauchy_distribution<RealType>(), |
| static_cast<RealType>(0.53958342416056554201085167134004L))), |
| static_cast<RealType>(-0.125), |
| tolerance); // % |
| BOOST_CHECK_CLOSE( |
| ::boost::math::quantile( |
| complement(cauchy_distribution<RealType>(), |
| static_cast<RealType>(0.35241638234956672582459892377526L))), |
| static_cast<RealType>(0.5), |
| tolerance); // % |
| BOOST_CHECK_CLOSE( |
| ::boost::math::quantile( |
| complement(cauchy_distribution<RealType>(), |
| static_cast<RealType>(0.64758361765043327417540107622474L))), |
| static_cast<RealType>(-0.5), |
| tolerance); // % |
| BOOST_CHECK_CLOSE( |
| ::boost::math::quantile( |
| complement(cauchy_distribution<RealType>(), |
| static_cast<RealType>(0.25))), |
| static_cast<RealType>(1.0), |
| tolerance); // % |
| BOOST_CHECK_CLOSE( |
| ::boost::math::quantile( |
| complement(cauchy_distribution<RealType>(), |
| static_cast<RealType>(0.75))), |
| static_cast<RealType>(-1.0), |
| tolerance); // % |
| BOOST_CHECK_CLOSE( |
| ::boost::math::quantile( |
| complement(cauchy_distribution<RealType>(), |
| static_cast<RealType>(0.14758361765043327417540107622474L))), |
| static_cast<RealType>(2.0), |
| tolerance); // % |
| BOOST_CHECK_CLOSE( |
| ::boost::math::quantile( |
| complement(cauchy_distribution<RealType>(), |
| static_cast<RealType>(0.85241638234956672582459892377526L))), |
| static_cast<RealType>(-2.0), |
| tolerance); // % |
| BOOST_CHECK_CLOSE( |
| ::boost::math::quantile( |
| complement(cauchy_distribution<RealType>(), |
| static_cast<RealType>(0.031725517430553569514977118601302L))), |
| static_cast<RealType>(10.0), |
| tolerance); // % |
| BOOST_CHECK_CLOSE( |
| ::boost::math::quantile( |
| complement(cauchy_distribution<RealType>(), |
| static_cast<RealType>(0.9682744825694464304850228813987L))), |
| static_cast<RealType>(-10.0), |
| tolerance); // % |
| |
| // |
| // PDF |
| // |
| BOOST_CHECK_CLOSE( |
| ::boost::math::pdf( |
| cauchy_distribution<RealType>(), |
| static_cast<RealType>(0.125)), // x |
| static_cast<RealType>(0.31341281101173235351410956479511L), // probability. |
| tolerance); // % |
| BOOST_CHECK_CLOSE( |
| ::boost::math::pdf( |
| cauchy_distribution<RealType>(), |
| static_cast<RealType>(-0.125)), // x |
| static_cast<RealType>(0.31341281101173235351410956479511L), // probability. |
| tolerance); // % |
| BOOST_CHECK_CLOSE( |
| ::boost::math::pdf( |
| cauchy_distribution<RealType>(), |
| static_cast<RealType>(0.5)), // x |
| static_cast<RealType>(0.25464790894703253723021402139602L), // probability. |
| tolerance); // % |
| BOOST_CHECK_CLOSE( |
| ::boost::math::pdf( |
| cauchy_distribution<RealType>(), |
| static_cast<RealType>(-0.5)), // x |
| static_cast<RealType>(0.25464790894703253723021402139602L), // probability. |
| tolerance); // % |
| BOOST_CHECK_CLOSE( |
| ::boost::math::pdf( |
| cauchy_distribution<RealType>(), |
| static_cast<RealType>(1.0)), // x |
| static_cast<RealType>(0.15915494309189533576888376337251L), // probability. |
| tolerance); // % |
| BOOST_CHECK_CLOSE( |
| ::boost::math::pdf( |
| cauchy_distribution<RealType>(), |
| static_cast<RealType>(-1.0)), // x |
| static_cast<RealType>(0.15915494309189533576888376337251L), // probability. |
| tolerance); // % |
| BOOST_CHECK_CLOSE( |
| ::boost::math::pdf( |
| cauchy_distribution<RealType>(), |
| static_cast<RealType>(2.0)), // x |
| static_cast<RealType>(0.063661977236758134307553505349006L), // probability. |
| tolerance); // % |
| BOOST_CHECK_CLOSE( |
| ::boost::math::pdf( |
| cauchy_distribution<RealType>(), |
| static_cast<RealType>(-2.0)), // x |
| static_cast<RealType>(0.063661977236758134307553505349006L), // probability. |
| tolerance); // % |
| BOOST_CHECK_CLOSE( |
| ::boost::math::pdf( |
| cauchy_distribution<RealType>(), |
| static_cast<RealType>(10.0)), // x |
| static_cast<RealType>(0.0031515830315226799162155200667825L), // probability. |
| tolerance); // % |
| BOOST_CHECK_CLOSE( |
| ::boost::math::pdf( |
| cauchy_distribution<RealType>(), |
| static_cast<RealType>(-10.0)), // x |
| static_cast<RealType>(0.0031515830315226799162155200667825L), // probability. |
| tolerance); // % |
| BOOST_CHECK_CLOSE( |
| ::boost::math::pdf( |
| cauchy_distribution<RealType>(2, 5), |
| static_cast<RealType>(1)), // x |
| static_cast<RealType>(0.061213439650728975295724524374044L), // probability. |
| tolerance); // % |
| BOOST_CHECK_CLOSE( |
| ::boost::math::pdf( |
| cauchy_distribution<RealType>(-2, 0.25), |
| static_cast<RealType>(1)), // x |
| static_cast<RealType>(0.0087809623774838805941453110826215L), // probability. |
| tolerance); // % |
| |
| // |
| // The following test values were calculated using MathCad, |
| // precision seems to be about 10^-13. |
| // |
| tolerance = (std::max)(tolerance, static_cast<RealType>(1e-11)); |
| BOOST_CHECK_CLOSE( |
| ::boost::math::cdf( |
| cauchy_distribution<RealType>(1, 1), |
| static_cast<RealType>(0.125)), // x |
| static_cast<RealType>(0.271189304634946L), // probability. |
| tolerance); // % |
| BOOST_CHECK_CLOSE( |
| ::boost::math::cdf( |
| complement(cauchy_distribution<RealType>(1, 1), |
| static_cast<RealType>(0.125))), // x |
| static_cast<RealType>(1 - 0.271189304634946L), // probability. |
| tolerance); // % |
| BOOST_CHECK_CLOSE( |
| ::boost::math::quantile( |
| cauchy_distribution<RealType>(1, 1), |
| static_cast<RealType>(0.271189304634946L)), // x |
| static_cast<RealType>(0.125), // probability. |
| tolerance); // % |
| BOOST_CHECK_CLOSE( |
| ::boost::math::quantile( |
| complement(cauchy_distribution<RealType>(1, 1), |
| static_cast<RealType>(1 - 0.271189304634946L))), // x |
| static_cast<RealType>(0.125), // probability. |
| tolerance); // % |
| BOOST_CHECK_CLOSE( |
| ::boost::math::cdf( |
| cauchy_distribution<RealType>(0, 1), |
| static_cast<RealType>(0.125)), // x |
| static_cast<RealType>(0.539583424160566L), // probability. |
| tolerance); // % |
| BOOST_CHECK_CLOSE( |
| ::boost::math::cdf( |
| cauchy_distribution<RealType>(0, 1), |
| static_cast<RealType>(0.5)), // x |
| static_cast<RealType>(0.647583617650433L), // probability. |
| tolerance); // % |
| BOOST_CHECK_CLOSE( |
| ::boost::math::cdf( |
| cauchy_distribution<RealType>(0, 1), |
| static_cast<RealType>(1)), // x |
| static_cast<RealType>(0.750000000000000), // probability. |
| tolerance); // % |
| BOOST_CHECK_CLOSE( |
| ::boost::math::cdf( |
| cauchy_distribution<RealType>(0, 1), |
| static_cast<RealType>(2)), // x |
| static_cast<RealType>(0.852416382349567), // probability. |
| tolerance); // % |
| BOOST_CHECK_CLOSE( |
| ::boost::math::cdf( |
| cauchy_distribution<RealType>(0, 1), |
| static_cast<RealType>(10)), // x |
| static_cast<RealType>(0.968274482569447), // probability. |
| tolerance); // % |
| BOOST_CHECK_CLOSE( |
| ::boost::math::cdf( |
| cauchy_distribution<RealType>(0, 1), |
| static_cast<RealType>(100)), // x |
| static_cast<RealType>(0.996817007235092), // probability. |
| tolerance); // % |
| |
| BOOST_CHECK_CLOSE( |
| ::boost::math::cdf( |
| cauchy_distribution<RealType>(0, 1), |
| static_cast<RealType>(-0.125)), // x |
| static_cast<RealType>(0.460416575839434), // probability. |
| tolerance); // % |
| BOOST_CHECK_CLOSE( |
| ::boost::math::cdf( |
| cauchy_distribution<RealType>(0, 1), |
| static_cast<RealType>(-0.5)), // x |
| static_cast<RealType>(0.352416382349567), // probability. |
| tolerance); // % |
| BOOST_CHECK_CLOSE( |
| ::boost::math::cdf( |
| cauchy_distribution<RealType>(0, 1), |
| static_cast<RealType>(-1)), // x |
| static_cast<RealType>(0.2500000000000000), // probability. |
| tolerance); // % |
| BOOST_CHECK_CLOSE( |
| ::boost::math::cdf( |
| cauchy_distribution<RealType>(0, 1), |
| static_cast<RealType>(-2)), // x |
| static_cast<RealType>(0.147583617650433), // probability. |
| tolerance); // % |
| BOOST_CHECK_CLOSE( |
| ::boost::math::cdf( |
| cauchy_distribution<RealType>(0, 1), |
| static_cast<RealType>(-10)), // x |
| static_cast<RealType>(0.031725517430554), // probability. |
| tolerance); // % |
| BOOST_CHECK_CLOSE( |
| ::boost::math::cdf( |
| cauchy_distribution<RealType>(0, 1), |
| static_cast<RealType>(-100)), // x |
| static_cast<RealType>(3.18299276490824E-3), // probability. |
| tolerance); // % |
| |
| BOOST_CHECK_CLOSE( |
| ::boost::math::cdf( |
| cauchy_distribution<RealType>(1, 5), |
| static_cast<RealType>(1.25)), // x |
| static_cast<RealType>(0.515902251256176), // probability. |
| tolerance); // % |
| BOOST_CHECK_CLOSE( |
| ::boost::math::cdf( |
| cauchy_distribution<RealType>(2, 2), |
| static_cast<RealType>(1.25)), // x |
| static_cast<RealType>(0.385799748780092), // probability. |
| tolerance); // % |
| BOOST_CHECK_CLOSE( |
| ::boost::math::cdf( |
| cauchy_distribution<RealType>(4, 0.125), |
| static_cast<RealType>(3)), // x |
| static_cast<RealType>(0.039583424160566), // probability. |
| tolerance); // % |
| BOOST_CHECK_CLOSE( |
| ::boost::math::cdf( |
| cauchy_distribution<RealType>(-2, static_cast<RealType>(0.0001)), |
| static_cast<RealType>(-3)), // x |
| static_cast<RealType>(3.1830988512275777e-5), // probability. |
| tolerance); // % |
| BOOST_CHECK_CLOSE( |
| ::boost::math::cdf( |
| cauchy_distribution<RealType>(4, 50), |
| static_cast<RealType>(-3)), // x |
| static_cast<RealType>(0.455724386698215), // probability. |
| tolerance); // % |
| BOOST_CHECK_CLOSE( |
| ::boost::math::cdf( |
| cauchy_distribution<RealType>(-4, 50), |
| static_cast<RealType>(-3)), // x |
| static_cast<RealType>(0.506365349100973), // probability. |
| tolerance); // % |
| |
| BOOST_CHECK_CLOSE( |
| ::boost::math::cdf( |
| complement(cauchy_distribution<RealType>(1, 5), |
| static_cast<RealType>(1.25))), // x |
| static_cast<RealType>(1-0.515902251256176), // probability. |
| tolerance); // % |
| BOOST_CHECK_CLOSE( |
| ::boost::math::cdf( |
| complement(cauchy_distribution<RealType>(2, 2), |
| static_cast<RealType>(1.25))), // x |
| static_cast<RealType>(1-0.385799748780092), // probability. |
| tolerance); // % |
| BOOST_CHECK_CLOSE( |
| ::boost::math::cdf( |
| complement(cauchy_distribution<RealType>(4, 0.125), |
| static_cast<RealType>(3))), // x |
| static_cast<RealType>(1-0.039583424160566), // probability. |
| tolerance); // % |
| BOOST_CHECK_CLOSE( |
| ::boost::math::cdf( |
| cauchy_distribution<RealType>(-2, static_cast<RealType>(0.001)), |
| static_cast<RealType>(-3)), // x |
| static_cast<RealType>(0.000318309780080539), // probability. |
| tolerance); // % |
| BOOST_CHECK_CLOSE( |
| ::boost::math::cdf( |
| complement(cauchy_distribution<RealType>(4, 50), |
| static_cast<RealType>(-3))), // x |
| static_cast<RealType>(1-0.455724386698215), // probability. |
| tolerance); // % |
| BOOST_CHECK_CLOSE( |
| ::boost::math::cdf( |
| complement(cauchy_distribution<RealType>(-4, 50), |
| static_cast<RealType>(-3))), // x |
| static_cast<RealType>(1-0.506365349100973), // probability. |
| tolerance); // % |
| |
| BOOST_CHECK_CLOSE( |
| ::boost::math::quantile( |
| cauchy_distribution<RealType>(1, 5), |
| static_cast<RealType>(0.515902251256176)), // x |
| static_cast<RealType>(1.25), // probability. |
| tolerance); // % |
| BOOST_CHECK_CLOSE( |
| ::boost::math::quantile( |
| cauchy_distribution<RealType>(2, 2), |
| static_cast<RealType>(0.385799748780092)), // x |
| static_cast<RealType>(1.25), // probability. |
| tolerance); // % |
| BOOST_CHECK_CLOSE( |
| ::boost::math::quantile( |
| cauchy_distribution<RealType>(4, 0.125), |
| static_cast<RealType>(0.039583424160566)), // x |
| static_cast<RealType>(3), // probability. |
| tolerance); // % |
| /* |
| BOOST_CHECK_CLOSE( |
| ::boost::math::quantile( |
| cauchy_distribution<RealType>(-2, 0.0001), |
| static_cast<RealType>(-3)), // x |
| static_cast<RealType>(0.000015915494296), // probability. |
| tolerance); // % |
| */ |
| BOOST_CHECK_CLOSE( |
| ::boost::math::quantile( |
| cauchy_distribution<RealType>(4, 50), |
| static_cast<RealType>(0.455724386698215)), // x |
| static_cast<RealType>(-3), // probability. |
| tolerance); // % |
| BOOST_CHECK_CLOSE( |
| ::boost::math::quantile( |
| cauchy_distribution<RealType>(-4, 50), |
| static_cast<RealType>(0.506365349100973)), // x |
| static_cast<RealType>(-3), // probability. |
| tolerance); // % |
| |
| BOOST_CHECK_CLOSE( |
| ::boost::math::quantile( |
| complement(cauchy_distribution<RealType>(1, 5), |
| static_cast<RealType>(1-0.515902251256176))), // x |
| static_cast<RealType>(1.25), // probability. |
| tolerance); // % |
| BOOST_CHECK_CLOSE( |
| ::boost::math::quantile( |
| complement(cauchy_distribution<RealType>(2, 2), |
| static_cast<RealType>(1-0.385799748780092))), // x |
| static_cast<RealType>(1.25), // probability. |
| tolerance); // % |
| BOOST_CHECK_CLOSE( |
| ::boost::math::quantile( |
| complement(cauchy_distribution<RealType>(4, 0.125), |
| static_cast<RealType>(1-0.039583424160566))), // x |
| static_cast<RealType>(3), // probability. |
| tolerance); // % |
| /* |
| BOOST_CHECK_CLOSE( |
| ::boost::math::quantile( |
| cauchy_distribution<RealType>(-2, 0.0001), |
| static_cast<RealType>(-3)), // x |
| static_cast<RealType>(0.000015915494296), // probability. |
| tolerance); // % |
| */ |
| BOOST_CHECK_CLOSE( |
| ::boost::math::quantile( |
| complement(cauchy_distribution<RealType>(4, 50), |
| static_cast<RealType>(1-0.455724386698215))), // x |
| static_cast<RealType>(-3), // probability. |
| tolerance); // % |
| BOOST_CHECK_CLOSE( |
| ::boost::math::quantile( |
| complement(cauchy_distribution<RealType>(-4, 50), |
| static_cast<RealType>(1-0.506365349100973))), // x |
| static_cast<RealType>(-3), // probability. |
| tolerance); // % |
| |
| cauchy_distribution<RealType> dist; // default (0, 1) |
| BOOST_CHECK_EQUAL( |
| mode(dist), |
| static_cast<RealType>(0)); |
| BOOST_CHECK_EQUAL( |
| median(dist), |
| static_cast<RealType>(0)); |
| // |
| // Things that now don't compile (BOOST-STATIC_ASSERT_FAILURE) by default. |
| // #define BOOST_MATH_ASSERT_UNDEFINED_POLICY false |
| // To compile even if Cauchy mean is used. |
| // See policy reference, mathematically undefined function policies |
| // |
| //BOOST_CHECK_THROW( |
| // mean(dist), |
| // std::domain_error); |
| //BOOST_CHECK_THROW( |
| // variance(dist), |
| // std::domain_error); |
| //BOOST_CHECK_THROW( |
| // standard_deviation(dist), |
| // std::domain_error); |
| //BOOST_CHECK_THROW( |
| // kurtosis(dist), |
| // std::domain_error); |
| //BOOST_CHECK_THROW( |
| // kurtosis_excess(dist), |
| // std::domain_error); |
| //BOOST_CHECK_THROW( |
| // skewness(dist), |
| // std::domain_error); |
| |
| BOOST_CHECK_THROW( |
| quantile(dist, RealType(0.0)), |
| std::overflow_error); |
| BOOST_CHECK_THROW( |
| quantile(dist, RealType(1.0)), |
| std::overflow_error); |
| BOOST_CHECK_THROW( |
| quantile(complement(dist, RealType(0.0))), |
| std::overflow_error); |
| BOOST_CHECK_THROW( |
| quantile(complement(dist, RealType(1.0))), |
| std::overflow_error); |
| |
| |
| } // template <class RealType>void test_spots(RealType) |
| |
| int test_main(int, char* []) |
| { |
| BOOST_MATH_CONTROL_FP; |
| // Check that can generate cauchy distribution using the two convenience methods: |
| boost::math::cauchy mycd1(1.); // Using typedef |
| cauchy_distribution<> mycd2(1.); // Using default RealType double. |
| cauchy_distribution<> C01; // Using default RealType double for Standard Cauchy. |
| BOOST_CHECK_EQUAL(C01.location(), 0); // Check standard values. |
| BOOST_CHECK_EQUAL(C01.scale(), 1); |
| |
| // Basic sanity-check spot values. |
| // (Parameter value, arbitrarily zero, only communicates the floating point type). |
| test_spots(0.0F); // Test float. OK at decdigits = 0 tolerance = 0.0001 % |
| test_spots(0.0); // Test double. OK at decdigits 7, tolerance = 1e07 % |
| #ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS |
| test_spots(0.0L); // Test long double. |
| #if !BOOST_WORKAROUND(__BORLANDC__, BOOST_TESTED_AT(0x582)) |
| test_spots(boost::math::concepts::real_concept(0.)); // Test real concept. |
| #endif |
| #else |
| std::cout << "<note>The long double tests have been disabled on this platform " |
| "either because the long double overloads of the usual math functions are " |
| "not available at all, or because they are too inaccurate for these tests " |
| "to pass.</note>" << std::cout; |
| #endif |
| |
| return 0; |
| } // int test_main(int, char* []) |
| |
| |
| /* |
| Output: |
| |
| Running 1 test case... |
| Tolerance for type float is 0.000596046 % |
| Tolerance for type double is 1.11022e-012 % |
| Tolerance for type long double is 1.11022e-012 % |
| Tolerance for type class boost::math::concepts::real_concept is 1.11022e-012 % |
| *** No errors detected |
| |
| |
| */ |
