test_cauchy.cpp

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      ::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.