test_students_t.cpp

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      ::boost::math::quantile(
         complement(
            students_t_distribution<RealType>(5.),  // degrees_of_freedom
            static_cast<RealType>(0.7))),  // probability.
         static_cast<RealType>(-0.559429644), // t
         tolerance);

   BOOST_CHECK_CLOSE( // Tests of p high.
      ::boost::math::cdf(
         students_t_distribution<RealType>(5.),  // degrees_of_freedom
         static_cast<RealType>(1.475884049)),  // t
         static_cast<RealType>(0.9), // probability.
         tolerance);
   BOOST_CHECK_CLOSE(
      ::boost::math::quantile(
         students_t_distribution<RealType>(5.),  // degrees_of_freedom
         static_cast<RealType>(0.9)),  // probability.
         static_cast<RealType>(1.475884049), // t
         tolerance);

   BOOST_CHECK_CLOSE( // Tests of p low.
      ::boost::math::cdf(
         students_t_distribution<RealType>(5.),  // degrees_of_freedom
         static_cast<RealType>(-1.475884049)),  // t
         static_cast<RealType>(0.1), // probability.
         tolerance);
   BOOST_CHECK_CLOSE(
      ::boost::math::quantile(
         students_t_distribution<RealType>(5.),  // degrees_of_freedom
         static_cast<RealType>(0.1)),  // probability.
         static_cast<RealType>(-1.475884049), // t
         tolerance);

   BOOST_CHECK_CLOSE(
      ::boost::math::cdf(
         students_t_distribution<RealType>(2.),  // degrees_of_freedom
         static_cast<RealType>(-6.96455673428326)),  // t
         static_cast<RealType>(0.01), // probability.
         tolerance);

   BOOST_CHECK_CLOSE(
      ::boost::math::quantile(
         students_t_distribution<RealType>(2.),  // degrees_of_freedom
         static_cast<RealType>(0.01)),  // probability.
         static_cast<RealType>(-6.96455673428326), // t
         tolerance);


  // Student's t pdf tests.
  // for PDF checks, use 100 eps tolerance expressed as a percent:
   tolerance = boost::math::tools::epsilon<RealType>() * 10000;

   for(unsigned i = 1; i < 20; i += 3)
   {
      for(RealType r = -10; r < 10; r += 0.125)
      {
         //std::cout << "df=" << i << " t=" << r << std::endl;
         BOOST_CHECK_CLOSE(
            boost::math::pdf(
               students_t_distribution<RealType>(static_cast<RealType>(i)),
               r),
            naive_pdf<RealType>(static_cast<RealType>(i), r),
            tolerance);
      }
   }

    RealType tol2 = boost::math::tools::epsilon<RealType>() * 5;
    students_t_distribution<RealType> dist(8);
    RealType x = static_cast<RealType>(0.125);
    using namespace std; // ADL of std names.
    // mean:
    BOOST_CHECK_CLOSE(
       mean(dist)
       , static_cast<RealType>(0), tol2);
    // variance:
    BOOST_CHECK_CLOSE(
       variance(dist)
       , static_cast<RealType>(8.0L / 6.0L), tol2);
    // std deviation:
    BOOST_CHECK_CLOSE(
       standard_deviation(dist)
       , static_cast<RealType>(sqrt(8.0L / 6.0L)), tol2);
    // hazard:
    BOOST_CHECK_CLOSE(
       hazard(dist, x)
       , pdf(dist, x) / cdf(complement(dist, x)), tol2);
    // cumulative hazard:
    BOOST_CHECK_CLOSE(
       chf(dist, x)
       , -log(cdf(complement(dist, x))), tol2);
    // coefficient_of_variation:
    BOOST_CHECK_THROW(
       coefficient_of_variation(dist),
       std::overflow_error);
    // mode:
    BOOST_CHECK_CLOSE(
       mean(dist)
       , static_cast<RealType>(0), tol2);
    // median:
    BOOST_CHECK_CLOSE(
       median(dist)
       , static_cast<RealType>(0), tol2);
    // skewness:
    BOOST_CHECK_CLOSE(
       skewness(dist)
       , static_cast<RealType>(0), tol2);
    // kurtosis:
    BOOST_CHECK_CLOSE(
       kurtosis(dist)
       , static_cast<RealType>(4.5), tol2);
    // kurtosis excess:
    BOOST_CHECK_CLOSE(
       kurtosis_excess(dist)
       , static_cast<RealType>(1.5), tol2);

    // Parameter estimation. These results are close to but
    // not identical to those reported on the NIST website at
    // http://www.itl.nist.gov/div898/handbook/prc/section2/prc222.htm
    // the NIST results appear to be calculated using a normal
    // approximation, which slightly under-estimates the degrees of
    // freedom required, particularly when the result is small.
    //
    BOOST_CHECK_EQUAL(
       ceil(students_t_distribution<RealType>::find_degrees_of_freedom(
         static_cast<RealType>(0.5),
         static_cast<RealType>(0.005),
         static_cast<RealType>(0.01),
         static_cast<RealType>(1.0))),
         99);
    BOOST_CHECK_EQUAL(
       ceil(students_t_distribution<RealType>::find_degrees_of_freedom(
         static_cast<RealType>(1.5),
         static_cast<RealType>(0.005),
         static_cast<RealType>(0.01),
         static_cast<RealType>(1.0))),
         14);
    BOOST_CHECK_EQUAL(
       ceil(students_t_distribution<RealType>::find_degrees_of_freedom(
         static_cast<RealType>(0.5),
         static_cast<RealType>(0.025),
         static_cast<RealType>(0.01),
         static_cast<RealType>(1.0))),
         76);
    BOOST_CHECK_EQUAL(
       ceil(students_t_distribution<RealType>::find_degrees_of_freedom(
         static_cast<RealType>(1.5),
         static_cast<RealType>(0.025),
         static_cast<RealType>(0.01),
         static_cast<RealType>(1.0))),
         11);
    BOOST_CHECK_EQUAL(
       ceil(students_t_distribution<RealType>::find_degrees_of_freedom(
         static_cast<RealType>(0.5),
         static_cast<RealType>(0.05),
         static_cast<RealType>(0.01),
         static_cast<RealType>(1.0))),
         65);
    BOOST_CHECK_EQUAL(
       ceil(students_t_distribution<RealType>::find_degrees_of_freedom(
         static_cast<RealType>(1.5),
         static_cast<RealType>(0.05),
         static_cast<RealType>(0.01),
         static_cast<RealType>(1.0))),
         9);

} // template <class RealType>void test_spots(RealType)

int test_main(int, char* [])
{
  // Check that can construct students_t distribution using the two convenience methods:
  using namespace boost::math;
  students_t myst1(2); // Using typedef
   students_t_distribution<> myst2(2); // Using default RealType double.
   //students_t_distribution<double> myst3(2); // Using explicit RealType double.

    // 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* [])

/*

Autorun "i:\boost-06-05-03-1300\libs\math\test\Math_test\debug\test_students_t.exe"
Running 1 test case...
Tolerance for type float is 0.0001 %
Tolerance for type double is 0.0001 %
Tolerance for type long double is 0.0001 %
Tolerance for type class boost::math::concepts::real_concept is 0.0001 %
*** No errors detected

*/