text: // Copyright Paul A. Bristow 2012.
  // Copyright John Maddock 2012.
  // Copyright Benjamin Sobotta 2012
  
  // 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)
  
  #ifdef _MSC_VER
  #  pragma warning (disable : 4127) // conditional expression is constant.
  #  pragma warning (disable : 4305) // 'initializing' : truncation from 'double' to 'const float'.
  #  pragma warning (disable : 4310) // cast truncates constant value.
  #  pragma warning (disable : 4512) // assignment operator could not be generated.
  #endif
  
  //#include <pch.hpp> // include directory libs/math/src/tr1/ is needed.
  
  #include <boost/math/concepts/real_concept.hpp> // for real_concept
  #include <boost/test/test_exec_monitor.hpp> // Boost.Test
  #include <boost/test/floating_point_comparison.hpp>
  
  #include <boost/math/distributions/skew_normal.hpp>
  using boost::math::skew_normal_distribution;
  using boost::math::skew_normal;
  
  #include <iostream>
  using std::cout;
  using std::endl;
  using std::setprecision;
  #include <limits>
  using std::numeric_limits;
  #include "test_out_of_range.hpp"
  
  template <class RealType>
  void check_skew_normal(RealType mean, RealType scale, RealType shape, RealType x, RealType p, RealType q, RealType tol)
  {
   using boost::math::skew_normal_distribution;
  
    BOOST_CHECK_CLOSE_FRACTION(
      ::boost::math::cdf(   // Check cdf
      skew_normal_distribution<RealType>(mean, scale, shape),      // distribution.
      x),    // random variable.
      p,     // probability.
      tol);   // tolerance.
    BOOST_CHECK_CLOSE_FRACTION(
      ::boost::math::cdf( // Check cdf complement
      complement( 
      skew_normal_distribution<RealType>(mean, scale, shape),   // distribution.
      x)),   // random variable.
      q,      // probability complement.
      tol);    // %tolerance.
    BOOST_CHECK_CLOSE_FRACTION(
      ::boost::math::quantile( // Check quantile
      skew_normal_distribution<RealType>(mean, scale, shape),    // distribution.
      p),   // probability.
      x,   // random variable.
      tol);   // tolerance.
    BOOST_CHECK_CLOSE_FRACTION(
      ::boost::math::quantile( // Check quantile complement
      complement(
      skew_normal_distribution<RealType>(mean, scale, shape),   // distribution.
      q)),   // probability complement.
      x,     // random variable.
      tol);  // tolerance.
  
     skew_normal_distribution<RealType> dist (mean, scale, shape);
  
     if((p < 0.999) && (q < 0.999))
     {  // We can only check this if P is not too close to 1,
        // so that we can guarantee Q is accurate:
        BOOST_CHECK_CLOSE_FRACTION(
          cdf(complement(dist, x)), q, tol); // 1 - cdf
        BOOST_CHECK_CLOSE_FRACTION(
          quantile(dist, p), x, tol); // quantile(cdf) = x
        BOOST_CHECK_CLOSE_FRACTION(
          quantile(complement(dist, q)), x, tol); // quantile(complement(1 - cdf)) = x
     }
  } // template <class RealType>void check_skew_normal()
  
  
  template <class RealType>
  void test_spots(RealType)
  {
     // Basic sanity checks
     RealType tolerance = 1e-4f; // 1e-4 (as %)
  
    // Check some bad parameters to the distribution,
  
     BOOST_CHECK_THROW(boost::math::skew_normal_distribution<RealType> nbad1(0, 0), std::domain_error); // zero sd
     BOOST_CHECK_THROW(boost::math::skew_normal_distribution<RealType> nbad1(0, -1), std::domain_error); // negative sd
  
    // Tests on extreme values of random variate x, if has numeric_limit infinity etc.
      skew_normal_distribution<RealType> N01;
    if(std::numeric_limits<RealType>::has_infinity)
    {
      BOOST_CHECK_EQUAL(pdf(N01, +std::numeric_limits<RealType>::infinity()), 0); // x = + infinity, pdf = 0
      BOOST_CHECK_EQUAL(pdf(N01, -std::numeric_limits<RealType>::infinity()), 0); // x = - infinity, pdf = 0
      BOOST_CHECK_EQUAL(cdf(N01, +std::numeric_limits<RealType>::infinity()), 1); // x = + infinity, cdf = 1
      BOOST_CHECK_EQUAL(cdf(N01, -std::numeric_limits<RealType>::infinity()), 0); // x = - infinity, cdf = 0
      BOOST_CHECK_EQUAL(cdf(complement(N01, +std::numeric_limits<RealType>::infinity())), 0); // x = + infinity, c cdf = 0
      BOOST_CHECK_EQUAL(cdf(complement(N01, -std::numeric_limits<RealType>::infinity())), 1); // x = - infinity, c cdf = 1
      BOOST_CHECK_THROW(boost::math::skew_normal_distribution<RealType> nbad1(std::numeric_limits<RealType>::infinity(), static_cast<RealType>(1)), std::domain_error); // +infinite mean
      BOOST_CHECK_THROW(boost::math::skew_normal_distribution<RealType> nbad1(-std::numeric_limits<RealType>::infinity(),  static_cast<RealType>(1)), std::domain_error); // -infinite mean
      BOOST_CHECK_THROW(boost::math::skew_normal_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, then these tests should throw.
      BOOST_CHECK_THROW(pdf(N01, +std::numeric_limits<RealType>::quiet_NaN()), std::domain_error); // x = NaN
      BOOST_CHECK_THROW(cdf(N01, +std::numeric_limits<RealType>::quiet_NaN()), std::domain_error); // x = NaN
      BOOST_CHECK_THROW(cdf(complement(N01, +std::numeric_limits<RealType>::quiet_NaN())), std::domain_error); // x = + infinity
      BOOST_CHECK_THROW(quantile(N01, +std::numeric_limits<RealType>::quiet_NaN()), std::domain_error); // p = + infinity
      BOOST_CHECK_THROW(quantile(complement(N01, +std::numeric_limits<RealType>::quiet_NaN())), std::domain_error); // p = + infinity
    }
  
     cout << "Tolerance for type " << typeid(RealType).name()  << " is " << tolerance << " %" << endl;
  
     // Tests where shape = 0, so same as normal tests.
     // (These might be removed later).
     check_skew_normal(
        static_cast<RealType>(5),
        static_cast<RealType>(2),
        static_cast<RealType>(0),
        static_cast<RealType>(4.8),
        static_cast<RealType>(0.46017),
        static_cast<RealType>(1 - 0.46017),
        tolerance);
  
     check_skew_normal(
        static_cast<RealType>(5),
        static_cast<RealType>(2),
        static_cast<RealType>(0),
        static_cast<RealType>(5.2),
        static_cast<RealType>(1 - 0.46017),
        static_cast<RealType>(0.46017),
        tolerance);
  
     check_skew_normal(
        static_cast<RealType>(5),
        static_cast<RealType>(2),
        static_cast<RealType>(0),
        static_cast<RealType>(2.2),
        static_cast<RealType>(0.08076),
        static_cast<RealType>(1 - 0.08076),
        tolerance);
  
     check_skew_normal(
        static_cast<RealType>(5),
        static_cast<RealType>(2),
        static_cast<RealType>(0),
        static_cast<RealType>(7.8),
        static_cast<RealType>(1 - 0.08076),
        static_cast<RealType>(0.08076),
        tolerance);
  
     check_skew_normal(
        static_cast<RealType>(-3),
        static_cast<RealType>(5),
        static_cast<RealType>(0),
        static_cast<RealType>(-4.5),
        static_cast<RealType>(0.38209),
        static_cast<RealType>(1 - 0.38209),
        tolerance);
  
     check_skew_normal(
        static_cast<RealType>(-3),
        static_cast<RealType>(5),
        static_cast<RealType>(0),
        static_cast<RealType>(-1.5),
        static_cast<RealType>(1 - 0.38209),
        static_cast<RealType>(0.38209),
        tolerance);
  
     check_skew_normal(
        static_cast<RealType>(-3),
        static_cast<RealType>(5),
        static_cast<RealType>(0),
        static_cast<RealType>(-8.5),
        static_cast<RealType>(0.13567),
        static_cast<RealType>(1 - 0.13567),
        tolerance);
  
     check_skew_normal(
        static_cast<RealType>(-3),
        static_cast<RealType>(5),
        static_cast<RealType>(0),
        static_cast<RealType>(2.5),
        static_cast<RealType>(1 - 0.13567),
        static_cast<RealType>(0.13567),
        tolerance);
  
     // Tests where shape != 0, specific to skew_normal distribution.
     //void check_skew_normal(RealType mean, RealType scale, RealType shape, RealType x, RealType p, RealType q, RealType tol)
        check_skew_normal( // 1st R example.
        static_cast<RealType>(1.1),
        static_cast<RealType>(2.2),
        static_cast<RealType>(-3.3),
        static_cast<RealType>(0.4), // x
        static_cast<RealType>(0.733918618927874), // p == psn
        static_cast<RealType>(1 - 0.733918618927874), // q 
        tolerance);
  
     // Not sure about these yet.
        //check_skew_normal( // 2nd R example.
        //static_cast<RealType>(1.1),
        //static_cast<RealType>(0.02),
        //static_cast<RealType>(0.03),
        //static_cast<RealType>(1.3), // x
        //static_cast<RealType>(0.01), // p
        //static_cast<RealType>(0.09), // q
        //tolerance);
        //check_skew_normal( // 3nd R example.
        //static_cast<RealType>(10.1),
        //static_cast<RealType>(5.),
        //static_cast<RealType>(-0.03),
        //static_cast<RealType>(-1.3), // x
        //static_cast<RealType>(0.01201290665838824), // p
        //static_cast<RealType>(1. - 0.01201290665838824), // q 0.987987101
        //tolerance);
  
      // Tests for PDF: we know that the normal peak value is at 1/sqrt(2*pi)
     //
     tolerance = boost::math::tools::epsilon<RealType>() * 5; // 5 eps as a fraction
     BOOST_CHECK_CLOSE_FRACTION(
        pdf(skew_normal_distribution<RealType>(), static_cast<RealType>(0)),
        static_cast<RealType>(0.3989422804014326779399460599343818684759L), // 1/sqrt(2*pi)
        tolerance);
     BOOST_CHECK_CLOSE_FRACTION(
        pdf(skew_normal_distribution<RealType>(3), static_cast<RealType>(3)),
        static_cast<RealType>(0.3989422804014326779399460599343818684759L),
        tolerance);
     BOOST_CHECK_CLOSE_FRACTION(
        pdf(skew_normal_distribution<RealType>(3, 5), static_cast<RealType>(3)),
        static_cast<RealType>(0.3989422804014326779399460599343818684759L / 5),
        tolerance);
  
     // Shape != 0.
     BOOST_CHECK_CLOSE_FRACTION(
        pdf(skew_normal_distribution<RealType>(3,5,1e-6), static_cast<RealType>(3)),
        static_cast<RealType>(0.3989422804014326779399460599343818684759L / 5),
        tolerance);
  
  
     // Checks on mean, variance cumulants etc.
     // Checks on shape ==0
  
      RealType tol5 = boost::math::tools::epsilon<RealType>() * 5;
      skew_normal_distribution<RealType> dist(8, 3);
      RealType x = static_cast<RealType>(0.125);
  
      BOOST_MATH_STD_USING // ADL of std math lib names
  
      // mean:
      BOOST_CHECK_CLOSE(
         mean(dist)
         , static_cast<RealType>(8), tol5);
      // variance:
      BOOST_CHECK_CLOSE(
         variance(dist)
         , static_cast<RealType>(9), tol5);
      // std deviation:
      BOOST_CHECK_CLOSE(
         standard_deviation(dist)
         , static_cast<RealType>(3), tol5);
      // hazard:
      BOOST_CHECK_CLOSE(
         hazard(dist, x)
         , pdf(dist, x) / cdf(complement(dist, x)), tol5);
      // cumulative hazard:
      BOOST_CHECK_CLOSE(
         chf(dist, x)
         , -log(cdf(complement(dist, x))), tol5);
      // coefficient_of_variation:
      BOOST_CHECK_CLOSE(
         coefficient_of_variation(dist)
         , standard_deviation(dist) / mean(dist), tol5);
      // mode: 
      BOOST_CHECK_CLOSE_FRACTION(mode(dist), static_cast<RealType>(8), 0.001);
  
      BOOST_CHECK_CLOSE(
         median(dist)
         , static_cast<RealType>(8), tol5);
  
      // skewness:
      BOOST_CHECK_CLOSE(
         skewness(dist)
         , static_cast<RealType>(0), tol5);
      // kurtosis:
      BOOST_CHECK_CLOSE(
         kurtosis(dist)
         , static_cast<RealType>(3), tol5);
      // kurtosis excess:
      BOOST_CHECK_CLOSE(
         kurtosis_excess(dist)
         , static_cast<RealType>(0), tol5);
  
      skew_normal_distribution<RealType> norm01(0, 1); // Test default (0, 1)
      BOOST_CHECK_CLOSE(
         mean(norm01),
         static_cast<RealType>(0), 0); // Mean == zero
  
      skew_normal_distribution<RealType> defsd_norm01(0); // Test default (0, sd = 1)
      BOOST_CHECK_CLOSE(
         mean(defsd_norm01),
         static_cast<RealType>(0), 0); // Mean == zero
  
      skew_normal_distribution<RealType> def_norm01; // Test default (0, sd = 1)
      BOOST_CHECK_CLOSE(
         mean(def_norm01),
         static_cast<RealType>(0), 0); // Mean == zero
  
      BOOST_CHECK_CLOSE(
         standard_deviation(def_norm01),
         static_cast<RealType>(1), 0);  // 
  
      BOOST_CHECK_CLOSE(
         mode(def_norm01),
         static_cast<RealType>(0), 0); // Mode == zero
  
  
      // Skew_normal tests with shape != 0.
      {
        //RealType tol5 = boost::math::tools::epsilon<RealType>() * 5;
        RealType tol100 = boost::math::tools::epsilon<RealType>() * 100;
        RealType tol1000 = boost::math::tools::epsilon<RealType>() * 1000;
  
        //skew_normal_distribution<RealType> dist(1.1, 0.02, 0.03);
  
        BOOST_MATH_STD_USING // ADL of std math lib names.
  
        // Test values from R = see skew_normal_drv.cpp which included the R code used.
        {
          skew_normal_distribution<RealType> dist(static_cast<RealType>(1.1l), static_cast<RealType>(2.2l), static_cast<RealType>(-3.3l));
  
          BOOST_CHECK_CLOSE(      // mean:
             mean(dist)
             , static_cast<RealType>(-0.579908992539856825862549L), tol100);
           BOOST_CHECK_CLOSE(      // variance:
            variance(dist)
            , static_cast<RealType>(2.0179057767837232633904L), tol100);
  
          BOOST_CHECK_CLOSE(      // skewness:
             skewness(dist)
             , static_cast<RealType>(-0.709854548171537509192897824663L), tol1000);
          BOOST_CHECK_CLOSE(      // kurtosis:
             kurtosis(dist)
             , static_cast<RealType>(3.5538752625241790601377L), tol1000);
          BOOST_CHECK_CLOSE(      // kurtosis excess:
             kurtosis_excess(dist)
             , static_cast<RealType>(0.5538752625241790601377L), tol1000);
  
          BOOST_CHECK_CLOSE(
            pdf(dist, static_cast<RealType>(0.4L)),
            static_cast<RealType>(0.294140110156599539564571L),
            tol100);
  
          BOOST_CHECK_CLOSE(
            cdf(dist, static_cast<RealType>(0.4L)),
            static_cast<RealType>(0.7339186189278737976326676452L),
            tol1000);
  
          BOOST_CHECK_CLOSE(
            quantile(dist, static_cast<RealType>(0.3L)),
            static_cast<RealType>(-1.180104068086875314419247L),
            tol1000);
  
  
        { // mode tests
  
          skew_normal_distribution<RealType> dist(static_cast<RealType>(0.l), static_cast<RealType>(1.l), static_cast<RealType>(4.l));
  
         // cout << "pdf(dist, 0) = " << pdf(dist, 0) <<  ", pdf(dist, 0.45) = " << pdf(dist, 0.45) << endl;
         // BOOST_CHECK_CLOSE(mode(dist), boost::math::constants::root_two<RealType>() / 2, tol5);
          BOOST_CHECK_CLOSE(mode(dist), static_cast<RealType>(0.41697299497388863932L), tol1000);
        }
  
  
        }
        {
          skew_normal_distribution<RealType> dist(static_cast<RealType>(1.1l), static_cast<RealType>(0.02l), static_cast<RealType>(0.03l));
  
          BOOST_CHECK_CLOSE(      // mean:
             mean(dist)
             , static_cast<RealType>(1.1004785154529557886162L), tol100);
          BOOST_CHECK_CLOSE(      // variance:
            variance(dist)
             , static_cast<RealType>(0.00039977102296128251645L), tol100);
  
          BOOST_CHECK_CLOSE(      // skewness:
             skewness(dist)
             , static_cast<RealType>(5.8834811259890359782e-006L), tol1000);
          BOOST_CHECK_CLOSE(      // kurtosis:
             kurtosis(dist)
             , static_cast<RealType>(3.L + 9.2903475812137800239002e-008L), tol1000);
          BOOST_CHECK_CLOSE(      // kurtosis excess:
             kurtosis_excess(dist)
             , static_cast<RealType>(9.2903475812137800239002e-008L), tol1000);
        }
        {
          skew_normal_distribution<RealType> dist(static_cast<RealType>(10.1l), static_cast<RealType>(5.l), static_cast<RealType>(-0.03l));
          BOOST_CHECK_CLOSE(      // mean:
             mean(dist)
             , static_cast<RealType>(9.9803711367610528459485937L), tol100);
          BOOST_CHECK_CLOSE(      // variance:
            variance(dist)
             , static_cast<RealType>(24.98568893508015727823L), tol100);
  
          BOOST_CHECK_CLOSE(      // skewness:
             skewness(dist)
             , static_cast<RealType>(-5.8834811259890359782085e-006L), tol1000);
          BOOST_CHECK_CLOSE(      // kurtosis:
             kurtosis(dist)
             , static_cast<RealType>(3.L + 9.2903475812137800239002e-008L), tol1000);
          BOOST_CHECK_CLOSE(      // kurtosis excess:
             kurtosis_excess(dist)
             , static_cast<RealType>(9.2903475812137800239002e-008L), tol1000);
        }
        {
          skew_normal_distribution<RealType> dist(static_cast<RealType>(-10.1l), static_cast<RealType>(5.l), static_cast<RealType>(30.l));
          BOOST_CHECK_CLOSE(      // mean:
             mean(dist)
             , static_cast<RealType>(-6.11279169674138408531365L), 2 * tol100);
          BOOST_CHECK_CLOSE(      // variance:
            variance(dist)
            , static_cast<RealType>(9.10216994642554914628242L), tol100 * 2);
  
          BOOST_CHECK_CLOSE(      // skewness:
             skewness(dist)
             , static_cast<RealType>(0.99072425443686904424L), tol1000);
          BOOST_CHECK_CLOSE(      // kurtosis:
             kurtosis(dist)
             , static_cast<RealType>(3.L + 0.8638862008406084244563L), tol1000);
          BOOST_CHECK_CLOSE(      // kurtosis excess:
             kurtosis_excess(dist)
             , static_cast<RealType>(0.8638862008406084244563L), tol1000);
        }
  
        BOOST_CHECK_THROW(cdf(skew_normal_distribution<RealType>(0, 0, 0), 0), std::domain_error);
        BOOST_CHECK_THROW(cdf(skew_normal_distribution<RealType>(0, -1, 0), 0), std::domain_error);
        BOOST_CHECK_THROW(quantile(skew_normal_distribution<RealType>(0, 1, 0), -1), std::domain_error);
        BOOST_CHECK_THROW(quantile(skew_normal_distribution<RealType>(0, 1, 0), 2), std::domain_error);
        check_out_of_range<skew_normal_distribution<RealType> >(1, 1, 1);
      }
  
  
  } // template <class RealType>void test_spots(RealType)
  
  int test_main(int, char* [])
  {
  
  
    using boost::math::skew_normal;
    using boost::math::skew_normal_distribution;
  
    //int precision = 17; // std::numeric_limits<double::max_digits10;
    double tolfeweps = numeric_limits<double>::epsilon() * 5;
    //double tol6decdigits = numeric_limits<float>::epsilon() * 2;
    // Check that can generate skew_normal distribution using the two convenience methods:
    boost::math::skew_normal w12(1., 2); // Using typedef.
    boost::math::skew_normal_distribution<> w01; // Use default unity values for mean and scale.
    // Note NOT myn01() as the compiler will interpret as a function!
  
    // Checks on constructors.
    // Default parameters.
    BOOST_CHECK_EQUAL(w01.location(), 0);
    BOOST_CHECK_EQUAL(w01.scale(), 1);
    BOOST_CHECK_EQUAL(w01.shape(), 0);
  
    skew_normal_distribution<> w23(2., 3); // Using default RealType double.
    BOOST_CHECK_EQUAL(w23.scale(), 3);
    BOOST_CHECK_EQUAL(w23.shape(), 0);
  
    skew_normal_distribution<> w123(1., 2., 3.); // Using default RealType double.
    BOOST_CHECK_EQUAL(w123.location(), 1.);
    BOOST_CHECK_EQUAL(w123.scale(), 2.);
    BOOST_CHECK_EQUAL(w123.shape(), 3.);
  
    BOOST_CHECK_CLOSE_FRACTION(mean(w01), static_cast<double>(0), tolfeweps); // Default mean == zero
    BOOST_CHECK_CLOSE_FRACTION(scale(w01), static_cast<double>(1), tolfeweps); // Default scale == unity
  
    // Basic sanity-check spot values for all floating-point types..
    // (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.
  #ifndef BOOST_MATH_NO_REAL_CONCEPT_TESTS
    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:
  
  
  */
  
  
  