triangular.hpp

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    {
      return 1 - (upper - x) *  (upper - x) / ((upper - lower) * (upper - mode));
    }
  } // RealType cdf(const triangular_distribution<RealType, Policy>& dist, const RealType& x)

  template <class RealType, class Policy>
  RealType quantile(const triangular_distribution<RealType, Policy>& dist, const RealType& p)
  {
    BOOST_MATH_STD_USING  // for ADL of std functions (sqrt).
    static const char* function = "boost::math::quantile(const triangular_distribution<%1%>&, %1%)";
    RealType lower = dist.lower();
    RealType mode = dist.mode();
    RealType upper = dist.upper();
    RealType result; // of checks
    if(false == detail::check_triangular(function,lower, mode, upper, &result, Policy()))
    {
      return result;
    }
    if(false == detail::check_probability(function, p, &result, Policy()))
    {
      return result;
    }
    if(p == 0)
    {
      return lower;
    }
    if(p == 1)
    {
      return upper;
    }
    RealType p0 = (mode - lower) / (upper - lower);
    RealType q = 1 - p;
    if (p < p0)
    {
      result = sqrt((upper - lower) * (mode - lower) * p) + lower;
    }
    else if (p == p0)
    {
      result = mode;
    }
    else // p > p0
    {
      result = upper - sqrt((upper - lower) * (upper - mode) * q);
    }
    return result;

  } // RealType quantile(const triangular_distribution<RealType, Policy>& dist, const RealType& q)

  template <class RealType, class Policy>
  RealType cdf(const complemented2_type<triangular_distribution<RealType, Policy>, RealType>& c)
  {
    static const char* function = "boost::math::cdf(const triangular_distribution<%1%>&, %1%)";
    RealType lower = c.dist.lower();
    RealType mode = c.dist.mode();
    RealType upper = c.dist.upper();
    RealType x = c.param;
    RealType result; // of checks.
    if(false == detail::check_triangular(function, lower, mode, upper, &result, Policy()))
    {
      return result;
    }
    if(false == detail::check_triangular_x(function, x, &result, Policy()))
    {
      return result;
    }
    if (x <= lower)
    {
      return 1;
    }
    if (x >= upper)
    {
      return 0;
    }
    if (x <= mode)
    {
      return 1 - ((x - lower) * (x - lower)) / ((upper - lower) * (mode - lower));
    }
    else
    {
      return (upper - x) *  (upper - x) / ((upper - lower) * (upper - mode));
    }
  } // RealType cdf(const complemented2_type<triangular_distribution<RealType, Policy>, RealType>& c)

  template <class RealType, class Policy>
  RealType quantile(const complemented2_type<triangular_distribution<RealType, Policy>, RealType>& c)
  {
    BOOST_MATH_STD_USING  // Aid ADL for sqrt.
    static const char* function = "boost::math::quantile(const triangular_distribution<%1%>&, %1%)";
    RealType l = c.dist.lower();
    RealType m = c.dist.mode();
    RealType u = c.dist.upper();
    RealType q = c.param; // probability 0 to 1.
    RealType result; // of checks.
    if(false == detail::check_triangular(function, l, m, u, &result, Policy()))
    {
      return result;
    }
    if(false == detail::check_probability(function, q, &result, Policy()))
    {
      return result;
    }
    if(q == 0)
    {
      return u;
    }
    if(q == 1)
    {
      return l;
    }
    RealType lower = c.dist.lower();
    RealType mode = c.dist.mode();
    RealType upper = c.dist.upper();

    RealType p = 1 - q;
    RealType p0 = (mode - lower) / (upper - lower);
    if(p < p0)
    {
      RealType s = (upper - lower) * (mode - lower);
      s *= p;
      result = sqrt((upper - lower) * (mode - lower) * p) + lower;
    }
    else if (p == p0)
    {
      result = mode;
    }
    else // p > p0
    {
      result = upper - sqrt((upper - lower) * (upper - mode) * q);
    }
    return result;
  } // RealType quantile(const complemented2_type<triangular_distribution<RealType, Policy>, RealType>& c)

  template <class RealType, class Policy>
  inline RealType mean(const triangular_distribution<RealType, Policy>& dist)
  {
    static const char* function = "boost::math::mean(const triangular_distribution<%1%>&)";
    RealType lower = dist.lower();
    RealType mode = dist.mode();
    RealType upper = dist.upper();
    RealType result;  // of checks.
    if(false == detail::check_triangular(function, lower, mode, upper, &result, Policy()))
    {
      return result;
    }
    return (lower + upper + mode) / 3;
  } // RealType mean(const triangular_distribution<RealType, Policy>& dist)


  template <class RealType, class Policy>
  inline RealType variance(const triangular_distribution<RealType, Policy>& dist)
  {
    static const char* function = "boost::math::mean(const triangular_distribution<%1%>&)";
    RealType lower = dist.lower();
    RealType mode = dist.mode();
    RealType upper = dist.upper();
    RealType result; // of checks.
    if(false == detail::check_triangular(function, lower, mode, upper, &result, Policy()))
    {
      return result;
    }
    return (lower * lower + upper * upper + mode * mode - lower * upper - lower * mode - upper * mode) / 18;
  } // RealType variance(const triangular_distribution<RealType, Policy>& dist)

  template <class RealType, class Policy>
  inline RealType mode(const triangular_distribution<RealType, Policy>& dist)
  {
    static const char* function = "boost::math::mode(const triangular_distribution<%1%>&)";
    RealType mode = dist.mode();
    RealType result; // of checks.
    if(false == detail::check_triangular_mode(function, mode, &result, Policy()))
    { // This should never happen!
      return result;
    }
    return mode;
  } // RealType mode

  template <class RealType, class Policy>
  inline RealType median(const triangular_distribution<RealType, Policy>& dist)
  {
    BOOST_MATH_STD_USING // ADL of std functions.
    static const char* function = "boost::math::median(const triangular_distribution<%1%>&)";
    RealType mode = dist.mode();
    RealType result; // of checks.
    if(false == detail::check_triangular_mode(function, mode, &result, Policy()))
    { // This should never happen!
      return result;
    }
    RealType lower = dist.lower();
    RealType upper = dist.upper();
    if (mode < (upper - lower) / 2)
    {
      return lower + sqrt((upper - lower) * (mode - lower)) / constants::root_two<RealType>();
    }
    else
    {
      return upper - sqrt((upper - lower) * (upper - mode)) / constants::root_two<RealType>();
    }
  } // RealType mode

  template <class RealType, class Policy>
  inline RealType skewness(const triangular_distribution<RealType, Policy>& dist)
  {
    BOOST_MATH_STD_USING  // for ADL of std functions
    using namespace boost::math::constants; // for root_two
    static const char* function = "boost::math::skewness(const triangular_distribution<%1%>&)";

    RealType lower = dist.lower();
    RealType mode = dist.mode();
    RealType upper = dist.upper();
    RealType result; // of checks.
    if(false == detail::check_triangular(function,lower, mode, upper, &result, Policy()))
    {
      return result;
    }
    return root_two<RealType>() * (lower + upper - 2 * mode) * (2 * lower - upper - mode) * (lower - 2 * upper + mode) /
      (5 * pow((lower * lower + upper + upper + mode * mode - lower * upper - lower * mode - upper * mode), RealType(3)/RealType(2)));
  } // RealType skewness(const triangular_distribution<RealType, Policy>& dist)

  template <class RealType, class Policy>
  inline RealType kurtosis(const triangular_distribution<RealType, Policy>& dist)
  { // These checks may be belt and braces as should have been checked on construction?
    static const char* function = "boost::math::kurtosis(const triangular_distribution<%1%>&)";
    RealType lower = dist.lower();
    RealType upper = dist.upper();
    RealType mode = dist.mode();
    RealType result;  // of checks.
    if(false == detail::check_triangular(function,lower, mode, upper, &result, Policy()))
    {
      return result;
    }
    return static_cast<RealType>(12)/5; //  12/5 = 2.4;
  } // RealType kurtosis_excess(const triangular_distribution<RealType, Policy>& dist)

  template <class RealType, class Policy>
  inline RealType kurtosis_excess(const triangular_distribution<RealType, Policy>& dist)
  { // These checks may be belt and braces as should have been checked on construction?
    static const char* function = "boost::math::kurtosis_excess(const triangular_distribution<%1%>&)";
    RealType lower = dist.lower();
    RealType upper = dist.upper();
    RealType mode = dist.mode();
    RealType result;  // of checks.
    if(false == detail::check_triangular(function,lower, mode, upper, &result, Policy()))
    {
      return result;
    }
    return static_cast<RealType>(-3)/5; // - 3/5 = -0.6
    // Assuming mathworld really means kurtosis excess?  Wikipedia now corrected to match this.
  }

} // namespace math
} // namespace boost

// This include must be at the end, *after* the accessors
// for this distribution have been defined, in order to
// keep compilers that support two-phase lookup happy.
#include <boost/math/distributions/detail/derived_accessors.hpp>

#endif // BOOST_STATS_TRIANGULAR_HPP