cannam@160: //  Copyright John Maddock 2006, 2007.
cannam@160: //  Copyright Paul A. Bristow 2006, 2007.
cannam@160: //  Use, modification and distribution are subject to the
cannam@160: //  Boost Software License, Version 1.0. (See accompanying file
cannam@160: //  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
cannam@160: 
cannam@160: #ifndef BOOST_STATS_TRIANGULAR_HPP
cannam@160: #define BOOST_STATS_TRIANGULAR_HPP
cannam@160: 
cannam@160: // http://mathworld.wolfram.com/TriangularDistribution.html
cannam@160: // Note that the 'constructors' defined by Wolfram are difference from those here,
cannam@160: // for example
cannam@160: // N[variance[triangulardistribution{1, +2}, 1.5], 50] computes 
cannam@160: // 0.041666666666666666666666666666666666666666666666667
cannam@160: // TriangularDistribution{1, +2}, 1.5 is the analog of triangular_distribution(1, 1.5, 2)
cannam@160: 
cannam@160: // http://en.wikipedia.org/wiki/Triangular_distribution
cannam@160: 
cannam@160: #include <boost/math/distributions/fwd.hpp>
cannam@160: #include <boost/math/special_functions/expm1.hpp>
cannam@160: #include <boost/math/distributions/detail/common_error_handling.hpp>
cannam@160: #include <boost/math/distributions/complement.hpp>
cannam@160: #include <boost/math/constants/constants.hpp>
cannam@160: 
cannam@160: #include <utility>
cannam@160: 
cannam@160: namespace boost{ namespace math
cannam@160: {
cannam@160:   namespace detail
cannam@160:   {
cannam@160:     template <class RealType, class Policy>
cannam@160:     inline bool check_triangular_lower(
cannam@160:       const char* function,
cannam@160:       RealType lower,
cannam@160:       RealType* result, const Policy& pol)
cannam@160:     {
cannam@160:       if((boost::math::isfinite)(lower))
cannam@160:       { // Any finite value is OK.
cannam@160:         return true;
cannam@160:       }
cannam@160:       else
cannam@160:       { // Not finite: infinity or NaN.
cannam@160:         *result = policies::raise_domain_error<RealType>(
cannam@160:           function,
cannam@160:           "Lower parameter is %1%, but must be finite!", lower, pol);
cannam@160:         return false;
cannam@160:       }
cannam@160:     } // bool check_triangular_lower(
cannam@160: 
cannam@160:     template <class RealType, class Policy>
cannam@160:     inline bool check_triangular_mode(
cannam@160:       const char* function,
cannam@160:       RealType mode,
cannam@160:       RealType* result, const Policy& pol)
cannam@160:     {
cannam@160:       if((boost::math::isfinite)(mode))
cannam@160:       { // any finite value is OK.
cannam@160:         return true;
cannam@160:       }
cannam@160:       else
cannam@160:       { // Not finite: infinity or NaN.
cannam@160:         *result = policies::raise_domain_error<RealType>(
cannam@160:           function,
cannam@160:           "Mode parameter is %1%, but must be finite!", mode, pol);
cannam@160:         return false;
cannam@160:       }
cannam@160:     } // bool check_triangular_mode(
cannam@160: 
cannam@160:     template <class RealType, class Policy>
cannam@160:     inline bool check_triangular_upper(
cannam@160:       const char* function,
cannam@160:       RealType upper,
cannam@160:       RealType* result, const Policy& pol)
cannam@160:     {
cannam@160:       if((boost::math::isfinite)(upper))
cannam@160:       { // any finite value is OK.
cannam@160:         return true;
cannam@160:       }
cannam@160:       else
cannam@160:       { // Not finite: infinity or NaN.
cannam@160:         *result = policies::raise_domain_error<RealType>(
cannam@160:           function,
cannam@160:           "Upper parameter is %1%, but must be finite!", upper, pol);
cannam@160:         return false;
cannam@160:       }
cannam@160:     } // bool check_triangular_upper(
cannam@160: 
cannam@160:     template <class RealType, class Policy>
cannam@160:     inline bool check_triangular_x(
cannam@160:       const char* function,
cannam@160:       RealType const& x,
cannam@160:       RealType* result, const Policy& pol)
cannam@160:     {
cannam@160:       if((boost::math::isfinite)(x))
cannam@160:       { // Any finite value is OK
cannam@160:         return true;
cannam@160:       }
cannam@160:       else
cannam@160:       { // Not finite: infinity or NaN.
cannam@160:         *result = policies::raise_domain_error<RealType>(
cannam@160:           function,
cannam@160:           "x parameter is %1%, but must be finite!", x, pol);
cannam@160:         return false;
cannam@160:       }
cannam@160:     } // bool check_triangular_x
cannam@160: 
cannam@160:     template <class RealType, class Policy>
cannam@160:     inline bool check_triangular(
cannam@160:       const char* function,
cannam@160:       RealType lower,
cannam@160:       RealType mode,
cannam@160:       RealType upper,
cannam@160:       RealType* result, const Policy& pol)
cannam@160:     {
cannam@160:       if ((check_triangular_lower(function, lower, result, pol) == false)
cannam@160:         || (check_triangular_mode(function, mode, result, pol) == false)
cannam@160:         || (check_triangular_upper(function, upper, result, pol) == false))
cannam@160:       { // Some parameter not finite.
cannam@160:         return false;
cannam@160:       }
cannam@160:       else if (lower >= upper) // lower == upper NOT useful.
cannam@160:       { // lower >= upper.
cannam@160:         *result = policies::raise_domain_error<RealType>(
cannam@160:           function,
cannam@160:           "lower parameter is %1%, but must be less than upper!", lower, pol);
cannam@160:         return false;
cannam@160:       }
cannam@160:       else
cannam@160:       { // Check lower <= mode <= upper.
cannam@160:         if (mode < lower)
cannam@160:         {
cannam@160:           *result = policies::raise_domain_error<RealType>(
cannam@160:             function,
cannam@160:             "mode parameter is %1%, but must be >= than lower!", lower, pol);
cannam@160:           return false;
cannam@160:         }
cannam@160:         if (mode > upper)
cannam@160:         {
cannam@160:           *result = policies::raise_domain_error<RealType>(
cannam@160:             function,
cannam@160:             "mode parameter is %1%, but must be <= than upper!", upper, pol);
cannam@160:           return false;
cannam@160:         }
cannam@160:         return true; // All OK.
cannam@160:       }
cannam@160:     } // bool check_triangular
cannam@160:   } // namespace detail
cannam@160: 
cannam@160:   template <class RealType = double, class Policy = policies::policy<> >
cannam@160:   class triangular_distribution
cannam@160:   {
cannam@160:   public:
cannam@160:     typedef RealType value_type;
cannam@160:     typedef Policy policy_type;
cannam@160: 
cannam@160:     triangular_distribution(RealType l_lower = -1, RealType l_mode = 0, RealType l_upper = 1)
cannam@160:       : m_lower(l_lower), m_mode(l_mode), m_upper(l_upper) // Constructor.
cannam@160:     { // Evans says 'standard triangular' is lower 0, mode 1/2, upper 1,
cannam@160:       // has median sqrt(c/2) for c <=1/2 and 1 - sqrt(1-c)/2 for c >= 1/2
cannam@160:       // But this -1, 0, 1 is more useful in most applications to approximate normal distribution,
cannam@160:       // where the central value is the most likely and deviations either side equally likely.
cannam@160:       RealType result;
cannam@160:       detail::check_triangular("boost::math::triangular_distribution<%1%>::triangular_distribution",l_lower, l_mode, l_upper, &result, Policy());
cannam@160:     }
cannam@160:     // Accessor functions.
cannam@160:     RealType lower()const
cannam@160:     {
cannam@160:       return m_lower;
cannam@160:     }
cannam@160:     RealType mode()const
cannam@160:     {
cannam@160:       return m_mode;
cannam@160:     }
cannam@160:     RealType upper()const
cannam@160:     {
cannam@160:       return m_upper;
cannam@160:     }
cannam@160:   private:
cannam@160:     // Data members:
cannam@160:     RealType m_lower;  // distribution lower aka a
cannam@160:     RealType m_mode;  // distribution mode aka c
cannam@160:     RealType m_upper;  // distribution upper aka b
cannam@160:   }; // class triangular_distribution
cannam@160: 
cannam@160:   typedef triangular_distribution<double> triangular;
cannam@160: 
cannam@160:   template <class RealType, class Policy>
cannam@160:   inline const std::pair<RealType, RealType> range(const triangular_distribution<RealType, Policy>& /* dist */)
cannam@160:   { // Range of permissible values for random variable x.
cannam@160:     using boost::math::tools::max_value;
cannam@160:     return std::pair<RealType, RealType>(-max_value<RealType>(), max_value<RealType>());
cannam@160:   }
cannam@160: 
cannam@160:   template <class RealType, class Policy>
cannam@160:   inline const std::pair<RealType, RealType> support(const triangular_distribution<RealType, Policy>& dist)
cannam@160:   { // Range of supported values for random variable x.
cannam@160:     // This is range where cdf rises from 0 to 1, and outside it, the pdf is zero.
cannam@160:     return std::pair<RealType, RealType>(dist.lower(), dist.upper());
cannam@160:   }
cannam@160: 
cannam@160:   template <class RealType, class Policy>
cannam@160:   RealType pdf(const triangular_distribution<RealType, Policy>& dist, const RealType& x)
cannam@160:   {
cannam@160:     static const char* function = "boost::math::pdf(const triangular_distribution<%1%>&, %1%)";
cannam@160:     RealType lower = dist.lower();
cannam@160:     RealType mode = dist.mode();
cannam@160:     RealType upper = dist.upper();
cannam@160:     RealType result = 0; // of checks.
cannam@160:     if(false == detail::check_triangular(function, lower, mode, upper, &result, Policy()))
cannam@160:     {
cannam@160:       return result;
cannam@160:     }
cannam@160:     if(false == detail::check_triangular_x(function, x, &result, Policy()))
cannam@160:     {
cannam@160:       return result;
cannam@160:     }
cannam@160:     if((x < lower) || (x > upper))
cannam@160:     {
cannam@160:       return 0;
cannam@160:     }
cannam@160:     if (x == lower)
cannam@160:     { // (mode - lower) == 0 which would lead to divide by zero!
cannam@160:       return (mode == lower) ? 2 / (upper - lower) : RealType(0);
cannam@160:     }
cannam@160:     else if (x == upper)
cannam@160:     {
cannam@160:       return (mode == upper) ? 2 / (upper - lower) : RealType(0);
cannam@160:     }
cannam@160:     else if (x <= mode)
cannam@160:     {
cannam@160:       return 2 * (x - lower) / ((upper - lower) * (mode - lower));
cannam@160:     }
cannam@160:     else
cannam@160:     {  // (x > mode)
cannam@160:       return 2 * (upper - x) / ((upper - lower) * (upper - mode));
cannam@160:     }
cannam@160:   } // RealType pdf(const triangular_distribution<RealType, Policy>& dist, const RealType& x)
cannam@160: 
cannam@160:   template <class RealType, class Policy>
cannam@160:   inline RealType cdf(const triangular_distribution<RealType, Policy>& dist, const RealType& x)
cannam@160:   {
cannam@160:     static const char* function = "boost::math::cdf(const triangular_distribution<%1%>&, %1%)";
cannam@160:     RealType lower = dist.lower();
cannam@160:     RealType mode = dist.mode();
cannam@160:     RealType upper = dist.upper();
cannam@160:     RealType result = 0; // of checks.
cannam@160:     if(false == detail::check_triangular(function, lower, mode, upper, &result, Policy()))
cannam@160:     {
cannam@160:       return result;
cannam@160:     }
cannam@160:     if(false == detail::check_triangular_x(function, x, &result, Policy()))
cannam@160:     {
cannam@160:       return result;
cannam@160:     }
cannam@160:     if((x <= lower))
cannam@160:     {
cannam@160:       return 0;
cannam@160:     }
cannam@160:     if (x >= upper)
cannam@160:     {
cannam@160:       return 1;
cannam@160:     }
cannam@160:     // else lower < x < upper
cannam@160:     if (x <= mode)
cannam@160:     {
cannam@160:       return ((x - lower) * (x - lower)) / ((upper - lower) * (mode - lower));
cannam@160:     }
cannam@160:     else
cannam@160:     {
cannam@160:       return 1 - (upper - x) *  (upper - x) / ((upper - lower) * (upper - mode));
cannam@160:     }
cannam@160:   } // RealType cdf(const triangular_distribution<RealType, Policy>& dist, const RealType& x)
cannam@160: 
cannam@160:   template <class RealType, class Policy>
cannam@160:   RealType quantile(const triangular_distribution<RealType, Policy>& dist, const RealType& p)
cannam@160:   {
cannam@160:     BOOST_MATH_STD_USING  // for ADL of std functions (sqrt).
cannam@160:     static const char* function = "boost::math::quantile(const triangular_distribution<%1%>&, %1%)";
cannam@160:     RealType lower = dist.lower();
cannam@160:     RealType mode = dist.mode();
cannam@160:     RealType upper = dist.upper();
cannam@160:     RealType result = 0; // of checks
cannam@160:     if(false == detail::check_triangular(function,lower, mode, upper, &result, Policy()))
cannam@160:     {
cannam@160:       return result;
cannam@160:     }
cannam@160:     if(false == detail::check_probability(function, p, &result, Policy()))
cannam@160:     {
cannam@160:       return result;
cannam@160:     }
cannam@160:     if(p == 0)
cannam@160:     {
cannam@160:       return lower;
cannam@160:     }
cannam@160:     if(p == 1)
cannam@160:     {
cannam@160:       return upper;
cannam@160:     }
cannam@160:     RealType p0 = (mode - lower) / (upper - lower);
cannam@160:     RealType q = 1 - p;
cannam@160:     if (p < p0)
cannam@160:     {
cannam@160:       result = sqrt((upper - lower) * (mode - lower) * p) + lower;
cannam@160:     }
cannam@160:     else if (p == p0)
cannam@160:     {
cannam@160:       result = mode;
cannam@160:     }
cannam@160:     else // p > p0
cannam@160:     {
cannam@160:       result = upper - sqrt((upper - lower) * (upper - mode) * q);
cannam@160:     }
cannam@160:     return result;
cannam@160: 
cannam@160:   } // RealType quantile(const triangular_distribution<RealType, Policy>& dist, const RealType& q)
cannam@160: 
cannam@160:   template <class RealType, class Policy>
cannam@160:   RealType cdf(const complemented2_type<triangular_distribution<RealType, Policy>, RealType>& c)
cannam@160:   {
cannam@160:     static const char* function = "boost::math::cdf(const triangular_distribution<%1%>&, %1%)";
cannam@160:     RealType lower = c.dist.lower();
cannam@160:     RealType mode = c.dist.mode();
cannam@160:     RealType upper = c.dist.upper();
cannam@160:     RealType x = c.param;
cannam@160:     RealType result = 0; // of checks.
cannam@160:     if(false == detail::check_triangular(function, lower, mode, upper, &result, Policy()))
cannam@160:     {
cannam@160:       return result;
cannam@160:     }
cannam@160:     if(false == detail::check_triangular_x(function, x, &result, Policy()))
cannam@160:     {
cannam@160:       return result;
cannam@160:     }
cannam@160:     if (x <= lower)
cannam@160:     {
cannam@160:       return 1;
cannam@160:     }
cannam@160:     if (x >= upper)
cannam@160:     {
cannam@160:       return 0;
cannam@160:     }
cannam@160:     if (x <= mode)
cannam@160:     {
cannam@160:       return 1 - ((x - lower) * (x - lower)) / ((upper - lower) * (mode - lower));
cannam@160:     }
cannam@160:     else
cannam@160:     {
cannam@160:       return (upper - x) *  (upper - x) / ((upper - lower) * (upper - mode));
cannam@160:     }
cannam@160:   } // RealType cdf(const complemented2_type<triangular_distribution<RealType, Policy>, RealType>& c)
cannam@160: 
cannam@160:   template <class RealType, class Policy>
cannam@160:   RealType quantile(const complemented2_type<triangular_distribution<RealType, Policy>, RealType>& c)
cannam@160:   {
cannam@160:     BOOST_MATH_STD_USING  // Aid ADL for sqrt.
cannam@160:     static const char* function = "boost::math::quantile(const triangular_distribution<%1%>&, %1%)";
cannam@160:     RealType l = c.dist.lower();
cannam@160:     RealType m = c.dist.mode();
cannam@160:     RealType u = c.dist.upper();
cannam@160:     RealType q = c.param; // probability 0 to 1.
cannam@160:     RealType result = 0; // of checks.
cannam@160:     if(false == detail::check_triangular(function, l, m, u, &result, Policy()))
cannam@160:     {
cannam@160:       return result;
cannam@160:     }
cannam@160:     if(false == detail::check_probability(function, q, &result, Policy()))
cannam@160:     {
cannam@160:       return result;
cannam@160:     }
cannam@160:     if(q == 0)
cannam@160:     {
cannam@160:       return u;
cannam@160:     }
cannam@160:     if(q == 1)
cannam@160:     {
cannam@160:       return l;
cannam@160:     }
cannam@160:     RealType lower = c.dist.lower();
cannam@160:     RealType mode = c.dist.mode();
cannam@160:     RealType upper = c.dist.upper();
cannam@160: 
cannam@160:     RealType p = 1 - q;
cannam@160:     RealType p0 = (mode - lower) / (upper - lower);
cannam@160:     if(p < p0)
cannam@160:     {
cannam@160:       RealType s = (upper - lower) * (mode - lower);
cannam@160:       s *= p;
cannam@160:       result = sqrt((upper - lower) * (mode - lower) * p) + lower;
cannam@160:     }
cannam@160:     else if (p == p0)
cannam@160:     {
cannam@160:       result = mode;
cannam@160:     }
cannam@160:     else // p > p0
cannam@160:     {
cannam@160:       result = upper - sqrt((upper - lower) * (upper - mode) * q);
cannam@160:     }
cannam@160:     return result;
cannam@160:   } // RealType quantile(const complemented2_type<triangular_distribution<RealType, Policy>, RealType>& c)
cannam@160: 
cannam@160:   template <class RealType, class Policy>
cannam@160:   inline RealType mean(const triangular_distribution<RealType, Policy>& dist)
cannam@160:   {
cannam@160:     static const char* function = "boost::math::mean(const triangular_distribution<%1%>&)";
cannam@160:     RealType lower = dist.lower();
cannam@160:     RealType mode = dist.mode();
cannam@160:     RealType upper = dist.upper();
cannam@160:     RealType result = 0;  // of checks.
cannam@160:     if(false == detail::check_triangular(function, lower, mode, upper, &result, Policy()))
cannam@160:     {
cannam@160:       return result;
cannam@160:     }
cannam@160:     return (lower + upper + mode) / 3;
cannam@160:   } // RealType mean(const triangular_distribution<RealType, Policy>& dist)
cannam@160: 
cannam@160: 
cannam@160:   template <class RealType, class Policy>
cannam@160:   inline RealType variance(const triangular_distribution<RealType, Policy>& dist)
cannam@160:   {
cannam@160:     static const char* function = "boost::math::mean(const triangular_distribution<%1%>&)";
cannam@160:     RealType lower = dist.lower();
cannam@160:     RealType mode = dist.mode();
cannam@160:     RealType upper = dist.upper();
cannam@160:     RealType result = 0; // of checks.
cannam@160:     if(false == detail::check_triangular(function, lower, mode, upper, &result, Policy()))
cannam@160:     {
cannam@160:       return result;
cannam@160:     }
cannam@160:     return (lower * lower + upper * upper + mode * mode - lower * upper - lower * mode - upper * mode) / 18;
cannam@160:   } // RealType variance(const triangular_distribution<RealType, Policy>& dist)
cannam@160: 
cannam@160:   template <class RealType, class Policy>
cannam@160:   inline RealType mode(const triangular_distribution<RealType, Policy>& dist)
cannam@160:   {
cannam@160:     static const char* function = "boost::math::mode(const triangular_distribution<%1%>&)";
cannam@160:     RealType mode = dist.mode();
cannam@160:     RealType result = 0; // of checks.
cannam@160:     if(false == detail::check_triangular_mode(function, mode, &result, Policy()))
cannam@160:     { // This should never happen!
cannam@160:       return result;
cannam@160:     }
cannam@160:     return mode;
cannam@160:   } // RealType mode
cannam@160: 
cannam@160:   template <class RealType, class Policy>
cannam@160:   inline RealType median(const triangular_distribution<RealType, Policy>& dist)
cannam@160:   {
cannam@160:     BOOST_MATH_STD_USING // ADL of std functions.
cannam@160:     static const char* function = "boost::math::median(const triangular_distribution<%1%>&)";
cannam@160:     RealType mode = dist.mode();
cannam@160:     RealType result = 0; // of checks.
cannam@160:     if(false == detail::check_triangular_mode(function, mode, &result, Policy()))
cannam@160:     { // This should never happen!
cannam@160:       return result;
cannam@160:     }
cannam@160:     RealType lower = dist.lower();
cannam@160:     RealType upper = dist.upper();
cannam@160:     if (mode >= (upper + lower) / 2)
cannam@160:     {
cannam@160:       return lower + sqrt((upper - lower) * (mode - lower)) / constants::root_two<RealType>();
cannam@160:     }
cannam@160:     else
cannam@160:     {
cannam@160:       return upper - sqrt((upper - lower) * (upper - mode)) / constants::root_two<RealType>();
cannam@160:     }
cannam@160:   } // RealType mode
cannam@160: 
cannam@160:   template <class RealType, class Policy>
cannam@160:   inline RealType skewness(const triangular_distribution<RealType, Policy>& dist)
cannam@160:   {
cannam@160:     BOOST_MATH_STD_USING  // for ADL of std functions
cannam@160:     using namespace boost::math::constants; // for root_two
cannam@160:     static const char* function = "boost::math::skewness(const triangular_distribution<%1%>&)";
cannam@160: 
cannam@160:     RealType lower = dist.lower();
cannam@160:     RealType mode = dist.mode();
cannam@160:     RealType upper = dist.upper();
cannam@160:     RealType result = 0; // of checks.
cannam@160:     if(false == boost::math::detail::check_triangular(function,lower, mode, upper, &result, Policy()))
cannam@160:     {
cannam@160:       return result;
cannam@160:     }
cannam@160:     return root_two<RealType>() * (lower + upper - 2 * mode) * (2 * lower - upper - mode) * (lower - 2 * upper + mode) /
cannam@160:       (5 * pow((lower * lower + upper * upper + mode * mode 
cannam@160:         - lower * upper - lower * mode - upper * mode), RealType(3)/RealType(2)));
cannam@160:     // #11768: Skewness formula for triangular distribution is incorrect -  corrected 29 Oct 2015 for release 1.61.
cannam@160:   } // RealType skewness(const triangular_distribution<RealType, Policy>& dist)
cannam@160: 
cannam@160:   template <class RealType, class Policy>
cannam@160:   inline RealType kurtosis(const triangular_distribution<RealType, Policy>& dist)
cannam@160:   { // These checks may be belt and braces as should have been checked on construction?
cannam@160:     static const char* function = "boost::math::kurtosis(const triangular_distribution<%1%>&)";
cannam@160:     RealType lower = dist.lower();
cannam@160:     RealType upper = dist.upper();
cannam@160:     RealType mode = dist.mode();
cannam@160:     RealType result = 0;  // of checks.
cannam@160:     if(false == detail::check_triangular(function,lower, mode, upper, &result, Policy()))
cannam@160:     {
cannam@160:       return result;
cannam@160:     }
cannam@160:     return static_cast<RealType>(12)/5; //  12/5 = 2.4;
cannam@160:   } // RealType kurtosis_excess(const triangular_distribution<RealType, Policy>& dist)
cannam@160: 
cannam@160:   template <class RealType, class Policy>
cannam@160:   inline RealType kurtosis_excess(const triangular_distribution<RealType, Policy>& dist)
cannam@160:   { // These checks may be belt and braces as should have been checked on construction?
cannam@160:     static const char* function = "boost::math::kurtosis_excess(const triangular_distribution<%1%>&)";
cannam@160:     RealType lower = dist.lower();
cannam@160:     RealType upper = dist.upper();
cannam@160:     RealType mode = dist.mode();
cannam@160:     RealType result = 0;  // of checks.
cannam@160:     if(false == detail::check_triangular(function,lower, mode, upper, &result, Policy()))
cannam@160:     {
cannam@160:       return result;
cannam@160:     }
cannam@160:     return static_cast<RealType>(-3)/5; // - 3/5 = -0.6
cannam@160:     // Assuming mathworld really means kurtosis excess?  Wikipedia now corrected to match this.
cannam@160:   }
cannam@160: 
cannam@160: } // namespace math
cannam@160: } // namespace boost
cannam@160: 
cannam@160: // This include must be at the end, *after* the accessors
cannam@160: // for this distribution have been defined, in order to
cannam@160: // keep compilers that support two-phase lookup happy.
cannam@160: #include <boost/math/distributions/detail/derived_accessors.hpp>
cannam@160: 
cannam@160: #endif // BOOST_STATS_TRIANGULAR_HPP
cannam@160: 
cannam@160: 
cannam@160: