Chris@16: //  Copyright John Maddock 2006, 2007.
Chris@16: //  Copyright Paul A. Bristow 2006, 2007.
Chris@16: //  Use, modification and distribution are subject to the
Chris@16: //  Boost Software License, Version 1.0. (See accompanying file
Chris@16: //  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
Chris@16: 
Chris@16: #ifndef BOOST_STATS_TRIANGULAR_HPP
Chris@16: #define BOOST_STATS_TRIANGULAR_HPP
Chris@16: 
Chris@16: // http://mathworld.wolfram.com/TriangularDistribution.html
Chris@16: // http://en.wikipedia.org/wiki/Triangular_distribution
Chris@16: 
Chris@16: #include <boost/math/distributions/fwd.hpp>
Chris@16: #include <boost/math/special_functions/expm1.hpp>
Chris@16: #include <boost/math/distributions/detail/common_error_handling.hpp>
Chris@16: #include <boost/math/distributions/complement.hpp>
Chris@16: #include <boost/math/constants/constants.hpp>
Chris@16: 
Chris@16: #include <utility>
Chris@16: 
Chris@16: namespace boost{ namespace math
Chris@16: {
Chris@16:   namespace detail
Chris@16:   {
Chris@16:     template <class RealType, class Policy>
Chris@16:     inline bool check_triangular_lower(
Chris@16:       const char* function,
Chris@16:       RealType lower,
Chris@16:       RealType* result, const Policy& pol)
Chris@16:     {
Chris@16:       if((boost::math::isfinite)(lower))
Chris@16:       { // Any finite value is OK.
Chris@16:         return true;
Chris@16:       }
Chris@16:       else
Chris@16:       { // Not finite: infinity or NaN.
Chris@16:         *result = policies::raise_domain_error<RealType>(
Chris@16:           function,
Chris@16:           "Lower parameter is %1%, but must be finite!", lower, pol);
Chris@16:         return false;
Chris@16:       }
Chris@16:     } // bool check_triangular_lower(
Chris@16: 
Chris@16:     template <class RealType, class Policy>
Chris@16:     inline bool check_triangular_mode(
Chris@16:       const char* function,
Chris@16:       RealType mode,
Chris@16:       RealType* result, const Policy& pol)
Chris@16:     {
Chris@16:       if((boost::math::isfinite)(mode))
Chris@16:       { // any finite value is OK.
Chris@16:         return true;
Chris@16:       }
Chris@16:       else
Chris@16:       { // Not finite: infinity or NaN.
Chris@16:         *result = policies::raise_domain_error<RealType>(
Chris@16:           function,
Chris@16:           "Mode parameter is %1%, but must be finite!", mode, pol);
Chris@16:         return false;
Chris@16:       }
Chris@16:     } // bool check_triangular_mode(
Chris@16: 
Chris@16:     template <class RealType, class Policy>
Chris@16:     inline bool check_triangular_upper(
Chris@16:       const char* function,
Chris@16:       RealType upper,
Chris@16:       RealType* result, const Policy& pol)
Chris@16:     {
Chris@16:       if((boost::math::isfinite)(upper))
Chris@16:       { // any finite value is OK.
Chris@16:         return true;
Chris@16:       }
Chris@16:       else
Chris@16:       { // Not finite: infinity or NaN.
Chris@16:         *result = policies::raise_domain_error<RealType>(
Chris@16:           function,
Chris@16:           "Upper parameter is %1%, but must be finite!", upper, pol);
Chris@16:         return false;
Chris@16:       }
Chris@16:     } // bool check_triangular_upper(
Chris@16: 
Chris@16:     template <class RealType, class Policy>
Chris@16:     inline bool check_triangular_x(
Chris@16:       const char* function,
Chris@16:       RealType const& x,
Chris@16:       RealType* result, const Policy& pol)
Chris@16:     {
Chris@16:       if((boost::math::isfinite)(x))
Chris@16:       { // Any finite value is OK
Chris@16:         return true;
Chris@16:       }
Chris@16:       else
Chris@16:       { // Not finite: infinity or NaN.
Chris@16:         *result = policies::raise_domain_error<RealType>(
Chris@16:           function,
Chris@16:           "x parameter is %1%, but must be finite!", x, pol);
Chris@16:         return false;
Chris@16:       }
Chris@16:     } // bool check_triangular_x
Chris@16: 
Chris@16:     template <class RealType, class Policy>
Chris@16:     inline bool check_triangular(
Chris@16:       const char* function,
Chris@16:       RealType lower,
Chris@16:       RealType mode,
Chris@16:       RealType upper,
Chris@16:       RealType* result, const Policy& pol)
Chris@16:     {
Chris@16:       if ((check_triangular_lower(function, lower, result, pol) == false)
Chris@16:         || (check_triangular_mode(function, mode, result, pol) == false)
Chris@16:         || (check_triangular_upper(function, upper, result, pol) == false))
Chris@16:       { // Some parameter not finite.
Chris@16:         return false;
Chris@16:       }
Chris@16:       else if (lower >= upper) // lower == upper NOT useful.
Chris@16:       { // lower >= upper.
Chris@16:         *result = policies::raise_domain_error<RealType>(
Chris@16:           function,
Chris@16:           "lower parameter is %1%, but must be less than upper!", lower, pol);
Chris@16:         return false;
Chris@16:       }
Chris@16:       else
Chris@16:       { // Check lower <= mode <= upper.
Chris@16:         if (mode < lower)
Chris@16:         {
Chris@16:           *result = policies::raise_domain_error<RealType>(
Chris@16:             function,
Chris@16:             "mode parameter is %1%, but must be >= than lower!", lower, pol);
Chris@16:           return false;
Chris@16:         }
Chris@16:         if (mode > upper)
Chris@16:         {
Chris@16:           *result = policies::raise_domain_error<RealType>(
Chris@16:             function,
Chris@16:             "mode parameter is %1%, but must be <= than upper!", upper, pol);
Chris@16:           return false;
Chris@16:         }
Chris@16:         return true; // All OK.
Chris@16:       }
Chris@16:     } // bool check_triangular
Chris@16:   } // namespace detail
Chris@16: 
Chris@16:   template <class RealType = double, class Policy = policies::policy<> >
Chris@16:   class triangular_distribution
Chris@16:   {
Chris@16:   public:
Chris@16:     typedef RealType value_type;
Chris@16:     typedef Policy policy_type;
Chris@16: 
Chris@16:     triangular_distribution(RealType l_lower = -1, RealType l_mode = 0, RealType l_upper = 1)
Chris@16:       : m_lower(l_lower), m_mode(l_mode), m_upper(l_upper) // Constructor.
Chris@16:     { // Evans says 'standard triangular' is lower 0, mode 1/2, upper 1,
Chris@16:       // has median sqrt(c/2) for c <=1/2 and 1 - sqrt(1-c)/2 for c >= 1/2
Chris@16:       // But this -1, 0, 1 is more useful in most applications to approximate normal distribution,
Chris@16:       // where the central value is the most likely and deviations either side equally likely.
Chris@16:       RealType result;
Chris@16:       detail::check_triangular("boost::math::triangular_distribution<%1%>::triangular_distribution",l_lower, l_mode, l_upper, &result, Policy());
Chris@16:     }
Chris@16:     // Accessor functions.
Chris@16:     RealType lower()const
Chris@16:     {
Chris@16:       return m_lower;
Chris@16:     }
Chris@16:     RealType mode()const
Chris@16:     {
Chris@16:       return m_mode;
Chris@16:     }
Chris@16:     RealType upper()const
Chris@16:     {
Chris@16:       return m_upper;
Chris@16:     }
Chris@16:   private:
Chris@16:     // Data members:
Chris@16:     RealType m_lower;  // distribution lower aka a
Chris@16:     RealType m_mode;  // distribution mode aka c
Chris@16:     RealType m_upper;  // distribution upper aka b
Chris@16:   }; // class triangular_distribution
Chris@16: 
Chris@16:   typedef triangular_distribution<double> triangular;
Chris@16: 
Chris@16:   template <class RealType, class Policy>
Chris@16:   inline const std::pair<RealType, RealType> range(const triangular_distribution<RealType, Policy>& /* dist */)
Chris@16:   { // Range of permissible values for random variable x.
Chris@16:     using boost::math::tools::max_value;
Chris@16:     return std::pair<RealType, RealType>(-max_value<RealType>(), max_value<RealType>());
Chris@16:   }
Chris@16: 
Chris@16:   template <class RealType, class Policy>
Chris@16:   inline const std::pair<RealType, RealType> support(const triangular_distribution<RealType, Policy>& dist)
Chris@16:   { // Range of supported values for random variable x.
Chris@16:     // This is range where cdf rises from 0 to 1, and outside it, the pdf is zero.
Chris@16:     return std::pair<RealType, RealType>(dist.lower(), dist.upper());
Chris@16:   }
Chris@16: 
Chris@16:   template <class RealType, class Policy>
Chris@16:   RealType pdf(const triangular_distribution<RealType, Policy>& dist, const RealType& x)
Chris@16:   {
Chris@16:     static const char* function = "boost::math::pdf(const triangular_distribution<%1%>&, %1%)";
Chris@16:     RealType lower = dist.lower();
Chris@16:     RealType mode = dist.mode();
Chris@16:     RealType upper = dist.upper();
Chris@16:     RealType result = 0; // of checks.
Chris@16:     if(false == detail::check_triangular(function, lower, mode, upper, &result, Policy()))
Chris@16:     {
Chris@16:       return result;
Chris@16:     }
Chris@16:     if(false == detail::check_triangular_x(function, x, &result, Policy()))
Chris@16:     {
Chris@16:       return result;
Chris@16:     }
Chris@16:     if((x < lower) || (x > upper))
Chris@16:     {
Chris@16:       return 0;
Chris@16:     }
Chris@16:     if (x == lower)
Chris@16:     { // (mode - lower) == 0 which would lead to divide by zero!
Chris@16:       return (mode == lower) ? 2 / (upper - lower) : RealType(0);
Chris@16:     }
Chris@16:     else if (x == upper)
Chris@16:     {
Chris@16:       return (mode == upper) ? 2 / (upper - lower) : RealType(0);
Chris@16:     }
Chris@16:     else if (x <= mode)
Chris@16:     {
Chris@16:       return 2 * (x - lower) / ((upper - lower) * (mode - lower));
Chris@16:     }
Chris@16:     else
Chris@16:     {  // (x > mode)
Chris@16:       return 2 * (upper - x) / ((upper - lower) * (upper - mode));
Chris@16:     }
Chris@16:   } // RealType pdf(const triangular_distribution<RealType, Policy>& dist, const RealType& x)
Chris@16: 
Chris@16:   template <class RealType, class Policy>
Chris@16:   inline RealType cdf(const triangular_distribution<RealType, Policy>& dist, const RealType& x)
Chris@16:   {
Chris@16:     static const char* function = "boost::math::cdf(const triangular_distribution<%1%>&, %1%)";
Chris@16:     RealType lower = dist.lower();
Chris@16:     RealType mode = dist.mode();
Chris@16:     RealType upper = dist.upper();
Chris@16:     RealType result = 0; // of checks.
Chris@16:     if(false == detail::check_triangular(function, lower, mode, upper, &result, Policy()))
Chris@16:     {
Chris@16:       return result;
Chris@16:     }
Chris@16:     if(false == detail::check_triangular_x(function, x, &result, Policy()))
Chris@16:     {
Chris@16:       return result;
Chris@16:     }
Chris@16:     if((x <= lower))
Chris@16:     {
Chris@16:       return 0;
Chris@16:     }
Chris@16:     if (x >= upper)
Chris@16:     {
Chris@16:       return 1;
Chris@16:     }
Chris@16:     // else lower < x < upper
Chris@16:     if (x <= mode)
Chris@16:     {
Chris@16:       return ((x - lower) * (x - lower)) / ((upper - lower) * (mode - lower));
Chris@16:     }
Chris@16:     else
Chris@16:     {
Chris@16:       return 1 - (upper - x) *  (upper - x) / ((upper - lower) * (upper - mode));
Chris@16:     }
Chris@16:   } // RealType cdf(const triangular_distribution<RealType, Policy>& dist, const RealType& x)
Chris@16: 
Chris@16:   template <class RealType, class Policy>
Chris@16:   RealType quantile(const triangular_distribution<RealType, Policy>& dist, const RealType& p)
Chris@16:   {
Chris@16:     BOOST_MATH_STD_USING  // for ADL of std functions (sqrt).
Chris@16:     static const char* function = "boost::math::quantile(const triangular_distribution<%1%>&, %1%)";
Chris@16:     RealType lower = dist.lower();
Chris@16:     RealType mode = dist.mode();
Chris@16:     RealType upper = dist.upper();
Chris@16:     RealType result = 0; // of checks
Chris@16:     if(false == detail::check_triangular(function,lower, mode, upper, &result, Policy()))
Chris@16:     {
Chris@16:       return result;
Chris@16:     }
Chris@16:     if(false == detail::check_probability(function, p, &result, Policy()))
Chris@16:     {
Chris@16:       return result;
Chris@16:     }
Chris@16:     if(p == 0)
Chris@16:     {
Chris@16:       return lower;
Chris@16:     }
Chris@16:     if(p == 1)
Chris@16:     {
Chris@16:       return upper;
Chris@16:     }
Chris@16:     RealType p0 = (mode - lower) / (upper - lower);
Chris@16:     RealType q = 1 - p;
Chris@16:     if (p < p0)
Chris@16:     {
Chris@16:       result = sqrt((upper - lower) * (mode - lower) * p) + lower;
Chris@16:     }
Chris@16:     else if (p == p0)
Chris@16:     {
Chris@16:       result = mode;
Chris@16:     }
Chris@16:     else // p > p0
Chris@16:     {
Chris@16:       result = upper - sqrt((upper - lower) * (upper - mode) * q);
Chris@16:     }
Chris@16:     return result;
Chris@16: 
Chris@16:   } // RealType quantile(const triangular_distribution<RealType, Policy>& dist, const RealType& q)
Chris@16: 
Chris@16:   template <class RealType, class Policy>
Chris@16:   RealType cdf(const complemented2_type<triangular_distribution<RealType, Policy>, RealType>& c)
Chris@16:   {
Chris@16:     static const char* function = "boost::math::cdf(const triangular_distribution<%1%>&, %1%)";
Chris@16:     RealType lower = c.dist.lower();
Chris@16:     RealType mode = c.dist.mode();
Chris@16:     RealType upper = c.dist.upper();
Chris@16:     RealType x = c.param;
Chris@16:     RealType result = 0; // of checks.
Chris@16:     if(false == detail::check_triangular(function, lower, mode, upper, &result, Policy()))
Chris@16:     {
Chris@16:       return result;
Chris@16:     }
Chris@16:     if(false == detail::check_triangular_x(function, x, &result, Policy()))
Chris@16:     {
Chris@16:       return result;
Chris@16:     }
Chris@16:     if (x <= lower)
Chris@16:     {
Chris@16:       return 1;
Chris@16:     }
Chris@16:     if (x >= upper)
Chris@16:     {
Chris@16:       return 0;
Chris@16:     }
Chris@16:     if (x <= mode)
Chris@16:     {
Chris@16:       return 1 - ((x - lower) * (x - lower)) / ((upper - lower) * (mode - lower));
Chris@16:     }
Chris@16:     else
Chris@16:     {
Chris@16:       return (upper - x) *  (upper - x) / ((upper - lower) * (upper - mode));
Chris@16:     }
Chris@16:   } // RealType cdf(const complemented2_type<triangular_distribution<RealType, Policy>, RealType>& c)
Chris@16: 
Chris@16:   template <class RealType, class Policy>
Chris@16:   RealType quantile(const complemented2_type<triangular_distribution<RealType, Policy>, RealType>& c)
Chris@16:   {
Chris@16:     BOOST_MATH_STD_USING  // Aid ADL for sqrt.
Chris@16:     static const char* function = "boost::math::quantile(const triangular_distribution<%1%>&, %1%)";
Chris@16:     RealType l = c.dist.lower();
Chris@16:     RealType m = c.dist.mode();
Chris@16:     RealType u = c.dist.upper();
Chris@16:     RealType q = c.param; // probability 0 to 1.
Chris@16:     RealType result = 0; // of checks.
Chris@16:     if(false == detail::check_triangular(function, l, m, u, &result, Policy()))
Chris@16:     {
Chris@16:       return result;
Chris@16:     }
Chris@16:     if(false == detail::check_probability(function, q, &result, Policy()))
Chris@16:     {
Chris@16:       return result;
Chris@16:     }
Chris@16:     if(q == 0)
Chris@16:     {
Chris@16:       return u;
Chris@16:     }
Chris@16:     if(q == 1)
Chris@16:     {
Chris@16:       return l;
Chris@16:     }
Chris@16:     RealType lower = c.dist.lower();
Chris@16:     RealType mode = c.dist.mode();
Chris@16:     RealType upper = c.dist.upper();
Chris@16: 
Chris@16:     RealType p = 1 - q;
Chris@16:     RealType p0 = (mode - lower) / (upper - lower);
Chris@16:     if(p < p0)
Chris@16:     {
Chris@16:       RealType s = (upper - lower) * (mode - lower);
Chris@16:       s *= p;
Chris@16:       result = sqrt((upper - lower) * (mode - lower) * p) + lower;
Chris@16:     }
Chris@16:     else if (p == p0)
Chris@16:     {
Chris@16:       result = mode;
Chris@16:     }
Chris@16:     else // p > p0
Chris@16:     {
Chris@16:       result = upper - sqrt((upper - lower) * (upper - mode) * q);
Chris@16:     }
Chris@16:     return result;
Chris@16:   } // RealType quantile(const complemented2_type<triangular_distribution<RealType, Policy>, RealType>& c)
Chris@16: 
Chris@16:   template <class RealType, class Policy>
Chris@16:   inline RealType mean(const triangular_distribution<RealType, Policy>& dist)
Chris@16:   {
Chris@16:     static const char* function = "boost::math::mean(const triangular_distribution<%1%>&)";
Chris@16:     RealType lower = dist.lower();
Chris@16:     RealType mode = dist.mode();
Chris@16:     RealType upper = dist.upper();
Chris@16:     RealType result = 0;  // of checks.
Chris@16:     if(false == detail::check_triangular(function, lower, mode, upper, &result, Policy()))
Chris@16:     {
Chris@16:       return result;
Chris@16:     }
Chris@16:     return (lower + upper + mode) / 3;
Chris@16:   } // RealType mean(const triangular_distribution<RealType, Policy>& dist)
Chris@16: 
Chris@16: 
Chris@16:   template <class RealType, class Policy>
Chris@16:   inline RealType variance(const triangular_distribution<RealType, Policy>& dist)
Chris@16:   {
Chris@16:     static const char* function = "boost::math::mean(const triangular_distribution<%1%>&)";
Chris@16:     RealType lower = dist.lower();
Chris@16:     RealType mode = dist.mode();
Chris@16:     RealType upper = dist.upper();
Chris@16:     RealType result = 0; // of checks.
Chris@16:     if(false == detail::check_triangular(function, lower, mode, upper, &result, Policy()))
Chris@16:     {
Chris@16:       return result;
Chris@16:     }
Chris@16:     return (lower * lower + upper * upper + mode * mode - lower * upper - lower * mode - upper * mode) / 18;
Chris@16:   } // RealType variance(const triangular_distribution<RealType, Policy>& dist)
Chris@16: 
Chris@16:   template <class RealType, class Policy>
Chris@16:   inline RealType mode(const triangular_distribution<RealType, Policy>& dist)
Chris@16:   {
Chris@16:     static const char* function = "boost::math::mode(const triangular_distribution<%1%>&)";
Chris@16:     RealType mode = dist.mode();
Chris@16:     RealType result = 0; // of checks.
Chris@16:     if(false == detail::check_triangular_mode(function, mode, &result, Policy()))
Chris@16:     { // This should never happen!
Chris@16:       return result;
Chris@16:     }
Chris@16:     return mode;
Chris@16:   } // RealType mode
Chris@16: 
Chris@16:   template <class RealType, class Policy>
Chris@16:   inline RealType median(const triangular_distribution<RealType, Policy>& dist)
Chris@16:   {
Chris@16:     BOOST_MATH_STD_USING // ADL of std functions.
Chris@16:     static const char* function = "boost::math::median(const triangular_distribution<%1%>&)";
Chris@16:     RealType mode = dist.mode();
Chris@16:     RealType result = 0; // of checks.
Chris@16:     if(false == detail::check_triangular_mode(function, mode, &result, Policy()))
Chris@16:     { // This should never happen!
Chris@16:       return result;
Chris@16:     }
Chris@16:     RealType lower = dist.lower();
Chris@16:     RealType upper = dist.upper();
Chris@16:     if (mode < (upper - lower) / 2)
Chris@16:     {
Chris@16:       return lower + sqrt((upper - lower) * (mode - lower)) / constants::root_two<RealType>();
Chris@16:     }
Chris@16:     else
Chris@16:     {
Chris@16:       return upper - sqrt((upper - lower) * (upper - mode)) / constants::root_two<RealType>();
Chris@16:     }
Chris@16:   } // RealType mode
Chris@16: 
Chris@16:   template <class RealType, class Policy>
Chris@16:   inline RealType skewness(const triangular_distribution<RealType, Policy>& dist)
Chris@16:   {
Chris@16:     BOOST_MATH_STD_USING  // for ADL of std functions
Chris@16:     using namespace boost::math::constants; // for root_two
Chris@16:     static const char* function = "boost::math::skewness(const triangular_distribution<%1%>&)";
Chris@16: 
Chris@16:     RealType lower = dist.lower();
Chris@16:     RealType mode = dist.mode();
Chris@16:     RealType upper = dist.upper();
Chris@16:     RealType result = 0; // of checks.
Chris@16:     if(false == boost::math::detail::check_triangular(function,lower, mode, upper, &result, Policy()))
Chris@16:     {
Chris@16:       return result;
Chris@16:     }
Chris@16:     return root_two<RealType>() * (lower + upper - 2 * mode) * (2 * lower - upper - mode) * (lower - 2 * upper + mode) /
Chris@16:       (5 * pow((lower * lower + upper + upper + mode * mode - lower * upper - lower * mode - upper * mode), RealType(3)/RealType(2)));
Chris@16:   } // RealType skewness(const triangular_distribution<RealType, Policy>& dist)
Chris@16: 
Chris@16:   template <class RealType, class Policy>
Chris@16:   inline RealType kurtosis(const triangular_distribution<RealType, Policy>& dist)
Chris@16:   { // These checks may be belt and braces as should have been checked on construction?
Chris@16:     static const char* function = "boost::math::kurtosis(const triangular_distribution<%1%>&)";
Chris@16:     RealType lower = dist.lower();
Chris@16:     RealType upper = dist.upper();
Chris@16:     RealType mode = dist.mode();
Chris@16:     RealType result = 0;  // of checks.
Chris@16:     if(false == detail::check_triangular(function,lower, mode, upper, &result, Policy()))
Chris@16:     {
Chris@16:       return result;
Chris@16:     }
Chris@16:     return static_cast<RealType>(12)/5; //  12/5 = 2.4;
Chris@16:   } // RealType kurtosis_excess(const triangular_distribution<RealType, Policy>& dist)
Chris@16: 
Chris@16:   template <class RealType, class Policy>
Chris@16:   inline RealType kurtosis_excess(const triangular_distribution<RealType, Policy>& dist)
Chris@16:   { // These checks may be belt and braces as should have been checked on construction?
Chris@16:     static const char* function = "boost::math::kurtosis_excess(const triangular_distribution<%1%>&)";
Chris@16:     RealType lower = dist.lower();
Chris@16:     RealType upper = dist.upper();
Chris@16:     RealType mode = dist.mode();
Chris@16:     RealType result = 0;  // of checks.
Chris@16:     if(false == detail::check_triangular(function,lower, mode, upper, &result, Policy()))
Chris@16:     {
Chris@16:       return result;
Chris@16:     }
Chris@16:     return static_cast<RealType>(-3)/5; // - 3/5 = -0.6
Chris@16:     // Assuming mathworld really means kurtosis excess?  Wikipedia now corrected to match this.
Chris@16:   }
Chris@16: 
Chris@16: } // namespace math
Chris@16: } // namespace boost
Chris@16: 
Chris@16: // This include must be at the end, *after* the accessors
Chris@16: // for this distribution have been defined, in order to
Chris@16: // keep compilers that support two-phase lookup happy.
Chris@16: #include <boost/math/distributions/detail/derived_accessors.hpp>
Chris@16: 
Chris@16: #endif // BOOST_STATS_TRIANGULAR_HPP
Chris@16: 
Chris@16: 
Chris@16: