Chris@16: //  Copyright John Maddock 2006.
Chris@16: //  Copyright Paul A. Bristow 2006.
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: // TODO deal with infinity as special better - or remove.
Chris@16: //
Chris@16: 
Chris@16: #ifndef BOOST_STATS_UNIFORM_HPP
Chris@16: #define BOOST_STATS_UNIFORM_HPP
Chris@16: 
Chris@16: // http://www.itl.nist.gov/div898/handbook/eda/section3/eda3668.htm
Chris@16: // http://mathworld.wolfram.com/UniformDistribution.html
Chris@16: // http://documents.wolfram.com/calculationcenter/v2/Functions/ListsMatrices/Statistics/UniformDistribution.html
Chris@16: // http://en.wikipedia.org/wiki/Uniform_distribution_%28continuous%29
Chris@16: 
Chris@16: #include <boost/math/distributions/fwd.hpp>
Chris@16: #include <boost/math/distributions/detail/common_error_handling.hpp>
Chris@16: #include <boost/math/distributions/complement.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_uniform_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.
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_uniform_lower(
Chris@16: 
Chris@16:     template <class RealType, class Policy>
Chris@16:     inline bool check_uniform_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.
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_uniform_upper(
Chris@16: 
Chris@16:     template <class RealType, class Policy>
Chris@16:     inline bool check_uniform_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..
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_uniform_x
Chris@16: 
Chris@16:     template <class RealType, class Policy>
Chris@16:     inline bool check_uniform(
Chris@16:       const char* function,
Chris@16:       RealType lower,
Chris@16:       RealType upper,
Chris@16:       RealType* result, const Policy& pol)
Chris@16:     {
Chris@16:       if((check_uniform_lower(function, lower, result, pol) == false)
Chris@16:         || (check_uniform_upper(function, upper, result, pol) == false))
Chris@16:       {
Chris@16:         return false;
Chris@16:       }
Chris@16:       else if (lower >= upper) // If lower == upper then 1 / (upper-lower) = 1/0 = +infinity!
Chris@16:       { // upper and lower have been checked before, so must be 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:       { // All OK,
Chris@16:         return true;
Chris@16:       }
Chris@16:     } // bool check_uniform(
Chris@16: 
Chris@16:   } // namespace detail
Chris@16: 
Chris@16:   template <class RealType = double, class Policy = policies::policy<> >
Chris@16:   class uniform_distribution
Chris@16:   {
Chris@16:   public:
Chris@16:     typedef RealType value_type;
Chris@16:     typedef Policy policy_type;
Chris@16: 
Chris@16:     uniform_distribution(RealType l_lower = 0, RealType l_upper = 1) // Constructor.
Chris@16:       : m_lower(l_lower), m_upper(l_upper) // Default is standard uniform distribution.
Chris@16:     {
Chris@16:       RealType result;
Chris@16:       detail::check_uniform("boost::math::uniform_distribution<%1%>::uniform_distribution", l_lower, 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: 
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_upper;  // distribution upper aka b.
Chris@16:   }; // class uniform_distribution
Chris@16: 
Chris@16:   typedef uniform_distribution<double> uniform;
Chris@16: 
Chris@16:   template <class RealType, class Policy>
Chris@16:   inline const std::pair<RealType, RealType> range(const uniform_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>()); // - to + 'infinity'.
Chris@16:      // Note RealType infinity is NOT permitted, only max_value.
Chris@16:   }
Chris@16: 
Chris@16:   template <class RealType, class Policy>
Chris@16:   inline const std::pair<RealType, RealType> support(const uniform_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:      using boost::math::tools::max_value;
Chris@16:      return std::pair<RealType, RealType>(dist.lower(),  dist.upper());
Chris@16:   }
Chris@16: 
Chris@16:   template <class RealType, class Policy>
Chris@16:   inline RealType pdf(const uniform_distribution<RealType, Policy>& dist, const RealType& x)
Chris@16:   {
Chris@16:     RealType lower = dist.lower();
Chris@16:     RealType upper = dist.upper();
Chris@16:     RealType result = 0; // of checks.
Chris@16:     if(false == detail::check_uniform("boost::math::pdf(const uniform_distribution<%1%>&, %1%)", lower, upper, &result, Policy()))
Chris@16:     {
Chris@16:       return result;
Chris@16:     }
Chris@16:     if(false == detail::check_uniform_x("boost::math::pdf(const uniform_distribution<%1%>&, %1%)", x, &result, Policy()))
Chris@16:     {
Chris@16:       return result;
Chris@16:     }
Chris@16: 
Chris@16:     if((x < lower) || (x > upper) )
Chris@16:     {
Chris@16:       return 0;
Chris@16:     }
Chris@16:     else
Chris@16:     {
Chris@16:       return 1 / (upper - lower);
Chris@16:     }
Chris@16:   } // RealType pdf(const uniform_distribution<RealType, Policy>& dist, const RealType& x)
Chris@16: 
Chris@16:   template <class RealType, class Policy>
Chris@16:   inline RealType cdf(const uniform_distribution<RealType, Policy>& dist, const RealType& x)
Chris@16:   {
Chris@16:     RealType lower = dist.lower();
Chris@16:     RealType upper = dist.upper();
Chris@16:     RealType result = 0; // of checks.
Chris@16:     if(false == detail::check_uniform("boost::math::cdf(const uniform_distribution<%1%>&, %1%)",lower, upper, &result, Policy()))
Chris@16:     {
Chris@16:       return result;
Chris@16:     }
Chris@16:     if(false == detail::check_uniform_x("boost::math::cdf(const uniform_distribution<%1%>&, %1%)", 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:     return (x - lower) / (upper - lower); // lower <= x <= upper
Chris@16:   } // RealType cdf(const uniform_distribution<RealType, Policy>& dist, const RealType& x)
Chris@16: 
Chris@16:   template <class RealType, class Policy>
Chris@16:   inline RealType quantile(const uniform_distribution<RealType, Policy>& dist, const RealType& p)
Chris@16:   {
Chris@16:     RealType lower = dist.lower();
Chris@16:     RealType upper = dist.upper();
Chris@16:     RealType result = 0; // of checks
Chris@16:     if(false == detail::check_uniform("boost::math::quantile(const uniform_distribution<%1%>&, %1%)",lower, upper, &result, Policy()))
Chris@16:     {
Chris@16:       return result;
Chris@16:     }
Chris@16:     if(false == detail::check_probability("boost::math::quantile(const uniform_distribution<%1%>&, %1%)", 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:     return p * (upper - lower) + lower;
Chris@16:   } // RealType quantile(const uniform_distribution<RealType, Policy>& dist, const RealType& p)
Chris@16: 
Chris@16:   template <class RealType, class Policy>
Chris@16:   inline RealType cdf(const complemented2_type<uniform_distribution<RealType, Policy>, RealType>& c)
Chris@16:   {
Chris@16:     RealType lower = c.dist.lower();
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_uniform("boost::math::cdf(const uniform_distribution<%1%>&, %1%)", lower, upper, &result, Policy()))
Chris@16:     {
Chris@16:       return result;
Chris@16:     }
Chris@16:     if(false == detail::check_uniform_x("boost::math::cdf(const uniform_distribution<%1%>&, %1%)", 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:     return (upper - x) / (upper - lower);
Chris@16:   } // RealType cdf(const complemented2_type<uniform_distribution<RealType, Policy>, RealType>& c)
Chris@16: 
Chris@16:   template <class RealType, class Policy>
Chris@16:   inline RealType quantile(const complemented2_type<uniform_distribution<RealType, Policy>, RealType>& c)
Chris@16:   {
Chris@16:     RealType lower = c.dist.lower();
Chris@16:     RealType upper = c.dist.upper();
Chris@16:     RealType q = c.param;
Chris@16:     RealType result = 0; // of checks.
Chris@16:     if(false == detail::check_uniform("boost::math::quantile(const uniform_distribution<%1%>&, %1%)", lower, upper, &result, Policy()))
Chris@16:     {
Chris@16:       return result;
Chris@16:     }
Chris@16:     if(false == detail::check_probability("boost::math::quantile(const uniform_distribution<%1%>&, %1%)", q, &result, Policy()))
Chris@16:       if(q == 0)
Chris@16:       {
Chris@16:         return lower;
Chris@16:       }
Chris@16:       if(q == 1)
Chris@16:       {
Chris@16:         return upper;
Chris@16:       }
Chris@16:       return -q * (upper - lower) + upper;
Chris@16:   } // RealType quantile(const complemented2_type<uniform_distribution<RealType, Policy>, RealType>& c)
Chris@16: 
Chris@16:   template <class RealType, class Policy>
Chris@16:   inline RealType mean(const uniform_distribution<RealType, Policy>& dist)
Chris@16:   {
Chris@16:     RealType lower = dist.lower();
Chris@16:     RealType upper = dist.upper();
Chris@16:     RealType result = 0;  // of checks.
Chris@16:     if(false == detail::check_uniform("boost::math::mean(const uniform_distribution<%1%>&)", lower, upper, &result, Policy()))
Chris@16:     {
Chris@16:       return result;
Chris@16:     }
Chris@16:     return (lower + upper ) / 2;
Chris@16:   } // RealType mean(const uniform_distribution<RealType, Policy>& dist)
Chris@16: 
Chris@16:   template <class RealType, class Policy>
Chris@16:   inline RealType variance(const uniform_distribution<RealType, Policy>& dist)
Chris@16:   {
Chris@16:     RealType lower = dist.lower();
Chris@16:     RealType upper = dist.upper();
Chris@16:     RealType result = 0; // of checks.
Chris@16:     if(false == detail::check_uniform("boost::math::variance(const uniform_distribution<%1%>&)", lower, upper, &result, Policy()))
Chris@16:     {
Chris@16:       return result;
Chris@16:     }
Chris@16:     return (upper - lower) * ( upper - lower) / 12;
Chris@16:     // for standard uniform = 0.833333333333333333333333333333333333333333;
Chris@16:   } // RealType variance(const uniform_distribution<RealType, Policy>& dist)
Chris@16: 
Chris@16:   template <class RealType, class Policy>
Chris@16:   inline RealType mode(const uniform_distribution<RealType, Policy>& dist)
Chris@16:   {
Chris@16:     RealType lower = dist.lower();
Chris@16:     RealType upper = dist.upper();
Chris@16:     RealType result = 0; // of checks.
Chris@16:     if(false == detail::check_uniform("boost::math::mode(const uniform_distribution<%1%>&)", lower, upper, &result, Policy()))
Chris@16:     {
Chris@16:       return result;
Chris@16:     }
Chris@16:     result = lower; // Any value [lower, upper] but arbitrarily choose lower.
Chris@16:     return result;
Chris@16:   }
Chris@16: 
Chris@16:   template <class RealType, class Policy>
Chris@16:   inline RealType median(const uniform_distribution<RealType, Policy>& dist)
Chris@16:   {
Chris@16:     RealType lower = dist.lower();
Chris@16:     RealType upper = dist.upper();
Chris@16:     RealType result = 0; // of checks.
Chris@16:     if(false == detail::check_uniform("boost::math::median(const uniform_distribution<%1%>&)", lower, upper, &result, Policy()))
Chris@16:     {
Chris@16:       return result;
Chris@16:     }
Chris@16:     return (lower + upper) / 2; //
Chris@16:   }
Chris@16:   template <class RealType, class Policy>
Chris@16:   inline RealType skewness(const uniform_distribution<RealType, Policy>& dist)
Chris@16:   {
Chris@16:     RealType lower = dist.lower();
Chris@16:     RealType upper = dist.upper();
Chris@16:     RealType result = 0; // of checks.
Chris@16:     if(false == detail::check_uniform("boost::math::skewness(const uniform_distribution<%1%>&)",lower, upper, &result, Policy()))
Chris@16:     {
Chris@16:       return result;
Chris@16:     }
Chris@16:     return 0;
Chris@16:   } // RealType skewness(const uniform_distribution<RealType, Policy>& dist)
Chris@16: 
Chris@16:   template <class RealType, class Policy>
Chris@16:   inline RealType kurtosis_excess(const uniform_distribution<RealType, Policy>& dist)
Chris@16:   {
Chris@16:     RealType lower = dist.lower();
Chris@16:     RealType upper = dist.upper();
Chris@16:     RealType result = 0;  // of checks.
Chris@16:     if(false == detail::check_uniform("boost::math::kurtosis_execess(const uniform_distribution<%1%>&)", lower, upper, &result, Policy()))
Chris@16:     {
Chris@16:       return result;
Chris@16:     }
Chris@16:     return static_cast<RealType>(-6)/5; //  -6/5 = -1.2;
Chris@16:   } // RealType kurtosis_excess(const uniform_distribution<RealType, Policy>& dist)
Chris@16: 
Chris@16:   template <class RealType, class Policy>
Chris@16:   inline RealType kurtosis(const uniform_distribution<RealType, Policy>& dist)
Chris@16:   {
Chris@16:     return kurtosis_excess(dist) + 3;
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_UNIFORM_HPP
Chris@16: 
Chris@16: 
Chris@16: