| // Copyright Thijs van den Berg, 2008. |
| // Copyright John Maddock 2008. |
| // Copyright Paul A. Bristow 2008. |
| |
| // 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) |
| |
| // This module implements the Laplace distribution. |
| // Weisstein, Eric W. "Laplace Distribution." From MathWorld--A Wolfram Web Resource. |
| // http://mathworld.wolfram.com/LaplaceDistribution.html |
| // http://en.wikipedia.org/wiki/Laplace_distribution |
| // |
| // Abramowitz and Stegun 1972, p 930 |
| // http://www.math.sfu.ca/~cbm/aands/page_930.htm |
| |
| #ifndef BOOST_STATS_LAPLACE_HPP |
| #define BOOST_STATS_LAPLACE_HPP |
| |
| #include <boost/math/distributions/detail/common_error_handling.hpp> |
| #include <boost/math/distributions/complement.hpp> |
| #include <boost/math/constants/constants.hpp> |
| #include <limits> |
| |
| namespace boost{ namespace math{ |
| |
| template <class RealType = double, class Policy = policies::policy<> > |
| class laplace_distribution |
| { |
| public: |
| // ---------------------------------- |
| // public Types |
| // ---------------------------------- |
| typedef RealType value_type; |
| typedef Policy policy_type; |
| |
| // ---------------------------------- |
| // Constructor(s) |
| // ---------------------------------- |
| laplace_distribution(RealType location = 0, RealType scale = 1) |
| : m_location(location), m_scale(scale) |
| { |
| RealType result; |
| check_parameters("boost::math::laplace_distribution<%1%>::laplace_distribution()", &result); |
| } |
| |
| |
| // ---------------------------------- |
| // Public functions |
| // ---------------------------------- |
| |
| RealType location() const |
| { |
| return m_location; |
| } |
| |
| RealType scale() const |
| { |
| return m_scale; |
| } |
| |
| bool check_parameters(const char* function, RealType* result) const |
| { |
| if(false == detail::check_scale(function, m_scale, result, Policy())) return false; |
| if(false == detail::check_location(function, m_location, result, Policy())) return false; |
| return true; |
| } |
| |
| |
| private: |
| RealType m_location; |
| RealType m_scale; |
| |
| }; // class laplace_distribution |
| |
| |
| |
| // |
| // Convenient type synonym |
| // |
| typedef laplace_distribution<double> laplace; |
| |
| // |
| // Non member functions |
| // |
| template <class RealType, class Policy> |
| inline const std::pair<RealType, RealType> range(const laplace_distribution<RealType, Policy>&) |
| { |
| using boost::math::tools::max_value; |
| return std::pair<RealType, RealType>(-max_value<RealType>(), max_value<RealType>()); |
| } |
| |
| template <class RealType, class Policy> |
| inline const std::pair<RealType, RealType> support(const laplace_distribution<RealType, Policy>&) |
| { |
| using boost::math::tools::max_value; |
| return std::pair<RealType, RealType>(-max_value<RealType>(), max_value<RealType>()); |
| } |
| |
| template <class RealType, class Policy> |
| inline RealType pdf(const laplace_distribution<RealType, Policy>& dist, const RealType& x) |
| { |
| BOOST_MATH_STD_USING // for ADL of std functions |
| |
| // Checking function argument |
| RealType result; |
| const char* function = "boost::math::pdf(const laplace_distribution<%1%>&, %1%))"; |
| if (false == dist.check_parameters(function, &result)) return result; |
| if (false == detail::check_x(function, x, &result, Policy())) return result; |
| |
| // Special pdf values |
| if((boost::math::isinf)(x)) |
| return 0; // pdf + and - infinity is zero. |
| |
| // General case |
| RealType scale( dist.scale() ); |
| RealType location( dist.location() ); |
| |
| RealType exponent = x - location; |
| if (exponent>0) exponent = -exponent; |
| exponent /= scale; |
| |
| result = exp(exponent); |
| result /= 2 * scale; |
| |
| return result; |
| } // pdf |
| |
| template <class RealType, class Policy> |
| inline RealType cdf(const laplace_distribution<RealType, Policy>& dist, const RealType& x) |
| { |
| BOOST_MATH_STD_USING // for ADL of std functions |
| |
| // Checking function argument |
| RealType result; |
| const char* function = "boost::math::cdf(const laplace_distribution<%1%>&, %1%)"; |
| if (false == dist.check_parameters(function, &result)) return result; |
| if (false == detail::check_x(function, x, &result, Policy())) return result; |
| |
| // Special cdf values |
| if((boost::math::isinf)(x)) |
| { |
| if(x < 0) return 0; // -infinity |
| return 1; // + infinity |
| } |
| |
| // General cdf values |
| RealType scale( dist.scale() ); |
| RealType location( dist.location() ); |
| |
| if (x < location) |
| result = exp( (x-location)/scale )/2; |
| else |
| result = 1 - exp( (location-x)/scale )/2; |
| |
| return result; |
| } // cdf |
| |
| |
| template <class RealType, class Policy> |
| inline RealType quantile(const laplace_distribution<RealType, Policy>& dist, const RealType& p) |
| { |
| BOOST_MATH_STD_USING // for ADL of std functions |
| |
| // Checking function argument |
| RealType result; |
| const char* function = "boost::math::quantile(const laplace_distribution<%1%>&, %1%)"; |
| if (false == dist.check_parameters(function, &result)) return result; |
| if(false == detail::check_probability(function, p, &result, Policy())) return result; |
| |
| // extreme values |
| if(p == 0) return -std::numeric_limits<RealType>::infinity(); |
| if(p == 1) return std::numeric_limits<RealType>::infinity(); |
| |
| // Calculate Quantile |
| RealType scale( dist.scale() ); |
| RealType location( dist.location() ); |
| |
| if (p - 0.5 < 0.0) |
| result = location + scale*log( static_cast<RealType>(p*2) ); |
| else |
| result = location - scale*log( static_cast<RealType>(-p*2 + 2) ); |
| |
| return result; |
| } // quantile |
| |
| |
| template <class RealType, class Policy> |
| inline RealType cdf(const complemented2_type<laplace_distribution<RealType, Policy>, RealType>& c) |
| { |
| BOOST_MATH_STD_USING // for ADL of std functions |
| |
| RealType scale = c.dist.scale(); |
| RealType location = c.dist.location(); |
| RealType x = c.param; |
| |
| // Checking function argument |
| RealType result; |
| const char* function = "boost::math::cdf(const complemented2_type<laplace_distribution<%1%>, %1%>&)"; |
| if(false == detail::check_x(function, x, &result, Policy()))return result; |
| |
| // Calculate cdf |
| |
| // Special cdf value |
| if((boost::math::isinf)(x)) |
| { |
| if(x < 0) return 1; // cdf complement -infinity is unity. |
| return 0; // cdf complement +infinity is zero |
| } |
| |
| // Cdf interval value |
| if (-x < location) |
| result = exp( (-x-location)/scale )/2; |
| else |
| result = 1 - exp( (location+x)/scale )/2; |
| |
| return result; |
| } // cdf complement |
| |
| |
| template <class RealType, class Policy> |
| inline RealType quantile(const complemented2_type<laplace_distribution<RealType, Policy>, RealType>& c) |
| { |
| BOOST_MATH_STD_USING // for ADL of std functions |
| |
| // Calculate quantile |
| RealType scale = c.dist.scale(); |
| RealType location = c.dist.location(); |
| RealType q = c.param; |
| |
| // Checking function argument |
| RealType result; |
| const char* function = "quantile(const complemented2_type<laplace_distribution<%1%>, %1%>&)"; |
| if(false == detail::check_probability(function, q, &result, Policy())) return result; |
| |
| |
| // extreme values |
| if(q == 0) return std::numeric_limits<RealType>::infinity(); |
| if(q == 1) return -std::numeric_limits<RealType>::infinity(); |
| |
| if (0.5 - q < 0.0) |
| result = location + scale*log( static_cast<RealType>(-q*2 + 2) ); |
| else |
| result = location - scale*log( static_cast<RealType>(q*2) ); |
| |
| |
| return result; |
| } // quantile |
| |
| template <class RealType, class Policy> |
| inline RealType mean(const laplace_distribution<RealType, Policy>& dist) |
| { |
| return dist.location(); |
| } |
| |
| template <class RealType, class Policy> |
| inline RealType standard_deviation(const laplace_distribution<RealType, Policy>& dist) |
| { |
| return constants::root_two<RealType>() * dist.scale(); |
| } |
| |
| template <class RealType, class Policy> |
| inline RealType mode(const laplace_distribution<RealType, Policy>& dist) |
| { |
| return dist.location(); |
| } |
| |
| template <class RealType, class Policy> |
| inline RealType median(const laplace_distribution<RealType, Policy>& dist) |
| { |
| return dist.location(); |
| } |
| |
| template <class RealType, class Policy> |
| inline RealType skewness(const laplace_distribution<RealType, Policy>& /*dist*/) |
| { |
| return 0; |
| } |
| |
| template <class RealType, class Policy> |
| inline RealType kurtosis(const laplace_distribution<RealType, Policy>& /*dist*/) |
| { |
| return 6; |
| } |
| |
| template <class RealType, class Policy> |
| inline RealType kurtosis_excess(const laplace_distribution<RealType, Policy>& /*dist*/) |
| { |
| return 3; |
| } |
| |
| } // 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_LAPLACE_HPP |
| |
| |