| // 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.
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| // http://mathworld.wolfram.com/LaplaceDistribution.html
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| // http://en.wikipedia.org/wiki/Laplace_distribution
|
| //
|
| // Abramowitz and Stegun 1972, p 930
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| // http://www.math.sfu.ca/~cbm/aands/page_930.htm
|
|
|
| #ifndef BOOST_STATS_LAPLACE_HPP
|
| #define BOOST_STATS_LAPLACE_HPP
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|
|
| #include <boost/math/distributions/detail/common_error_handling.hpp>
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| #include <boost/math/distributions/complement.hpp>
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| #include <boost/math/constants/constants.hpp>
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| #include <limits>
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|
|
| namespace boost{ namespace math{
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|
|
| template <class RealType = double, class Policy = policies::policy<> >
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| class laplace_distribution
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| {
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| public:
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| // ----------------------------------
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| // public Types
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| // ----------------------------------
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| typedef RealType value_type;
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| typedef Policy policy_type;
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|
|
| // ----------------------------------
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| // Constructor(s)
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| // ----------------------------------
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| laplace_distribution(RealType location = 0, RealType scale = 1)
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| : m_location(location), m_scale(scale)
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| {
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| RealType result;
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| check_parameters("boost::math::laplace_distribution<%1%>::laplace_distribution()", &result);
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| }
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|
|
|
|
| // ----------------------------------
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| // Public functions
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| // ----------------------------------
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|
|
| RealType location() const
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| {
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| return m_location;
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| }
|
|
|
| RealType scale() const
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| {
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| return m_scale;
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| }
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|
|
| bool check_parameters(const char* function, RealType* result) const
|
| {
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| if(false == detail::check_scale(function, m_scale, result, Policy())) return false;
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| if(false == detail::check_location(function, m_location, result, Policy())) return false;
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| return true;
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| }
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|
|
| private:
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| RealType m_location;
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| RealType m_scale;
|
| }; // class laplace_distribution
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|
|
| //
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| // Convenient type synonym for double
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| typedef laplace_distribution<double> laplace;
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|
|
| //
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| // Non member functions
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| template <class RealType, class Policy>
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| inline const std::pair<RealType, RealType> range(const laplace_distribution<RealType, Policy>&)
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| {
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| using boost::math::tools::max_value;
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| return std::pair<RealType, RealType>(-max_value<RealType>(), max_value<RealType>());
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| }
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|
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| template <class RealType, class Policy>
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| inline const std::pair<RealType, RealType> support(const laplace_distribution<RealType, Policy>&)
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| {
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| using boost::math::tools::max_value;
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| return std::pair<RealType, RealType>(-max_value<RealType>(), max_value<RealType>());
|
| }
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|
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| template <class RealType, class Policy>
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| inline RealType pdf(const laplace_distribution<RealType, Policy>& dist, const RealType& x)
|
| {
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| BOOST_MATH_STD_USING // for ADL of std functions
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|
|
| // Checking function argument
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| RealType result;
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| const char* function = "boost::math::pdf(const laplace_distribution<%1%>&, %1%))";
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| if (false == dist.check_parameters(function, &result)) return result;
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| if (false == detail::check_x(function, x, &result, Policy())) return result;
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|
|
| // Special pdf values
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| if((boost::math::isinf)(x))
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| return 0; // pdf + and - infinity is zero.
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|
|
| // General case
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| RealType scale( dist.scale() );
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| RealType location( dist.location() );
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|
|
| RealType exponent = x - location;
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| if (exponent>0) exponent = -exponent;
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| exponent /= scale;
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|
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| result = exp(exponent);
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| result /= 2 * scale;
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|
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| return result;
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| } // pdf
|
|
|
| template <class RealType, class Policy>
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| inline RealType cdf(const laplace_distribution<RealType, Policy>& dist, const RealType& x)
|
| {
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| BOOST_MATH_STD_USING // for ADL of std functions
|
|
|
| // Checking function argument
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| RealType result;
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| const char* function = "boost::math::cdf(const laplace_distribution<%1%>&, %1%)";
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| if (false == dist.check_parameters(function, &result)) return result;
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| if (false == detail::check_x(function, x, &result, Policy())) return result;
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|
|
| // Special cdf values:
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| if((boost::math::isinf)(x))
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| {
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| if(x < 0) return 0; // -infinity
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| return 1; // + infinity
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| }
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|
|
| // General cdf values
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| RealType scale( dist.scale() );
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| RealType location( dist.location() );
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|
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| if (x < location)
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| result = exp( (x-location)/scale )/2;
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| else
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| result = 1 - exp( (location-x)/scale )/2;
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|
|
| return result;
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| } // cdf
|
|
|
|
|
| template <class RealType, class Policy>
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| inline RealType quantile(const laplace_distribution<RealType, Policy>& dist, const RealType& p)
|
| {
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| BOOST_MATH_STD_USING // for ADL of std functions.
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|
|
| // Checking function argument
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| RealType result;
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| const char* function = "boost::math::quantile(const laplace_distribution<%1%>&, %1%)";
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| if (false == dist.check_parameters(function, &result)) return result;
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| if(false == detail::check_probability(function, p, &result, Policy())) return result;
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|
|
| // Extreme values of p:
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| if(p == 0)
|
| {
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| result = policies::raise_overflow_error<RealType>(function,
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| "probability parameter is 0, but must be > 0!", Policy());
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| return -result; // -std::numeric_limits<RealType>::infinity();
|
| }
|
|
|
| if(p == 1)
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| {
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| result = policies::raise_overflow_error<RealType>(function,
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| "probability parameter is 1, but must be < 1!", Policy());
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| return result; // std::numeric_limits<RealType>::infinity();
|
| }
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| // Calculate Quantile
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| RealType scale( dist.scale() );
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| RealType location( dist.location() );
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|
|
| if (p - 0.5 < 0.0)
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| result = location + scale*log( static_cast<RealType>(p*2) );
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| else
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| result = location - scale*log( static_cast<RealType>(-p*2 + 2) );
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|
|
| return result;
|
| } // quantile
|
|
|
|
|
| template <class RealType, class Policy>
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| inline RealType cdf(const complemented2_type<laplace_distribution<RealType, Policy>, RealType>& c)
|
| {
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| BOOST_MATH_STD_USING // for ADL of std functions
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|
|
| RealType scale = c.dist.scale();
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| RealType location = c.dist.location();
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| RealType x = c.param;
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|
|
| // Checking function argument
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| RealType result;
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| const char* function = "boost::math::cdf(const complemented2_type<laplace_distribution<%1%>, %1%>&)";
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| if(false == detail::check_x(function, x, &result, Policy()))return result;
|
|
|
| // Calculate cdf
|
|
|
| // Special cdf value
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| if((boost::math::isinf)(x))
|
| {
|
| if(x < 0) return 1; // cdf complement -infinity is unity.
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| return 0; // cdf complement +infinity is zero
|
| }
|
|
|
| // Cdf interval value
|
| if (-x < location)
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| result = exp( (-x-location)/scale )/2;
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| else
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| result = 1 - exp( (location+x)/scale )/2;
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|
|
| return result;
|
| } // cdf complement
|
|
|
|
|
| template <class RealType, class Policy>
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| 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();
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| RealType location = c.dist.location();
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| RealType q = c.param;
|
|
|
| // Checking function argument
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| RealType result;
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| const char* function = "quantile(const complemented2_type<laplace_distribution<%1%>, %1%>&)";
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| if(false == detail::check_probability(function, q, &result, Policy())) return result;
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|
|
|
|
| // extreme values
|
| if(q == 0) return std::numeric_limits<RealType>::infinity();
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| if(q == 1) return -std::numeric_limits<RealType>::infinity();
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|
|
| if (0.5 - q < 0.0)
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| result = location + scale*log( static_cast<RealType>(-q*2 + 2) );
|
| else
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| result = location - scale*log( static_cast<RealType>(q*2) );
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|
|
|
|
| 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>
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| inline RealType kurtosis_excess(const laplace_distribution<RealType, Policy>& /*dist*/)
|
| {
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| 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
|
|
|
|
|
