Chris@16: //  Copyright Thijs van den Berg, 2008.
Chris@16: //  Copyright John Maddock 2008.
Chris@101: //  Copyright Paul A. Bristow 2008, 2014.
Chris@16: 
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: // This module implements the Laplace distribution.
Chris@16: // Weisstein, Eric W. "Laplace Distribution." From MathWorld--A Wolfram Web Resource.
Chris@16: // http://mathworld.wolfram.com/LaplaceDistribution.html
Chris@16: // http://en.wikipedia.org/wiki/Laplace_distribution
Chris@16: //
Chris@16: // Abramowitz and Stegun 1972, p 930
Chris@16: // http://www.math.sfu.ca/~cbm/aands/page_930.htm
Chris@16: 
Chris@16: #ifndef BOOST_STATS_LAPLACE_HPP
Chris@16: #define BOOST_STATS_LAPLACE_HPP
Chris@16: 
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: #include <limits>
Chris@16: 
Chris@16: namespace boost{ namespace math{
Chris@16: 
Chris@101: #ifdef BOOST_MSVC
Chris@101: #  pragma warning(push)
Chris@101: #  pragma warning(disable:4127) // conditional expression is constant
Chris@101: #endif
Chris@101: 
Chris@16: template <class RealType = double, class Policy = policies::policy<> >
Chris@16: class laplace_distribution
Chris@16: {
Chris@16: public:
Chris@16:    // ----------------------------------
Chris@16:    // public Types
Chris@16:    // ----------------------------------
Chris@16:    typedef RealType value_type;
Chris@16:    typedef Policy policy_type;
Chris@16: 
Chris@16:    // ----------------------------------
Chris@16:    // Constructor(s)
Chris@16:    // ----------------------------------
Chris@16:    laplace_distribution(RealType l_location = 0, RealType l_scale = 1)
Chris@16:       : m_location(l_location), m_scale(l_scale)
Chris@16:    {
Chris@16:       RealType result;
Chris@16:       check_parameters("boost::math::laplace_distribution<%1%>::laplace_distribution()", &result);
Chris@16:    }
Chris@16: 
Chris@16: 
Chris@16:    // ----------------------------------
Chris@16:    // Public functions
Chris@16:    // ----------------------------------
Chris@16: 
Chris@16:    RealType location() const
Chris@16:    {
Chris@16:       return m_location;
Chris@16:    }
Chris@16: 
Chris@16:    RealType scale() const
Chris@16:    {
Chris@16:       return m_scale;
Chris@16:    }
Chris@16: 
Chris@16:    bool check_parameters(const char* function, RealType* result) const
Chris@16:    {
Chris@16:          if(false == detail::check_scale(function, m_scale, result, Policy())) return false;
Chris@16:          if(false == detail::check_location(function, m_location, result, Policy())) return false;
Chris@16:          return true;
Chris@16:    }
Chris@16: 
Chris@16: private:
Chris@16:    RealType m_location;
Chris@16:    RealType m_scale;
Chris@16: }; // class laplace_distribution
Chris@16: 
Chris@16: //
Chris@101: // Convenient type synonym for double.
Chris@16: typedef laplace_distribution<double> laplace;
Chris@16: 
Chris@16: //
Chris@101: // Non-member functions.
Chris@16: template <class RealType, class Policy>
Chris@16: inline const std::pair<RealType, RealType> range(const laplace_distribution<RealType, Policy>&)
Chris@16: {
Chris@101:    if (std::numeric_limits<RealType>::has_infinity)
Chris@101:   {  // Can use infinity.
Chris@101:      return std::pair<RealType, RealType>(-std::numeric_limits<RealType>::infinity(), std::numeric_limits<RealType>::infinity()); // - to + infinity.
Chris@101:   }
Chris@101:   else
Chris@101:   { // Can only use max_value.
Chris@101:     using boost::math::tools::max_value;
Chris@101:     return std::pair<RealType, RealType>(-max_value<RealType>(), max_value<RealType>()); // - to + max value.
Chris@101:   }
Chris@101: 
Chris@16: }
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline const std::pair<RealType, RealType> support(const laplace_distribution<RealType, Policy>&)
Chris@16: {
Chris@101:   if (std::numeric_limits<RealType>::has_infinity)
Chris@101:   { // Can Use infinity.
Chris@101:      return std::pair<RealType, RealType>(-std::numeric_limits<RealType>::infinity(), std::numeric_limits<RealType>::infinity()); // - to + infinity.
Chris@101:   }
Chris@101:   else
Chris@101:   { // Can only use max_value.
Chris@101:     using boost::math::tools::max_value;
Chris@101:     return std::pair<RealType, RealType>(-max_value<RealType>(), max_value<RealType>()); // - to + max value.
Chris@101:   }
Chris@16: }
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline RealType pdf(const laplace_distribution<RealType, Policy>& dist, const RealType& x)
Chris@16: {
Chris@16:    BOOST_MATH_STD_USING // for ADL of std functions
Chris@16: 
Chris@16:    // Checking function argument
Chris@16:    RealType result = 0;
Chris@16:    const char* function = "boost::math::pdf(const laplace_distribution<%1%>&, %1%))";
Chris@101: 
Chris@101:    // Check scale and location.
Chris@16:    if (false == dist.check_parameters(function, &result)) return result;
Chris@101:    // Special pdf values.
Chris@101:    if((boost::math::isinf)(x))
Chris@101:    {
Chris@101:       return 0; // pdf + and - infinity is zero.
Chris@101:    }
Chris@16:    if (false == detail::check_x(function, x, &result, Policy())) return result;
Chris@16: 
Chris@16:    // General case
Chris@16:    RealType scale( dist.scale() );
Chris@16:    RealType location( dist.location() );
Chris@16: 
Chris@16:    RealType exponent = x - location;
Chris@16:    if (exponent>0) exponent = -exponent;
Chris@16:    exponent /= scale;
Chris@16: 
Chris@16:    result = exp(exponent);
Chris@16:    result /= 2 * scale;
Chris@16: 
Chris@16:    return result;
Chris@16: } // pdf
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline RealType cdf(const laplace_distribution<RealType, Policy>& dist, const RealType& x)
Chris@16: {
Chris@101:    BOOST_MATH_STD_USING  // For ADL of std functions.
Chris@16: 
Chris@16:    RealType result = 0;
Chris@101:    // Checking function argument.
Chris@16:    const char* function = "boost::math::cdf(const laplace_distribution<%1%>&, %1%)";
Chris@101:    // Check scale and location.
Chris@16:    if (false == dist.check_parameters(function, &result)) return result;
Chris@16: 
Chris@16:    // Special cdf values:
Chris@16:    if((boost::math::isinf)(x))
Chris@16:    {
Chris@101:      if(x < 0) return 0; // -infinity.
Chris@101:      return 1; // + infinity.
Chris@16:    }
Chris@101:    if (false == detail::check_x(function, x, &result, Policy())) return result;
Chris@16: 
Chris@16:    // General cdf  values
Chris@16:    RealType scale( dist.scale() );
Chris@16:    RealType location( dist.location() );
Chris@16: 
Chris@16:    if (x < location)
Chris@16:    {
Chris@16:       result = exp( (x-location)/scale )/2;
Chris@16:    }
Chris@16:    else
Chris@16:    {
Chris@16:       result = 1 - exp( (location-x)/scale )/2;
Chris@16:    }
Chris@16:    return result;
Chris@16: } // cdf
Chris@16: 
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline RealType quantile(const laplace_distribution<RealType, Policy>& dist, const RealType& p)
Chris@16: {
Chris@16:    BOOST_MATH_STD_USING // for ADL of std functions.
Chris@16: 
Chris@16:    // Checking function argument
Chris@16:    RealType result = 0;
Chris@16:    const char* function = "boost::math::quantile(const laplace_distribution<%1%>&, %1%)";
Chris@16:    if (false == dist.check_parameters(function, &result)) return result;
Chris@16:    if(false == detail::check_probability(function, p, &result, Policy())) return result;
Chris@16: 
Chris@16:    // Extreme values of p:
Chris@16:    if(p == 0)
Chris@16:    {
Chris@16:       result = policies::raise_overflow_error<RealType>(function,
Chris@16:         "probability parameter is 0, but must be > 0!", Policy());
Chris@16:       return -result; // -std::numeric_limits<RealType>::infinity();
Chris@16:    }
Chris@16:   
Chris@16:    if(p == 1)
Chris@16:    {
Chris@16:       result = policies::raise_overflow_error<RealType>(function,
Chris@16:         "probability parameter is 1, but must be < 1!", Policy());
Chris@16:       return result; // std::numeric_limits<RealType>::infinity();
Chris@16:    }
Chris@16:    // Calculate Quantile
Chris@16:    RealType scale( dist.scale() );
Chris@16:    RealType location( dist.location() );
Chris@16: 
Chris@16:    if (p - 0.5 < 0.0)
Chris@16:       result = location + scale*log( static_cast<RealType>(p*2) );
Chris@16:    else
Chris@16:       result = location - scale*log( static_cast<RealType>(-p*2 + 2) );
Chris@16: 
Chris@16:    return result;
Chris@16: } // quantile
Chris@16: 
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline RealType cdf(const complemented2_type<laplace_distribution<RealType, Policy>, RealType>& c)
Chris@16: {
Chris@101:    // Calculate complement of cdf.
Chris@16:    BOOST_MATH_STD_USING // for ADL of std functions
Chris@16: 
Chris@16:    RealType scale = c.dist.scale();
Chris@16:    RealType location = c.dist.location();
Chris@16:    RealType x = c.param;
Chris@101:    RealType result = 0;
Chris@16: 
Chris@101:    // Checking function argument.
Chris@16:    const char* function = "boost::math::cdf(const complemented2_type<laplace_distribution<%1%>, %1%>&)";
Chris@16: 
Chris@101:    // Check scale and location.
Chris@101:    //if(false == detail::check_scale(function, scale, result, Policy())) return false;
Chris@101:    //if(false == detail::check_location(function, location, result, Policy())) return false;
Chris@101:     if (false == c.dist.check_parameters(function, &result)) return result;
Chris@16: 
Chris@101:    // Special cdf values.
Chris@16:    if((boost::math::isinf)(x))
Chris@16:    {
Chris@16:      if(x < 0) return 1; // cdf complement -infinity is unity.
Chris@16:      return 0; // cdf complement +infinity is zero.
Chris@16:    }
Chris@101:    if(false == detail::check_x(function, x, &result, Policy()))return result;
Chris@16: 
Chris@16:    // Cdf interval value.
Chris@16:    if (-x < -location)
Chris@16:    {
Chris@16:       result = exp( (-x+location)/scale )/2;
Chris@16:    }
Chris@16:    else
Chris@16:    {
Chris@16:       result = 1 - exp( (-location+x)/scale )/2;
Chris@16:    }
Chris@16:    return result;
Chris@16: } // cdf complement
Chris@16: 
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline RealType quantile(const complemented2_type<laplace_distribution<RealType, Policy>, RealType>& c)
Chris@16: {
Chris@16:    BOOST_MATH_STD_USING // for ADL of std functions.
Chris@16: 
Chris@16:    // Calculate quantile.
Chris@16:    RealType scale = c.dist.scale();
Chris@16:    RealType location = c.dist.location();
Chris@16:    RealType q = c.param;
Chris@101:    RealType result = 0;
Chris@16: 
Chris@16:    // Checking function argument.
Chris@16:    const char* function = "quantile(const complemented2_type<laplace_distribution<%1%>, %1%>&)";
Chris@101:    if (false == c.dist.check_parameters(function, &result)) return result;
Chris@101:    
Chris@101:    // Extreme values.
Chris@101:    if(q == 0)
Chris@101:    {
Chris@101:        return std::numeric_limits<RealType>::infinity();
Chris@101:    }
Chris@101:    if(q == 1)
Chris@101:    {
Chris@101:        return -std::numeric_limits<RealType>::infinity();
Chris@101:    }
Chris@16:    if(false == detail::check_probability(function, q, &result, Policy())) return result;
Chris@16: 
Chris@16:    if (0.5 - q < 0.0)
Chris@16:       result = location + scale*log( static_cast<RealType>(-q*2 + 2) );
Chris@16:    else
Chris@16:       result = location - scale*log( static_cast<RealType>(q*2) );
Chris@16: 
Chris@16: 
Chris@16:    return result;
Chris@16: } // quantile
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline RealType mean(const laplace_distribution<RealType, Policy>& dist)
Chris@16: {
Chris@16:    return dist.location();
Chris@16: }
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline RealType standard_deviation(const laplace_distribution<RealType, Policy>& dist)
Chris@16: {
Chris@16:    return constants::root_two<RealType>() * dist.scale();
Chris@16: }
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline RealType mode(const laplace_distribution<RealType, Policy>& dist)
Chris@16: {
Chris@16:    return dist.location();
Chris@16: }
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline RealType median(const laplace_distribution<RealType, Policy>& dist)
Chris@16: {
Chris@16:    return dist.location();
Chris@16: }
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline RealType skewness(const laplace_distribution<RealType, Policy>& /*dist*/)
Chris@16: {
Chris@16:    return 0;
Chris@16: }
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline RealType kurtosis(const laplace_distribution<RealType, Policy>& /*dist*/)
Chris@16: {
Chris@16:    return 6;
Chris@16: }
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline RealType kurtosis_excess(const laplace_distribution<RealType, Policy>& /*dist*/)
Chris@16: {
Chris@16:    return 3;
Chris@16: }
Chris@16: 
Chris@101: #ifdef BOOST_MSVC
Chris@101: #  pragma warning(pop)
Chris@101: #endif
Chris@101: 
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_LAPLACE_HPP
Chris@16: 
Chris@16: