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//  Copyright Thijs van den Berg, 2008.

//  Copyright John Maddock 2008.

//  Copyright Paul A. Bristow 2008, 2014.

//  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{

#ifdef BOOST_MSVC

#  pragma warning(push)

#  pragma warning(disable:4127) // conditional expression is constant

#endif

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 l_location = 0, RealType l_scale = 1)

      : m_location(l_location), m_scale(l_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 for double.

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>&)

{

   if (std::numeric_limits<RealType>::has_infinity)

  {  // Can use infinity.

     return std::pair<RealType, RealType>(-std::numeric_limits<RealType>::infinity(), std::numeric_limits<RealType>::infinity()); // - to + infinity.

  }

  else

  { // Can only use max_value.

    using boost::math::tools::max_value;

    return std::pair<RealType, RealType>(-max_value<RealType>(), max_value<RealType>()); // - to + max value.

  }

}

template <class RealType, class Policy>

inline const std::pair<RealType, RealType> support(const laplace_distribution<RealType, Policy>&)

{

  if (std::numeric_limits<RealType>::has_infinity)

  { // Can Use infinity.

     return std::pair<RealType, RealType>(-std::numeric_limits<RealType>::infinity(), std::numeric_limits<RealType>::infinity()); // - to + infinity.

  }

  else

  { // Can only use max_value.

    using boost::math::tools::max_value;

    return std::pair<RealType, RealType>(-max_value<RealType>(), max_value<RealType>()); // - to + max value.

  }

}

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 = 0;

   const char* function = "boost::math::pdf(const laplace_distribution<%1%>&, %1%))";

   // Check scale and location.

   if (false == dist.check_parameters(function, &result)) return result;

   // Special pdf values.

   if((boost::math::isinf)(x))

   {

      return 0; // pdf + and - infinity is zero.

   }

   if (false == detail::check_x(function, x, &result, Policy())) return result;

   // 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.

   RealType result = 0;

   // Checking function argument.

   const char* function = "boost::math::cdf(const laplace_distribution<%1%>&, %1%)";

   // Check scale and location.

   if (false == dist.check_parameters(function, &result)) return result;

   // Special cdf values:

   if((boost::math::isinf)(x))

   {

     if(x < 0) return 0; // -infinity.

     return 1; // + infinity.

   }

   if (false == detail::check_x(function, x, &result, Policy())) return result;

   // 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 = 0;

   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 of p:

   if(p == 0)

   {

      result = policies::raise_overflow_error<RealType>(function,

        "probability parameter is 0, but must be > 0!", Policy());

      return -result; // -std::numeric_limits<RealType>::infinity();

   }

   if(p == 1)

   {

      result = policies::raise_overflow_error<RealType>(function,

        "probability parameter is 1, but must be < 1!", Policy());

      return result; // 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)

{

   // Calculate complement of cdf.

   BOOST_MATH_STD_USING // for ADL of std functions

   RealType scale = c.dist.scale();

   RealType location = c.dist.location();

   RealType x = c.param;

   RealType result = 0;

   // Checking function argument.

   const char* function = "boost::math::cdf(const complemented2_type<laplace_distribution<%1%>, %1%>&)";

   // Check scale and location.

   //if(false == detail::check_scale(function, scale, result, Policy())) return false;

   //if(false == detail::check_location(function, location, result, Policy())) return false;

    if (false == c.dist.check_parameters(function, &result)) return result;

   // Special cdf values.

   if((boost::math::isinf)(x))

   {

     if(x < 0) return 1; // cdf complement -infinity is unity.

     return 0; // cdf complement +infinity is zero.

   }

   if(false == detail::check_x(function, x, &result, Policy()))return result;

   // 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;

   RealType result = 0;

   // Checking function argument.

   const char* function = "quantile(const complemented2_type<laplace_distribution<%1%>, %1%>&)";

   if (false == c.dist.check_parameters(function, &result)) return result;

   // Extreme values.

   if(q == 0)

   {

       return std::numeric_limits<RealType>::infinity();

   }

   if(q == 1)

   {

       return -std::numeric_limits<RealType>::infinity();

   }

   if(false == detail::check_probability(function, q, &result, Policy())) return result;

   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;

}

#ifdef BOOST_MSVC

#  pragma warning(pop)

#endif

} // 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