//  Copyright John Maddock 2006.

//  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)



#ifndef BOOST_STATS_EXTREME_VALUE_HPP

#define BOOST_STATS_EXTREME_VALUE_HPP



#include <boost/math/distributions/fwd.hpp>

#include <boost/math/constants/constants.hpp>

#include <boost/math/special_functions/log1p.hpp>

#include <boost/math/special_functions/expm1.hpp>

#include <boost/math/distributions/complement.hpp>

#include <boost/math/distributions/detail/common_error_handling.hpp>

#include <cmath>



//

// This is the maximum extreme value distribution, see

// http://www.itl.nist.gov/div898/handbook/eda/section3/eda366g.htm

// and http://mathworld.wolfram.com/ExtremeValueDistribution.html

// Also known as a Fisher-Tippett distribution, a log-Weibull

// distribution or a Gumbel distribution.



#include <utility>



#ifdef BOOST_MSVC

# pragma warning(push)

# pragma warning(disable: 4702) // unreachable code (return after domain_error throw).

#endif



namespace boost{ namespace math{



namespace detail{

//

// Error check:

//

template <class RealType, class Policy>

inline bool verify_scale_b(const char* function, RealType b, RealType* presult, const Policy& pol)

{

   if(b <= 0)

   {

      *presult = policies::raise_domain_error<RealType>(

         function,

         "The scale parameter \"b\" must be > 0, but was: %1%.", b, pol);

      return false;

   }

   return true;

}



} // namespace detail



template <class RealType = double, class Policy = policies::policy<> >

class extreme_value_distribution

{

public:

   typedef RealType value_type;

   typedef Policy policy_type;



   extreme_value_distribution(RealType a = 0, RealType b = 1)

      : m_a(a), m_b(b)

   {

      RealType err;

      detail::verify_scale_b("boost::math::extreme_value_distribution<%1%>::extreme_value_distribution", b, &err, Policy());

   } // extreme_value_distribution



   RealType location()const { return m_a; }

   RealType scale()const { return m_b; }



private:

   RealType m_a, m_b;

};



typedef extreme_value_distribution<double> extreme_value;



template <class RealType, class Policy>

inline const std::pair<RealType, RealType> range(const extreme_value_distribution<RealType, Policy>& /*dist*/)

{ // Range of permissible values for random variable x.

   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 extreme_value_distribution<RealType, Policy>& /*dist*/)

{ // Range of supported values for random variable x.

   // This is range where cdf rises from 0 to 1, and outside it, the pdf is zero.

   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 extreme_value_distribution<RealType, Policy>& dist, const RealType& x)

{

   BOOST_MATH_STD_USING // for ADL of std functions



   RealType a = dist.location();

   RealType b = dist.scale();

   RealType result;

   if(0 == detail::verify_scale_b("boost::math::pdf(const extreme_value_distribution<%1%>&, %1%)", b, &result, Policy()))

      return result;

   result = exp((a-x)/b) * exp(-exp((a-x)/b)) / b;

   return result;

} // pdf



template <class RealType, class Policy>

inline RealType cdf(const extreme_value_distribution<RealType, Policy>& dist, const RealType& x)

{

   BOOST_MATH_STD_USING // for ADL of std functions



   RealType a = dist.location();

   RealType b = dist.scale();

   RealType result;

   if(0 == detail::verify_scale_b("boost::math::cdf(const extreme_value_distribution<%1%>&, %1%)", b, &result, Policy()))

      return result;



   result = exp(-exp((a-x)/b));



   return result;

} // cdf



template <class RealType, class Policy>

RealType quantile(const extreme_value_distribution<RealType, Policy>& dist, const RealType& p)

{

   BOOST_MATH_STD_USING // for ADL of std functions



   static const char* function = "boost::math::quantile(const extreme_value_distribution<%1%>&, %1%)";



   RealType a = dist.location();

   RealType b = dist.scale();

   RealType result;

   if(0 == detail::verify_scale_b(function, b, &result, Policy()))

      return result;

   if(0 == detail::check_probability(function, p, &result, Policy()))

      return result;



   if(p == 0)

      return -policies::raise_overflow_error<RealType>(function, 0, Policy());

   if(p == 1)

      return policies::raise_overflow_error<RealType>(function, 0, Policy());



   result = a - log(-log(p)) * b;



   return result;

} // quantile



template <class RealType, class Policy>

inline RealType cdf(const complemented2_type<extreme_value_distribution<RealType, Policy>, RealType>& c)

{

   BOOST_MATH_STD_USING // for ADL of std functions



   RealType a = c.dist.location();

   RealType b = c.dist.scale();

   RealType result;

   if(0 == detail::verify_scale_b("boost::math::cdf(const extreme_value_distribution<%1%>&, %1%)", b, &result, Policy()))

      return result;



   result = -boost::math::expm1(-exp((a-c.param)/b), Policy());



   return result;

}



template <class RealType, class Policy>

RealType quantile(const complemented2_type<extreme_value_distribution<RealType, Policy>, RealType>& c)

{

   BOOST_MATH_STD_USING // for ADL of std functions



   static const char* function = "boost::math::quantile(const extreme_value_distribution<%1%>&, %1%)";



   RealType a = c.dist.location();

   RealType b = c.dist.scale();

   RealType q = c.param;

   RealType result;

   if(0 == detail::verify_scale_b(function, b, &result, Policy()))

      return result;

   if(0 == detail::check_probability(function, q, &result, Policy()))

      return result;



   if(q == 0)

      return policies::raise_overflow_error<RealType>(function, 0, Policy());

   if(q == 1)

      return -policies::raise_overflow_error<RealType>(function, 0, Policy());



   result = a - log(-boost::math::log1p(-q, Policy())) * b;



   return result;

}



template <class RealType, class Policy>

inline RealType mean(const extreme_value_distribution<RealType, Policy>& dist)

{

   RealType a = dist.location();

   RealType b = dist.scale();

   RealType result;

   if(0 == detail::verify_scale_b("boost::math::mean(const extreme_value_distribution<%1%>&)", b, &result, Policy()))

      return result;

   return a + constants::euler<RealType>() * b;

}



template <class RealType, class Policy>

inline RealType standard_deviation(const extreme_value_distribution<RealType, Policy>& dist)

{

   BOOST_MATH_STD_USING // for ADL of std functions.



   RealType b = dist.scale();

   RealType result;

   if(0 == detail::verify_scale_b("boost::math::standard_deviation(const extreme_value_distribution<%1%>&)", b, &result, Policy()))

      return result;

   return constants::pi<RealType>() * b / sqrt(static_cast<RealType>(6));

}



template <class RealType, class Policy>

inline RealType mode(const extreme_value_distribution<RealType, Policy>& dist)

{

   return dist.location();

}



template <class RealType, class Policy>

inline RealType median(const extreme_value_distribution<RealType, Policy>& dist)

{

  using constants::ln_ln_two;

   return dist.location() - dist.scale() * ln_ln_two<RealType>();

}



template <class RealType, class Policy>

inline RealType skewness(const extreme_value_distribution<RealType, Policy>& /*dist*/)

{

   //

   // This is 12 * sqrt(6) * zeta(3) / pi^3:

   // See http://mathworld.wolfram.com/ExtremeValueDistribution.html

   //

   return static_cast<RealType>(1.1395470994046486574927930193898461120875997958366L);

}



template <class RealType, class Policy>

inline RealType kurtosis(const extreme_value_distribution<RealType, Policy>& /*dist*/)

{

   // See http://mathworld.wolfram.com/ExtremeValueDistribution.html

   return RealType(27) / 5;

}



template <class RealType, class Policy>

inline RealType kurtosis_excess(const extreme_value_distribution<RealType, Policy>& /*dist*/)

{

   // See http://mathworld.wolfram.com/ExtremeValueDistribution.html

   return RealType(12) / 5;

}





} // namespace math

} // namespace boost



#ifdef BOOST_MSVC

# pragma warning(pop)

#endif



// 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_EXTREME_VALUE_HPP

