text: //  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 <boost/config/no_tr1/cmath.hpp>
  
  //
  // 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) || !(boost::math::isfinite)(b))
     {
        *presult = policies::raise_domain_error<RealType>(
           function,
           "The scale parameter \"b\" must be finite and > 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());
        detail::check_finite("boost::math::extreme_value_distribution<%1%>::extreme_value_distribution", a, &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>(
        std::numeric_limits<RealType>::has_infinity ? -std::numeric_limits<RealType>::infinity() : -max_value<RealType>(), 
        std::numeric_limits<RealType>::has_infinity ? std::numeric_limits<RealType>::infinity() : 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
  
     static const char* function = "boost::math::pdf(const extreme_value_distribution<%1%>&, %1%)";
  
     RealType a = dist.location();
     RealType b = dist.scale();
     RealType result = 0;
     if((boost::math::isinf)(x))
        return 0.0f;
     if(0 == detail::verify_scale_b(function, b, &result, Policy()))
        return result;
     if(0 == detail::check_finite(function, a, &result, Policy()))
        return result;
     if(0 == detail::check_x(function, x, &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
  
     static const char* function = "boost::math::cdf(const extreme_value_distribution<%1%>&, %1%)";
  
     if((boost::math::isinf)(x))
        return x < 0 ? 0.0f : 1.0f;
     RealType a = dist.location();
     RealType b = dist.scale();
     RealType result = 0;
     if(0 == detail::verify_scale_b(function, b, &result, Policy()))
        return result;
     if(0 == detail::check_finite(function, a, &result, Policy()))
        return result;
     if(0 == detail::check_finite(function, a, &result, Policy()))
        return result;
     if(0 == detail::check_x("boost::math::cdf(const extreme_value_distribution<%1%>&, %1%)", x, &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 = 0;
     if(0 == detail::verify_scale_b(function, b, &result, Policy()))
        return result;
     if(0 == detail::check_finite(function, a, &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
  
     static const char* function = "boost::math::cdf(const extreme_value_distribution<%1%>&, %1%)";
  
     if((boost::math::isinf)(c.param))
        return c.param < 0 ? 1.0f : 0.0f;
     RealType a = c.dist.location();
     RealType b = c.dist.scale();
     RealType result = 0;
     if(0 == detail::verify_scale_b(function, b, &result, Policy()))
        return result;
     if(0 == detail::check_finite(function, a, &result, Policy()))
        return result;
     if(0 == detail::check_x(function, c.param, &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 = 0;
     if(0 == detail::verify_scale_b(function, b, &result, Policy()))
        return result;
     if(0 == detail::check_finite(function, a, &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 = 0;
     if(0 == detail::verify_scale_b("boost::math::mean(const extreme_value_distribution<%1%>&)", b, &result, Policy()))
        return result;
     if(0 == detail::check_scale("boost::math::mean(const extreme_value_distribution<%1%>&)", a, &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 = 0;
     if(0 == detail::verify_scale_b("boost::math::standard_deviation(const extreme_value_distribution<%1%>&)", b, &result, Policy()))
        return result;
     if(0 == detail::check_scale("boost::math::standard_deviation(const extreme_value_distribution<%1%>&)", dist.location(), &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
  