| // 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) |
| { |
| *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 |