301 lines
10 KiB
Plaintext
301 lines
10 KiB
Plaintext
// Copyright John Maddock 2006.
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// Use, modification and distribution are subject to the
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// Boost Software License, Version 1.0. (See accompanying file
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// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
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#ifndef BOOST_STATS_EXTREME_VALUE_HPP
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#define BOOST_STATS_EXTREME_VALUE_HPP
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#include <boost/math/distributions/fwd.hpp>
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#include <boost/math/constants/constants.hpp>
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#include <boost/math/special_functions/log1p.hpp>
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#include <boost/math/special_functions/expm1.hpp>
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#include <boost/math/distributions/complement.hpp>
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#include <boost/math/distributions/detail/common_error_handling.hpp>
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#include <boost/config/no_tr1/cmath.hpp>
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//
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// This is the maximum extreme value distribution, see
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// http://www.itl.nist.gov/div898/handbook/eda/section3/eda366g.htm
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// and http://mathworld.wolfram.com/ExtremeValueDistribution.html
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// Also known as a Fisher-Tippett distribution, a log-Weibull
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// distribution or a Gumbel distribution.
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#include <utility>
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#ifdef BOOST_MSVC
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# pragma warning(push)
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# pragma warning(disable: 4702) // unreachable code (return after domain_error throw).
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#endif
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namespace boost{ namespace math{
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namespace detail{
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//
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// Error check:
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//
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template <class RealType, class Policy>
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inline bool verify_scale_b(const char* function, RealType b, RealType* presult, const Policy& pol)
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{
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if((b <= 0) || !(boost::math::isfinite)(b))
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{
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*presult = policies::raise_domain_error<RealType>(
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function,
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"The scale parameter \"b\" must be finite and > 0, but was: %1%.", b, pol);
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return false;
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}
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return true;
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}
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} // namespace detail
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template <class RealType = double, class Policy = policies::policy<> >
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class extreme_value_distribution
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{
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public:
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typedef RealType value_type;
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typedef Policy policy_type;
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extreme_value_distribution(RealType a = 0, RealType b = 1)
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: m_a(a), m_b(b)
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{
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RealType err;
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detail::verify_scale_b("boost::math::extreme_value_distribution<%1%>::extreme_value_distribution", b, &err, Policy());
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detail::check_finite("boost::math::extreme_value_distribution<%1%>::extreme_value_distribution", a, &err, Policy());
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} // extreme_value_distribution
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RealType location()const { return m_a; }
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RealType scale()const { return m_b; }
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private:
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RealType m_a, m_b;
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};
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typedef extreme_value_distribution<double> extreme_value;
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template <class RealType, class Policy>
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inline const std::pair<RealType, RealType> range(const extreme_value_distribution<RealType, Policy>& /*dist*/)
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{ // Range of permissible values for random variable x.
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using boost::math::tools::max_value;
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return std::pair<RealType, RealType>(
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std::numeric_limits<RealType>::has_infinity ? -std::numeric_limits<RealType>::infinity() : -max_value<RealType>(),
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std::numeric_limits<RealType>::has_infinity ? std::numeric_limits<RealType>::infinity() : max_value<RealType>());
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}
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template <class RealType, class Policy>
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inline const std::pair<RealType, RealType> support(const extreme_value_distribution<RealType, Policy>& /*dist*/)
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{ // Range of supported values for random variable x.
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// This is range where cdf rises from 0 to 1, and outside it, the pdf is zero.
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using boost::math::tools::max_value;
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return std::pair<RealType, RealType>(-max_value<RealType>(), max_value<RealType>());
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}
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template <class RealType, class Policy>
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inline RealType pdf(const extreme_value_distribution<RealType, Policy>& dist, const RealType& x)
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{
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BOOST_MATH_STD_USING // for ADL of std functions
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static const char* function = "boost::math::pdf(const extreme_value_distribution<%1%>&, %1%)";
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RealType a = dist.location();
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RealType b = dist.scale();
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RealType result = 0;
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if(0 == detail::verify_scale_b(function, b, &result, Policy()))
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return result;
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if(0 == detail::check_finite(function, a, &result, Policy()))
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return result;
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if((boost::math::isinf)(x))
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return 0.0f;
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if(0 == detail::check_x(function, x, &result, Policy()))
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return result;
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RealType e = (a - x) / b;
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if(e < tools::log_max_value<RealType>())
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result = exp(e) * exp(-exp(e)) / b;
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// else.... result *must* be zero since exp(e) is infinite...
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return result;
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} // pdf
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template <class RealType, class Policy>
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inline RealType cdf(const extreme_value_distribution<RealType, Policy>& dist, const RealType& x)
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{
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BOOST_MATH_STD_USING // for ADL of std functions
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static const char* function = "boost::math::cdf(const extreme_value_distribution<%1%>&, %1%)";
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if((boost::math::isinf)(x))
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return x < 0 ? 0.0f : 1.0f;
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RealType a = dist.location();
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RealType b = dist.scale();
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RealType result = 0;
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if(0 == detail::verify_scale_b(function, b, &result, Policy()))
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return result;
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if(0 == detail::check_finite(function, a, &result, Policy()))
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return result;
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if(0 == detail::check_finite(function, a, &result, Policy()))
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return result;
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if(0 == detail::check_x("boost::math::cdf(const extreme_value_distribution<%1%>&, %1%)", x, &result, Policy()))
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return result;
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result = exp(-exp((a-x)/b));
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return result;
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} // cdf
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template <class RealType, class Policy>
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RealType quantile(const extreme_value_distribution<RealType, Policy>& dist, const RealType& p)
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{
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BOOST_MATH_STD_USING // for ADL of std functions
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static const char* function = "boost::math::quantile(const extreme_value_distribution<%1%>&, %1%)";
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RealType a = dist.location();
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RealType b = dist.scale();
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RealType result = 0;
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if(0 == detail::verify_scale_b(function, b, &result, Policy()))
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return result;
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if(0 == detail::check_finite(function, a, &result, Policy()))
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return result;
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if(0 == detail::check_probability(function, p, &result, Policy()))
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return result;
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if(p == 0)
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return -policies::raise_overflow_error<RealType>(function, 0, Policy());
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if(p == 1)
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return policies::raise_overflow_error<RealType>(function, 0, Policy());
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result = a - log(-log(p)) * b;
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return result;
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} // quantile
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template <class RealType, class Policy>
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inline RealType cdf(const complemented2_type<extreme_value_distribution<RealType, Policy>, RealType>& c)
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{
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BOOST_MATH_STD_USING // for ADL of std functions
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static const char* function = "boost::math::cdf(const extreme_value_distribution<%1%>&, %1%)";
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if((boost::math::isinf)(c.param))
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return c.param < 0 ? 1.0f : 0.0f;
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RealType a = c.dist.location();
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RealType b = c.dist.scale();
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RealType result = 0;
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if(0 == detail::verify_scale_b(function, b, &result, Policy()))
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return result;
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if(0 == detail::check_finite(function, a, &result, Policy()))
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return result;
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if(0 == detail::check_x(function, c.param, &result, Policy()))
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return result;
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result = -boost::math::expm1(-exp((a-c.param)/b), Policy());
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return result;
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}
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template <class RealType, class Policy>
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RealType quantile(const complemented2_type<extreme_value_distribution<RealType, Policy>, RealType>& c)
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{
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BOOST_MATH_STD_USING // for ADL of std functions
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static const char* function = "boost::math::quantile(const extreme_value_distribution<%1%>&, %1%)";
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RealType a = c.dist.location();
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RealType b = c.dist.scale();
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RealType q = c.param;
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RealType result = 0;
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if(0 == detail::verify_scale_b(function, b, &result, Policy()))
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return result;
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if(0 == detail::check_finite(function, a, &result, Policy()))
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return result;
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if(0 == detail::check_probability(function, q, &result, Policy()))
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return result;
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if(q == 0)
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return policies::raise_overflow_error<RealType>(function, 0, Policy());
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if(q == 1)
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return -policies::raise_overflow_error<RealType>(function, 0, Policy());
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result = a - log(-boost::math::log1p(-q, Policy())) * b;
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return result;
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}
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template <class RealType, class Policy>
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inline RealType mean(const extreme_value_distribution<RealType, Policy>& dist)
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{
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RealType a = dist.location();
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RealType b = dist.scale();
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RealType result = 0;
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if(0 == detail::verify_scale_b("boost::math::mean(const extreme_value_distribution<%1%>&)", b, &result, Policy()))
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return result;
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if(0 == detail::check_scale("boost::math::mean(const extreme_value_distribution<%1%>&)", a, &result, Policy()))
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return result;
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return a + constants::euler<RealType>() * b;
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}
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template <class RealType, class Policy>
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inline RealType standard_deviation(const extreme_value_distribution<RealType, Policy>& dist)
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{
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BOOST_MATH_STD_USING // for ADL of std functions.
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RealType b = dist.scale();
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RealType result = 0;
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if(0 == detail::verify_scale_b("boost::math::standard_deviation(const extreme_value_distribution<%1%>&)", b, &result, Policy()))
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return result;
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if(0 == detail::check_scale("boost::math::standard_deviation(const extreme_value_distribution<%1%>&)", dist.location(), &result, Policy()))
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return result;
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return constants::pi<RealType>() * b / sqrt(static_cast<RealType>(6));
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}
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template <class RealType, class Policy>
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inline RealType mode(const extreme_value_distribution<RealType, Policy>& dist)
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{
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return dist.location();
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}
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template <class RealType, class Policy>
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inline RealType median(const extreme_value_distribution<RealType, Policy>& dist)
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{
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using constants::ln_ln_two;
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return dist.location() - dist.scale() * ln_ln_two<RealType>();
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}
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template <class RealType, class Policy>
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inline RealType skewness(const extreme_value_distribution<RealType, Policy>& /*dist*/)
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{
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//
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// This is 12 * sqrt(6) * zeta(3) / pi^3:
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// See http://mathworld.wolfram.com/ExtremeValueDistribution.html
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//
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return static_cast<RealType>(1.1395470994046486574927930193898461120875997958366L);
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}
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template <class RealType, class Policy>
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inline RealType kurtosis(const extreme_value_distribution<RealType, Policy>& /*dist*/)
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{
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// See http://mathworld.wolfram.com/ExtremeValueDistribution.html
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return RealType(27) / 5;
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}
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template <class RealType, class Policy>
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inline RealType kurtosis_excess(const extreme_value_distribution<RealType, Policy>& /*dist*/)
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{
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// See http://mathworld.wolfram.com/ExtremeValueDistribution.html
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return RealType(12) / 5;
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}
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} // namespace math
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} // namespace boost
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#ifdef BOOST_MSVC
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# pragma warning(pop)
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#endif
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// This include must be at the end, *after* the accessors
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// for this distribution have been defined, in order to
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// keep compilers that support two-phase lookup happy.
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#include <boost/math/distributions/detail/derived_accessors.hpp>
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#endif // BOOST_STATS_EXTREME_VALUE_HPP
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