Chris@16: //  Copyright John Maddock 2006.
Chris@16: //  Use, modification and distribution are subject to the
Chris@16: //  Boost Software License, Version 1.0. (See accompanying file
Chris@16: //  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
Chris@16: 
Chris@16: #ifndef BOOST_STATS_EXTREME_VALUE_HPP
Chris@16: #define BOOST_STATS_EXTREME_VALUE_HPP
Chris@16: 
Chris@16: #include <boost/math/distributions/fwd.hpp>
Chris@16: #include <boost/math/constants/constants.hpp>
Chris@16: #include <boost/math/special_functions/log1p.hpp>
Chris@16: #include <boost/math/special_functions/expm1.hpp>
Chris@16: #include <boost/math/distributions/complement.hpp>
Chris@16: #include <boost/math/distributions/detail/common_error_handling.hpp>
Chris@16: #include <boost/config/no_tr1/cmath.hpp>
Chris@16: 
Chris@16: //
Chris@16: // This is the maximum extreme value distribution, see
Chris@16: // http://www.itl.nist.gov/div898/handbook/eda/section3/eda366g.htm
Chris@16: // and http://mathworld.wolfram.com/ExtremeValueDistribution.html
Chris@16: // Also known as a Fisher-Tippett distribution, a log-Weibull
Chris@16: // distribution or a Gumbel distribution.
Chris@16: 
Chris@16: #include <utility>
Chris@16: 
Chris@16: #ifdef BOOST_MSVC
Chris@16: # pragma warning(push)
Chris@16: # pragma warning(disable: 4702) // unreachable code (return after domain_error throw).
Chris@16: #endif
Chris@16: 
Chris@16: namespace boost{ namespace math{
Chris@16: 
Chris@16: namespace detail{
Chris@16: //
Chris@16: // Error check:
Chris@16: //
Chris@16: template <class RealType, class Policy>
Chris@16: inline bool verify_scale_b(const char* function, RealType b, RealType* presult, const Policy& pol)
Chris@16: {
Chris@16:    if((b <= 0) || !(boost::math::isfinite)(b))
Chris@16:    {
Chris@16:       *presult = policies::raise_domain_error<RealType>(
Chris@16:          function,
Chris@16:          "The scale parameter \"b\" must be finite and > 0, but was: %1%.", b, pol);
Chris@16:       return false;
Chris@16:    }
Chris@16:    return true;
Chris@16: }
Chris@16: 
Chris@16: } // namespace detail
Chris@16: 
Chris@16: template <class RealType = double, class Policy = policies::policy<> >
Chris@16: class extreme_value_distribution
Chris@16: {
Chris@16: public:
Chris@16:    typedef RealType value_type;
Chris@16:    typedef Policy policy_type;
Chris@16: 
Chris@16:    extreme_value_distribution(RealType a = 0, RealType b = 1)
Chris@16:       : m_a(a), m_b(b)
Chris@16:    {
Chris@16:       RealType err;
Chris@16:       detail::verify_scale_b("boost::math::extreme_value_distribution<%1%>::extreme_value_distribution", b, &err, Policy());
Chris@16:       detail::check_finite("boost::math::extreme_value_distribution<%1%>::extreme_value_distribution", a, &err, Policy());
Chris@16:    } // extreme_value_distribution
Chris@16: 
Chris@16:    RealType location()const { return m_a; }
Chris@16:    RealType scale()const { return m_b; }
Chris@16: 
Chris@16: private:
Chris@16:    RealType m_a, m_b;
Chris@16: };
Chris@16: 
Chris@16: typedef extreme_value_distribution<double> extreme_value;
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline const std::pair<RealType, RealType> range(const extreme_value_distribution<RealType, Policy>& /*dist*/)
Chris@16: { // Range of permissible values for random variable x.
Chris@16:    using boost::math::tools::max_value;
Chris@16:    return std::pair<RealType, RealType>(
Chris@16:       std::numeric_limits<RealType>::has_infinity ? -std::numeric_limits<RealType>::infinity() : -max_value<RealType>(), 
Chris@16:       std::numeric_limits<RealType>::has_infinity ? std::numeric_limits<RealType>::infinity() : max_value<RealType>());
Chris@16: }
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline const std::pair<RealType, RealType> support(const extreme_value_distribution<RealType, Policy>& /*dist*/)
Chris@16: { // Range of supported values for random variable x.
Chris@16:    // This is range where cdf rises from 0 to 1, and outside it, the pdf is zero.
Chris@16:    using boost::math::tools::max_value;
Chris@16:    return std::pair<RealType, RealType>(-max_value<RealType>(),  max_value<RealType>());
Chris@16: }
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline RealType pdf(const extreme_value_distribution<RealType, Policy>& dist, const RealType& x)
Chris@16: {
Chris@16:    BOOST_MATH_STD_USING // for ADL of std functions
Chris@16: 
Chris@16:    static const char* function = "boost::math::pdf(const extreme_value_distribution<%1%>&, %1%)";
Chris@16: 
Chris@16:    RealType a = dist.location();
Chris@16:    RealType b = dist.scale();
Chris@16:    RealType result = 0;
Chris@16:    if((boost::math::isinf)(x))
Chris@16:       return 0.0f;
Chris@16:    if(0 == detail::verify_scale_b(function, b, &result, Policy()))
Chris@16:       return result;
Chris@16:    if(0 == detail::check_finite(function, a, &result, Policy()))
Chris@16:       return result;
Chris@16:    if(0 == detail::check_x(function, x, &result, Policy()))
Chris@16:       return result;
Chris@101:    RealType e = (a - x) / b;
Chris@101:    if(e < tools::log_max_value<RealType>())
Chris@101:       result = exp(e) * exp(-exp(e)) / b;
Chris@101:    // else.... result *must* be zero since exp(e) is infinite...
Chris@16:    return result;
Chris@16: } // pdf
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline RealType cdf(const extreme_value_distribution<RealType, Policy>& dist, const RealType& x)
Chris@16: {
Chris@16:    BOOST_MATH_STD_USING // for ADL of std functions
Chris@16: 
Chris@16:    static const char* function = "boost::math::cdf(const extreme_value_distribution<%1%>&, %1%)";
Chris@16: 
Chris@16:    if((boost::math::isinf)(x))
Chris@16:       return x < 0 ? 0.0f : 1.0f;
Chris@16:    RealType a = dist.location();
Chris@16:    RealType b = dist.scale();
Chris@16:    RealType result = 0;
Chris@16:    if(0 == detail::verify_scale_b(function, b, &result, Policy()))
Chris@16:       return result;
Chris@16:    if(0 == detail::check_finite(function, a, &result, Policy()))
Chris@16:       return result;
Chris@16:    if(0 == detail::check_finite(function, a, &result, Policy()))
Chris@16:       return result;
Chris@16:    if(0 == detail::check_x("boost::math::cdf(const extreme_value_distribution<%1%>&, %1%)", x, &result, Policy()))
Chris@16:       return result;
Chris@16: 
Chris@16:    result = exp(-exp((a-x)/b));
Chris@16: 
Chris@16:    return result;
Chris@16: } // cdf
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: RealType quantile(const extreme_value_distribution<RealType, Policy>& dist, const RealType& p)
Chris@16: {
Chris@16:    BOOST_MATH_STD_USING // for ADL of std functions
Chris@16: 
Chris@16:    static const char* function = "boost::math::quantile(const extreme_value_distribution<%1%>&, %1%)";
Chris@16: 
Chris@16:    RealType a = dist.location();
Chris@16:    RealType b = dist.scale();
Chris@16:    RealType result = 0;
Chris@16:    if(0 == detail::verify_scale_b(function, b, &result, Policy()))
Chris@16:       return result;
Chris@16:    if(0 == detail::check_finite(function, a, &result, Policy()))
Chris@16:       return result;
Chris@16:    if(0 == detail::check_probability(function, p, &result, Policy()))
Chris@16:       return result;
Chris@16: 
Chris@16:    if(p == 0)
Chris@16:       return -policies::raise_overflow_error<RealType>(function, 0, Policy());
Chris@16:    if(p == 1)
Chris@16:       return policies::raise_overflow_error<RealType>(function, 0, Policy());
Chris@16: 
Chris@16:    result = a - log(-log(p)) * b;
Chris@16: 
Chris@16:    return result;
Chris@16: } // quantile
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline RealType cdf(const complemented2_type<extreme_value_distribution<RealType, Policy>, RealType>& c)
Chris@16: {
Chris@16:    BOOST_MATH_STD_USING // for ADL of std functions
Chris@16: 
Chris@16:    static const char* function = "boost::math::cdf(const extreme_value_distribution<%1%>&, %1%)";
Chris@16: 
Chris@16:    if((boost::math::isinf)(c.param))
Chris@16:       return c.param < 0 ? 1.0f : 0.0f;
Chris@16:    RealType a = c.dist.location();
Chris@16:    RealType b = c.dist.scale();
Chris@16:    RealType result = 0;
Chris@16:    if(0 == detail::verify_scale_b(function, b, &result, Policy()))
Chris@16:       return result;
Chris@16:    if(0 == detail::check_finite(function, a, &result, Policy()))
Chris@16:       return result;
Chris@16:    if(0 == detail::check_x(function, c.param, &result, Policy()))
Chris@16:       return result;
Chris@16: 
Chris@16:    result = -boost::math::expm1(-exp((a-c.param)/b), Policy());
Chris@16: 
Chris@16:    return result;
Chris@16: }
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: RealType quantile(const complemented2_type<extreme_value_distribution<RealType, Policy>, RealType>& c)
Chris@16: {
Chris@16:    BOOST_MATH_STD_USING // for ADL of std functions
Chris@16: 
Chris@16:    static const char* function = "boost::math::quantile(const extreme_value_distribution<%1%>&, %1%)";
Chris@16: 
Chris@16:    RealType a = c.dist.location();
Chris@16:    RealType b = c.dist.scale();
Chris@16:    RealType q = c.param;
Chris@16:    RealType result = 0;
Chris@16:    if(0 == detail::verify_scale_b(function, b, &result, Policy()))
Chris@16:       return result;
Chris@16:    if(0 == detail::check_finite(function, a, &result, Policy()))
Chris@16:       return result;
Chris@16:    if(0 == detail::check_probability(function, q, &result, Policy()))
Chris@16:       return result;
Chris@16: 
Chris@16:    if(q == 0)
Chris@16:       return policies::raise_overflow_error<RealType>(function, 0, Policy());
Chris@16:    if(q == 1)
Chris@16:       return -policies::raise_overflow_error<RealType>(function, 0, Policy());
Chris@16: 
Chris@16:    result = a - log(-boost::math::log1p(-q, Policy())) * b;
Chris@16: 
Chris@16:    return result;
Chris@16: }
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline RealType mean(const extreme_value_distribution<RealType, Policy>& dist)
Chris@16: {
Chris@16:    RealType a = dist.location();
Chris@16:    RealType b = dist.scale();
Chris@16:    RealType result = 0;
Chris@16:    if(0 == detail::verify_scale_b("boost::math::mean(const extreme_value_distribution<%1%>&)", b, &result, Policy()))
Chris@16:       return result;
Chris@16:    if(0 == detail::check_scale("boost::math::mean(const extreme_value_distribution<%1%>&)", a, &result, Policy()))
Chris@16:       return result;
Chris@16:    return a + constants::euler<RealType>() * b;
Chris@16: }
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline RealType standard_deviation(const extreme_value_distribution<RealType, Policy>& dist)
Chris@16: {
Chris@16:    BOOST_MATH_STD_USING // for ADL of std functions.
Chris@16: 
Chris@16:    RealType b = dist.scale();
Chris@16:    RealType result = 0;
Chris@16:    if(0 == detail::verify_scale_b("boost::math::standard_deviation(const extreme_value_distribution<%1%>&)", b, &result, Policy()))
Chris@16:       return result;
Chris@16:    if(0 == detail::check_scale("boost::math::standard_deviation(const extreme_value_distribution<%1%>&)", dist.location(), &result, Policy()))
Chris@16:       return result;
Chris@16:    return constants::pi<RealType>() * b / sqrt(static_cast<RealType>(6));
Chris@16: }
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline RealType mode(const extreme_value_distribution<RealType, Policy>& dist)
Chris@16: {
Chris@16:    return dist.location();
Chris@16: }
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline RealType median(const extreme_value_distribution<RealType, Policy>& dist)
Chris@16: {
Chris@16:   using constants::ln_ln_two;
Chris@16:    return dist.location() - dist.scale() * ln_ln_two<RealType>();
Chris@16: }
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline RealType skewness(const extreme_value_distribution<RealType, Policy>& /*dist*/)
Chris@16: {
Chris@16:    //
Chris@16:    // This is 12 * sqrt(6) * zeta(3) / pi^3:
Chris@16:    // See http://mathworld.wolfram.com/ExtremeValueDistribution.html
Chris@16:    //
Chris@16:    return static_cast<RealType>(1.1395470994046486574927930193898461120875997958366L);
Chris@16: }
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline RealType kurtosis(const extreme_value_distribution<RealType, Policy>& /*dist*/)
Chris@16: {
Chris@16:    // See http://mathworld.wolfram.com/ExtremeValueDistribution.html
Chris@16:    return RealType(27) / 5;
Chris@16: }
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline RealType kurtosis_excess(const extreme_value_distribution<RealType, Policy>& /*dist*/)
Chris@16: {
Chris@16:    // See http://mathworld.wolfram.com/ExtremeValueDistribution.html
Chris@16:    return RealType(12) / 5;
Chris@16: }
Chris@16: 
Chris@16: 
Chris@16: } // namespace math
Chris@16: } // namespace boost
Chris@16: 
Chris@16: #ifdef BOOST_MSVC
Chris@16: # pragma warning(pop)
Chris@16: #endif
Chris@16: 
Chris@16: // This include must be at the end, *after* the accessors
Chris@16: // for this distribution have been defined, in order to
Chris@16: // keep compilers that support two-phase lookup happy.
Chris@16: #include <boost/math/distributions/detail/derived_accessors.hpp>
Chris@16: 
Chris@16: #endif // BOOST_STATS_EXTREME_VALUE_HPP