| // 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_MATH_DISTRIBUTIONS_FISHER_F_HPP |
| #define BOOST_MATH_DISTRIBUTIONS_FISHER_F_HPP |
| |
| #include <boost/math/distributions/fwd.hpp> |
| #include <boost/math/special_functions/beta.hpp> // for incomplete beta. |
| #include <boost/math/distributions/complement.hpp> // complements |
| #include <boost/math/distributions/detail/common_error_handling.hpp> // error checks |
| #include <boost/math/special_functions/fpclassify.hpp> |
| |
| #include <utility> |
| |
| namespace boost{ namespace math{ |
| |
| template <class RealType = double, class Policy = policies::policy<> > |
| class fisher_f_distribution |
| { |
| public: |
| typedef RealType value_type; |
| typedef Policy policy_type; |
| |
| fisher_f_distribution(const RealType& i, const RealType& j) : m_df1(i), m_df2(j) |
| { |
| static const char* function = "fisher_f_distribution<%1%>::fisher_f_distribution"; |
| RealType result; |
| detail::check_df( |
| function, m_df1, &result, Policy()); |
| detail::check_df( |
| function, m_df2, &result, Policy()); |
| } // fisher_f_distribution |
| |
| RealType degrees_of_freedom1()const |
| { |
| return m_df1; |
| } |
| RealType degrees_of_freedom2()const |
| { |
| return m_df2; |
| } |
| |
| private: |
| // |
| // Data members: |
| // |
| RealType m_df1; // degrees of freedom are a real number. |
| RealType m_df2; // degrees of freedom are a real number. |
| }; |
| |
| typedef fisher_f_distribution<double> fisher_f; |
| |
| template <class RealType, class Policy> |
| inline const std::pair<RealType, RealType> range(const fisher_f_distribution<RealType, Policy>& /*dist*/) |
| { // Range of permissible values for random variable x. |
| using boost::math::tools::max_value; |
| return std::pair<RealType, RealType>(static_cast<RealType>(0), max_value<RealType>()); |
| } |
| |
| template <class RealType, class Policy> |
| inline const std::pair<RealType, RealType> support(const fisher_f_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>(static_cast<RealType>(0), max_value<RealType>()); |
| } |
| |
| template <class RealType, class Policy> |
| RealType pdf(const fisher_f_distribution<RealType, Policy>& dist, const RealType& x) |
| { |
| BOOST_MATH_STD_USING // for ADL of std functions |
| RealType df1 = dist.degrees_of_freedom1(); |
| RealType df2 = dist.degrees_of_freedom2(); |
| // Error check: |
| RealType error_result; |
| static const char* function = "boost::math::pdf(fisher_f_distribution<%1%> const&, %1%)"; |
| if(false == detail::check_df( |
| function, df1, &error_result, Policy()) |
| && detail::check_df( |
| function, df2, &error_result, Policy())) |
| return error_result; |
| |
| if((x < 0) || !(boost::math::isfinite)(x)) |
| { |
| return policies::raise_domain_error<RealType>( |
| function, "Random variable parameter was %1%, but must be > 0 !", x, Policy()); |
| } |
| |
| if(x == 0) |
| { |
| // special cases: |
| if(df1 < 2) |
| return policies::raise_overflow_error<RealType>( |
| function, 0, Policy()); |
| else if(df1 == 2) |
| return 1; |
| else |
| return 0; |
| } |
| |
| // |
| // You reach this formula by direct differentiation of the |
| // cdf expressed in terms of the incomplete beta. |
| // |
| // There are two versions so we don't pass a value of z |
| // that is very close to 1 to ibeta_derivative: for some values |
| // of df1 and df2, all the change takes place in this area. |
| // |
| RealType v1x = df1 * x; |
| RealType result; |
| if(v1x > df2) |
| { |
| result = (df2 * df1) / ((df2 + v1x) * (df2 + v1x)); |
| result *= ibeta_derivative(df2 / 2, df1 / 2, df2 / (df2 + v1x), Policy()); |
| } |
| else |
| { |
| result = df2 + df1 * x; |
| result = (result * df1 - x * df1 * df1) / (result * result); |
| result *= ibeta_derivative(df1 / 2, df2 / 2, v1x / (df2 + v1x), Policy()); |
| } |
| return result; |
| } // pdf |
| |
| template <class RealType, class Policy> |
| inline RealType cdf(const fisher_f_distribution<RealType, Policy>& dist, const RealType& x) |
| { |
| static const char* function = "boost::math::cdf(fisher_f_distribution<%1%> const&, %1%)"; |
| RealType df1 = dist.degrees_of_freedom1(); |
| RealType df2 = dist.degrees_of_freedom2(); |
| // Error check: |
| RealType error_result; |
| if(false == detail::check_df( |
| function, df1, &error_result, Policy()) |
| && detail::check_df( |
| function, df2, &error_result, Policy())) |
| return error_result; |
| |
| if((x < 0) || !(boost::math::isfinite)(x)) |
| { |
| return policies::raise_domain_error<RealType>( |
| function, "Random Variable parameter was %1%, but must be > 0 !", x, Policy()); |
| } |
| |
| RealType v1x = df1 * x; |
| // |
| // There are two equivalent formulas used here, the aim is |
| // to prevent the final argument to the incomplete beta |
| // from being too close to 1: for some values of df1 and df2 |
| // the rate of change can be arbitrarily large in this area, |
| // whilst the value we're passing will have lost information |
| // content as a result of being 0.999999something. Better |
| // to switch things around so we're passing 1-z instead. |
| // |
| return v1x > df2 |
| ? boost::math::ibetac(df2 / 2, df1 / 2, df2 / (df2 + v1x), Policy()) |
| : boost::math::ibeta(df1 / 2, df2 / 2, v1x / (df2 + v1x), Policy()); |
| } // cdf |
| |
| template <class RealType, class Policy> |
| inline RealType quantile(const fisher_f_distribution<RealType, Policy>& dist, const RealType& p) |
| { |
| static const char* function = "boost::math::quantile(fisher_f_distribution<%1%> const&, %1%)"; |
| RealType df1 = dist.degrees_of_freedom1(); |
| RealType df2 = dist.degrees_of_freedom2(); |
| // Error check: |
| RealType error_result; |
| if(false == detail::check_df( |
| function, df1, &error_result, Policy()) |
| && detail::check_df( |
| function, df2, &error_result, Policy()) |
| && detail::check_probability( |
| function, p, &error_result, Policy())) |
| return error_result; |
| |
| // With optimizations turned on, gcc wrongly warns about y being used |
| // uninitializated unless we initialize it to something: |
| RealType x, y(0); |
| |
| x = boost::math::ibeta_inv(df1 / 2, df2 / 2, p, &y, Policy()); |
| |
| return df2 * x / (df1 * y); |
| } // quantile |
| |
| template <class RealType, class Policy> |
| inline RealType cdf(const complemented2_type<fisher_f_distribution<RealType, Policy>, RealType>& c) |
| { |
| static const char* function = "boost::math::cdf(fisher_f_distribution<%1%> const&, %1%)"; |
| RealType df1 = c.dist.degrees_of_freedom1(); |
| RealType df2 = c.dist.degrees_of_freedom2(); |
| RealType x = c.param; |
| // Error check: |
| RealType error_result; |
| if(false == detail::check_df( |
| function, df1, &error_result, Policy()) |
| && detail::check_df( |
| function, df2, &error_result, Policy())) |
| return error_result; |
| |
| if((x < 0) || !(boost::math::isfinite)(x)) |
| { |
| return policies::raise_domain_error<RealType>( |
| function, "Random Variable parameter was %1%, but must be > 0 !", x, Policy()); |
| } |
| |
| RealType v1x = df1 * x; |
| // |
| // There are two equivalent formulas used here, the aim is |
| // to prevent the final argument to the incomplete beta |
| // from being too close to 1: for some values of df1 and df2 |
| // the rate of change can be arbitrarily large in this area, |
| // whilst the value we're passing will have lost information |
| // content as a result of being 0.999999something. Better |
| // to switch things around so we're passing 1-z instead. |
| // |
| return v1x > df2 |
| ? boost::math::ibeta(df2 / 2, df1 / 2, df2 / (df2 + v1x), Policy()) |
| : boost::math::ibetac(df1 / 2, df2 / 2, v1x / (df2 + v1x), Policy()); |
| } |
| |
| template <class RealType, class Policy> |
| inline RealType quantile(const complemented2_type<fisher_f_distribution<RealType, Policy>, RealType>& c) |
| { |
| static const char* function = "boost::math::quantile(fisher_f_distribution<%1%> const&, %1%)"; |
| RealType df1 = c.dist.degrees_of_freedom1(); |
| RealType df2 = c.dist.degrees_of_freedom2(); |
| RealType p = c.param; |
| // Error check: |
| RealType error_result; |
| if(false == detail::check_df( |
| function, df1, &error_result, Policy()) |
| && detail::check_df( |
| function, df2, &error_result, Policy()) |
| && detail::check_probability( |
| function, p, &error_result, Policy())) |
| return error_result; |
| |
| RealType x, y; |
| |
| x = boost::math::ibetac_inv(df1 / 2, df2 / 2, p, &y, Policy()); |
| |
| return df2 * x / (df1 * y); |
| } |
| |
| template <class RealType, class Policy> |
| inline RealType mean(const fisher_f_distribution<RealType, Policy>& dist) |
| { // Mean of F distribution = v. |
| static const char* function = "boost::math::mean(fisher_f_distribution<%1%> const&)"; |
| RealType df1 = dist.degrees_of_freedom1(); |
| RealType df2 = dist.degrees_of_freedom2(); |
| // Error check: |
| RealType error_result; |
| if(false == detail::check_df( |
| function, df1, &error_result, Policy()) |
| && detail::check_df( |
| function, df2, &error_result, Policy())) |
| return error_result; |
| if(df2 <= 2) |
| { |
| return policies::raise_domain_error<RealType>( |
| function, "Second degree of freedom was %1% but must be > 2 in order for the distribution to have a mean.", df2, Policy()); |
| } |
| return df2 / (df2 - 2); |
| } // mean |
| |
| template <class RealType, class Policy> |
| inline RealType variance(const fisher_f_distribution<RealType, Policy>& dist) |
| { // Variance of F distribution. |
| static const char* function = "boost::math::variance(fisher_f_distribution<%1%> const&)"; |
| RealType df1 = dist.degrees_of_freedom1(); |
| RealType df2 = dist.degrees_of_freedom2(); |
| // Error check: |
| RealType error_result; |
| if(false == detail::check_df( |
| function, df1, &error_result, Policy()) |
| && detail::check_df( |
| function, df2, &error_result, Policy())) |
| return error_result; |
| if(df2 <= 4) |
| { |
| return policies::raise_domain_error<RealType>( |
| function, "Second degree of freedom was %1% but must be > 4 in order for the distribution to have a valid variance.", df2, Policy()); |
| } |
| return 2 * df2 * df2 * (df1 + df2 - 2) / (df1 * (df2 - 2) * (df2 - 2) * (df2 - 4)); |
| } // variance |
| |
| template <class RealType, class Policy> |
| inline RealType mode(const fisher_f_distribution<RealType, Policy>& dist) |
| { |
| static const char* function = "boost::math::mode(fisher_f_distribution<%1%> const&)"; |
| RealType df1 = dist.degrees_of_freedom1(); |
| RealType df2 = dist.degrees_of_freedom2(); |
| // Error check: |
| RealType error_result; |
| if(false == detail::check_df( |
| function, df1, &error_result, Policy()) |
| && detail::check_df( |
| function, df2, &error_result, Policy())) |
| return error_result; |
| if(df2 <= 2) |
| { |
| return policies::raise_domain_error<RealType>( |
| function, "Second degree of freedom was %1% but must be > 2 in order for the distribution to have a mode.", df2, Policy()); |
| } |
| return df2 * (df1 - 2) / (df1 * (df2 + 2)); |
| } |
| |
| //template <class RealType, class Policy> |
| //inline RealType median(const fisher_f_distribution<RealType, Policy>& dist) |
| //{ // Median of Fisher F distribution is not defined. |
| // return tools::domain_error<RealType>(BOOST_CURRENT_FUNCTION, "Median is not implemented, result is %1%!", std::numeric_limits<RealType>::quiet_NaN()); |
| // } // median |
| |
| // Now implemented via quantile(half) in derived accessors. |
| |
| template <class RealType, class Policy> |
| inline RealType skewness(const fisher_f_distribution<RealType, Policy>& dist) |
| { |
| static const char* function = "boost::math::skewness(fisher_f_distribution<%1%> const&)"; |
| BOOST_MATH_STD_USING // ADL of std names |
| // See http://mathworld.wolfram.com/F-Distribution.html |
| RealType df1 = dist.degrees_of_freedom1(); |
| RealType df2 = dist.degrees_of_freedom2(); |
| // Error check: |
| RealType error_result; |
| if(false == detail::check_df( |
| function, df1, &error_result, Policy()) |
| && detail::check_df( |
| function, df2, &error_result, Policy())) |
| return error_result; |
| if(df2 <= 6) |
| { |
| return policies::raise_domain_error<RealType>( |
| function, "Second degree of freedom was %1% but must be > 6 in order for the distribution to have a skewness.", df2, Policy()); |
| } |
| return 2 * (df2 + 2 * df1 - 2) * sqrt((2 * df2 - 8) / (df1 * (df2 + df1 - 2))) / (df2 - 6); |
| } |
| |
| template <class RealType, class Policy> |
| RealType kurtosis_excess(const fisher_f_distribution<RealType, Policy>& dist); |
| |
| template <class RealType, class Policy> |
| inline RealType kurtosis(const fisher_f_distribution<RealType, Policy>& dist) |
| { |
| return 3 + kurtosis_excess(dist); |
| } |
| |
| template <class RealType, class Policy> |
| inline RealType kurtosis_excess(const fisher_f_distribution<RealType, Policy>& dist) |
| { |
| static const char* function = "boost::math::kurtosis_excess(fisher_f_distribution<%1%> const&)"; |
| // See http://mathworld.wolfram.com/F-Distribution.html |
| RealType df1 = dist.degrees_of_freedom1(); |
| RealType df2 = dist.degrees_of_freedom2(); |
| // Error check: |
| RealType error_result; |
| if(false == detail::check_df( |
| function, df1, &error_result, Policy()) |
| && detail::check_df( |
| function, df2, &error_result, Policy())) |
| return error_result; |
| if(df2 <= 8) |
| { |
| return policies::raise_domain_error<RealType>( |
| function, "Second degree of freedom was %1% but must be > 8 in order for the distribution to have a kutosis.", df2, Policy()); |
| } |
| RealType df2_2 = df2 * df2; |
| RealType df1_2 = df1 * df1; |
| RealType n = -16 + 20 * df2 - 8 * df2_2 + df2_2 * df2 + 44 * df1 - 32 * df2 * df1 + 5 * df2_2 * df1 - 22 * df1_2 + 5 * df2 * df1_2; |
| n *= 12; |
| RealType d = df1 * (df2 - 6) * (df2 - 8) * (df1 + df2 - 2); |
| return n / d; |
| } |
| |
| } // namespace math |
| } // namespace boost |
| |
| // 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_MATH_DISTRIBUTIONS_FISHER_F_HPP |