| // 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>
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|
|
| #include <utility>
|
|
|
| namespace boost{ namespace math{
|
|
|
| template <class RealType = double, class Policy = policies::policy<> >
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| class fisher_f_distribution
|
| {
|
| public:
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| typedef RealType value_type;
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| typedef Policy policy_type;
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|
|
| 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";
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| RealType result;
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| detail::check_df(
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| function, m_df1, &result, Policy());
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| detail::check_df(
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| 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:
|
| //
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| RealType m_df1; // degrees of freedom are a real number.
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| 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.
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| using boost::math::tools::max_value;
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| 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*/)
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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>(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:
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| RealType error_result;
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| static const char* function = "boost::math::pdf(fisher_f_distribution<%1%> const&, %1%)";
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| if(false == detail::check_df(
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| function, df1, &error_result, Policy())
|
| && detail::check_df(
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| function, df2, &error_result, Policy()))
|
| return error_result;
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|
|
| if((x < 0) || !(boost::math::isfinite)(x))
|
| {
|
| return policies::raise_domain_error<RealType>(
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| function, "Random variable parameter was %1%, but must be > 0 !", x, Policy());
|
| }
|
|
|
| if(x == 0)
|
| {
|
| // special cases:
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| if(df1 < 2)
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| return policies::raise_overflow_error<RealType>(
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| function, 0, Policy());
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| else if(df1 == 2)
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| return 1;
|
| else
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| 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
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| // that is very close to 1 to ibeta_derivative: for some values
|
| // of df1 and df2, all the change takes place in this area.
|
| //
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| RealType v1x = df1 * x;
|
| RealType result;
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| if(v1x > df2)
|
| {
|
| result = (df2 * df1) / ((df2 + v1x) * (df2 + v1x));
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| result *= ibeta_derivative(df2 / 2, df1 / 2, df2 / (df2 + v1x), Policy());
|
| }
|
| else
|
| {
|
| result = df2 + df1 * x;
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| result = (result * df1 - x * df1 * df1) / (result * result);
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| 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%)";
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| RealType df1 = dist.degrees_of_freedom1();
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| RealType df2 = dist.degrees_of_freedom2();
|
| // Error check:
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| RealType error_result;
|
| if(false == detail::check_df(
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| function, df1, &error_result, Policy())
|
| && detail::check_df(
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| 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(
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| function, df1, &error_result, Policy())
|
| && detail::check_df(
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| function, df2, &error_result, Policy())
|
| && detail::check_probability(
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| 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());
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|
|
| 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();
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| 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
|
