388 lines
14 KiB
Plaintext
388 lines
14 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.
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// (See accompanying file LICENSE_1_0.txt
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// or copy at http://www.boost.org/LICENSE_1_0.txt)
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#ifndef BOOST_MATH_DISTRIBUTIONS_FISHER_F_HPP
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#define BOOST_MATH_DISTRIBUTIONS_FISHER_F_HPP
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#include <boost/math/distributions/fwd.hpp>
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#include <boost/math/special_functions/beta.hpp> // for incomplete beta.
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#include <boost/math/distributions/complement.hpp> // complements
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#include <boost/math/distributions/detail/common_error_handling.hpp> // error checks
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#include <boost/math/special_functions/fpclassify.hpp>
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#include <utility>
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namespace boost{ namespace math{
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template <class RealType = double, class Policy = policies::policy<> >
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class fisher_f_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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fisher_f_distribution(const RealType& i, const RealType& j) : m_df1(i), m_df2(j)
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{
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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());
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} // fisher_f_distribution
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RealType degrees_of_freedom1()const
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{
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return m_df1;
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}
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RealType degrees_of_freedom2()const
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{
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return m_df2;
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}
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private:
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//
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// Data members:
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//
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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.
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};
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typedef fisher_f_distribution<double> fisher_f;
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template <class RealType, class Policy>
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inline const std::pair<RealType, RealType> range(const fisher_f_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>(static_cast<RealType>(0), 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 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>());
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}
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template <class RealType, class Policy>
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RealType pdf(const fisher_f_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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RealType df1 = dist.degrees_of_freedom1();
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RealType df2 = dist.degrees_of_freedom2();
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// Error check:
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RealType error_result = 0;
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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())
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&& detail::check_df(
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function, df2, &error_result, Policy())))
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return error_result;
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if((x < 0) || !(boost::math::isfinite)(x))
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{
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return policies::raise_domain_error<RealType>(
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function, "Random variable parameter was %1%, but must be > 0 !", x, Policy());
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}
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if(x == 0)
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{
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// 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;
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else
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return 0;
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}
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//
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// You reach this formula by direct differentiation of the
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// cdf expressed in terms of the incomplete beta.
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//
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// 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
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// of df1 and df2, all the change takes place in this area.
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//
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RealType v1x = df1 * x;
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RealType result;
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if(v1x > df2)
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{
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result = (df2 * df1) / ((df2 + v1x) * (df2 + v1x));
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result *= ibeta_derivative(df2 / 2, df1 / 2, df2 / (df2 + v1x), Policy());
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}
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else
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{
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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());
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}
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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 fisher_f_distribution<RealType, Policy>& dist, const RealType& x)
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{
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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();
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// Error check:
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RealType error_result = 0;
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if(false == detail::check_df(
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function, df1, &error_result, Policy())
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&& detail::check_df(
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function, df2, &error_result, Policy()))
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return error_result;
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if((x < 0) || !(boost::math::isfinite)(x))
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{
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return policies::raise_domain_error<RealType>(
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function, "Random Variable parameter was %1%, but must be > 0 !", x, Policy());
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}
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RealType v1x = df1 * x;
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//
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// There are two equivalent formulas used here, the aim is
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// to prevent the final argument to the incomplete beta
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// from being too close to 1: for some values of df1 and df2
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// the rate of change can be arbitrarily large in this area,
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// whilst the value we're passing will have lost information
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// content as a result of being 0.999999something. Better
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// to switch things around so we're passing 1-z instead.
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//
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return v1x > df2
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? boost::math::ibetac(df2 / 2, df1 / 2, df2 / (df2 + v1x), Policy())
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: boost::math::ibeta(df1 / 2, df2 / 2, v1x / (df2 + v1x), Policy());
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} // cdf
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template <class RealType, class Policy>
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inline RealType quantile(const fisher_f_distribution<RealType, Policy>& dist, const RealType& p)
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{
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static const char* function = "boost::math::quantile(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();
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// Error check:
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RealType error_result = 0;
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if(false == (detail::check_df(
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function, df1, &error_result, Policy())
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&& detail::check_df(
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function, df2, &error_result, Policy())
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&& detail::check_probability(
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function, p, &error_result, Policy())))
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return error_result;
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// With optimizations turned on, gcc wrongly warns about y being used
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// uninitializated unless we initialize it to something:
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RealType x, y(0);
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x = boost::math::ibeta_inv(df1 / 2, df2 / 2, p, &y, Policy());
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return df2 * x / (df1 * y);
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} // quantile
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template <class RealType, class Policy>
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inline RealType cdf(const complemented2_type<fisher_f_distribution<RealType, Policy>, RealType>& c)
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{
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static const char* function = "boost::math::cdf(fisher_f_distribution<%1%> const&, %1%)";
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RealType df1 = c.dist.degrees_of_freedom1();
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RealType df2 = c.dist.degrees_of_freedom2();
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RealType x = c.param;
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// Error check:
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RealType error_result = 0;
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if(false == detail::check_df(
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function, df1, &error_result, Policy())
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&& detail::check_df(
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function, df2, &error_result, Policy()))
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return error_result;
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if((x < 0) || !(boost::math::isfinite)(x))
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{
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return policies::raise_domain_error<RealType>(
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function, "Random Variable parameter was %1%, but must be > 0 !", x, Policy());
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}
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RealType v1x = df1 * x;
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//
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// There are two equivalent formulas used here, the aim is
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// to prevent the final argument to the incomplete beta
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// from being too close to 1: for some values of df1 and df2
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// the rate of change can be arbitrarily large in this area,
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// whilst the value we're passing will have lost information
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// content as a result of being 0.999999something. Better
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// to switch things around so we're passing 1-z instead.
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//
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return v1x > df2
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? boost::math::ibeta(df2 / 2, df1 / 2, df2 / (df2 + v1x), Policy())
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: boost::math::ibetac(df1 / 2, df2 / 2, v1x / (df2 + v1x), Policy());
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}
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template <class RealType, class Policy>
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inline RealType quantile(const complemented2_type<fisher_f_distribution<RealType, Policy>, RealType>& c)
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{
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static const char* function = "boost::math::quantile(fisher_f_distribution<%1%> const&, %1%)";
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RealType df1 = c.dist.degrees_of_freedom1();
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RealType df2 = c.dist.degrees_of_freedom2();
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RealType p = c.param;
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// Error check:
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RealType error_result = 0;
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if(false == (detail::check_df(
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function, df1, &error_result, Policy())
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&& detail::check_df(
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function, df2, &error_result, Policy())
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&& detail::check_probability(
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function, p, &error_result, Policy())))
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return error_result;
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RealType x, y;
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x = boost::math::ibetac_inv(df1 / 2, df2 / 2, p, &y, Policy());
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return df2 * x / (df1 * y);
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}
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template <class RealType, class Policy>
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inline RealType mean(const fisher_f_distribution<RealType, Policy>& dist)
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{ // Mean of F distribution = v.
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static const char* function = "boost::math::mean(fisher_f_distribution<%1%> const&)";
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RealType df1 = dist.degrees_of_freedom1();
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RealType df2 = dist.degrees_of_freedom2();
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// Error check:
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RealType error_result = 0;
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if(false == detail::check_df(
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function, df1, &error_result, Policy())
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&& detail::check_df(
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function, df2, &error_result, Policy()))
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return error_result;
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if(df2 <= 2)
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{
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return policies::raise_domain_error<RealType>(
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function, "Second degree of freedom was %1% but must be > 2 in order for the distribution to have a mean.", df2, Policy());
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}
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return df2 / (df2 - 2);
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} // mean
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template <class RealType, class Policy>
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inline RealType variance(const fisher_f_distribution<RealType, Policy>& dist)
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{ // Variance of F distribution.
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static const char* function = "boost::math::variance(fisher_f_distribution<%1%> const&)";
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RealType df1 = dist.degrees_of_freedom1();
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RealType df2 = dist.degrees_of_freedom2();
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// Error check:
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RealType error_result = 0;
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if(false == detail::check_df(
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function, df1, &error_result, Policy())
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&& detail::check_df(
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function, df2, &error_result, Policy()))
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return error_result;
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if(df2 <= 4)
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{
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return policies::raise_domain_error<RealType>(
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function, "Second degree of freedom was %1% but must be > 4 in order for the distribution to have a valid variance.", df2, Policy());
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}
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return 2 * df2 * df2 * (df1 + df2 - 2) / (df1 * (df2 - 2) * (df2 - 2) * (df2 - 4));
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} // variance
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template <class RealType, class Policy>
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inline RealType mode(const fisher_f_distribution<RealType, Policy>& dist)
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{
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static const char* function = "boost::math::mode(fisher_f_distribution<%1%> const&)";
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RealType df1 = dist.degrees_of_freedom1();
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RealType df2 = dist.degrees_of_freedom2();
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// Error check:
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RealType error_result = 0;
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if(false == detail::check_df(
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function, df1, &error_result, Policy())
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&& detail::check_df(
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function, df2, &error_result, Policy()))
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return error_result;
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if(df2 <= 2)
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{
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return policies::raise_domain_error<RealType>(
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function, "Second degree of freedom was %1% but must be > 2 in order for the distribution to have a mode.", df2, Policy());
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}
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return df2 * (df1 - 2) / (df1 * (df2 + 2));
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}
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//template <class RealType, class Policy>
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//inline RealType median(const fisher_f_distribution<RealType, Policy>& dist)
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//{ // Median of Fisher F distribution is not defined.
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// return tools::domain_error<RealType>(BOOST_CURRENT_FUNCTION, "Median is not implemented, result is %1%!", std::numeric_limits<RealType>::quiet_NaN());
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// } // median
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// Now implemented via quantile(half) in derived accessors.
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template <class RealType, class Policy>
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inline RealType skewness(const fisher_f_distribution<RealType, Policy>& dist)
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{
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static const char* function = "boost::math::skewness(fisher_f_distribution<%1%> const&)";
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BOOST_MATH_STD_USING // ADL of std names
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// See http://mathworld.wolfram.com/F-Distribution.html
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RealType df1 = dist.degrees_of_freedom1();
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RealType df2 = dist.degrees_of_freedom2();
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// Error check:
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RealType error_result = 0;
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if(false == detail::check_df(
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function, df1, &error_result, Policy())
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&& detail::check_df(
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function, df2, &error_result, Policy()))
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return error_result;
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if(df2 <= 6)
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{
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return policies::raise_domain_error<RealType>(
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function, "Second degree of freedom was %1% but must be > 6 in order for the distribution to have a skewness.", df2, Policy());
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}
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return 2 * (df2 + 2 * df1 - 2) * sqrt((2 * df2 - 8) / (df1 * (df2 + df1 - 2))) / (df2 - 6);
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}
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template <class RealType, class Policy>
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RealType kurtosis_excess(const fisher_f_distribution<RealType, Policy>& dist);
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template <class RealType, class Policy>
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inline RealType kurtosis(const fisher_f_distribution<RealType, Policy>& dist)
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{
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return 3 + kurtosis_excess(dist);
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}
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template <class RealType, class Policy>
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inline RealType kurtosis_excess(const fisher_f_distribution<RealType, Policy>& dist)
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{
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static const char* function = "boost::math::kurtosis_excess(fisher_f_distribution<%1%> const&)";
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// See http://mathworld.wolfram.com/F-Distribution.html
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RealType df1 = dist.degrees_of_freedom1();
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RealType df2 = dist.degrees_of_freedom2();
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// Error check:
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RealType error_result = 0;
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if(false == detail::check_df(
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function, df1, &error_result, Policy())
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&& detail::check_df(
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function, df2, &error_result, Policy()))
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return error_result;
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if(df2 <= 8)
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{
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return policies::raise_domain_error<RealType>(
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function, "Second degree of freedom was %1% but must be > 8 in order for the distribution to have a kutosis.", df2, Policy());
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}
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RealType df2_2 = df2 * df2;
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RealType df1_2 = df1 * df1;
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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;
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n *= 12;
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RealType d = df1 * (df2 - 6) * (df2 - 8) * (df1 + df2 - 2);
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return n / d;
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}
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} // namespace math
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} // namespace boost
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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_MATH_DISTRIBUTIONS_FISHER_F_HPP
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