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vn-verdnaturachat/ios/Pods/boost-for-react-native/boost/math/distributions/fisher_f.hpp

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// 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 = 0;
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 = 0;
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 = 0;
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 = 0;
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 = 0;
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 = 0;
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 = 0;
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 = 0;
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 = 0;
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 = 0;
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
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