411 lines
16 KiB
Plaintext
411 lines
16 KiB
Plaintext
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// boost\math\distributions\non_central_f.hpp
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// Copyright John Maddock 2008.
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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_SPECIAL_NON_CENTRAL_F_HPP
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#define BOOST_MATH_SPECIAL_NON_CENTRAL_F_HPP
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#include <boost/math/distributions/non_central_beta.hpp>
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#include <boost/math/distributions/detail/generic_mode.hpp>
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#include <boost/math/special_functions/pow.hpp>
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namespace boost
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{
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namespace math
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{
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template <class RealType = double, class Policy = policies::policy<> >
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class non_central_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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non_central_f_distribution(RealType v1_, RealType v2_, RealType lambda) : v1(v1_), v2(v2_), ncp(lambda)
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{
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const char* function = "boost::math::non_central_f_distribution<%1%>::non_central_f_distribution(%1%,%1%)";
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RealType r;
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detail::check_df(
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function,
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v1, &r, Policy());
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detail::check_df(
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function,
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v2, &r, Policy());
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detail::check_non_centrality(
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function,
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lambda,
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&r,
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Policy());
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} // non_central_f_distribution constructor.
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RealType degrees_of_freedom1()const
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{
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return v1;
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}
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RealType degrees_of_freedom2()const
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{
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return v2;
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}
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RealType non_centrality() const
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{ // Private data getter function.
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return ncp;
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}
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private:
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// Data member, initialized by constructor.
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RealType v1; // alpha.
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RealType v2; // beta.
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RealType ncp; // non-centrality parameter
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}; // template <class RealType, class Policy> class non_central_f_distribution
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typedef non_central_f_distribution<double> non_central_f; // Reserved name of type double.
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// Non-member functions to give properties of the distribution.
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template <class RealType, class Policy>
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inline const std::pair<RealType, RealType> range(const non_central_f_distribution<RealType, Policy>& /* dist */)
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{ // Range of permissible values for random variable k.
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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 non_central_f_distribution<RealType, Policy>& /* dist */)
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{ // Range of supported values for random variable k.
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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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inline RealType mean(const non_central_f_distribution<RealType, Policy>& dist)
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{
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const char* function = "mean(non_central_f_distribution<%1%> const&)";
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RealType v1 = dist.degrees_of_freedom1();
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RealType v2 = dist.degrees_of_freedom2();
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RealType l = dist.non_centrality();
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RealType r;
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if(!detail::check_df(
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function,
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v1, &r, Policy())
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!detail::check_df(
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function,
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v2, &r, Policy())
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!detail::check_non_centrality(
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function,
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l,
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&r,
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Policy()))
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return r;
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if(v2 <= 2)
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return policies::raise_domain_error(
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function,
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"Second degrees of freedom parameter was %1%, but must be > 2 !",
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v2, Policy());
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return v2 * (v1 + l) / (v1 * (v2 - 2));
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} // mean
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template <class RealType, class Policy>
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inline RealType mode(const non_central_f_distribution<RealType, Policy>& dist)
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{ // mode.
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static const char* function = "mode(non_central_chi_squared_distribution<%1%> const&)";
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RealType n = dist.degrees_of_freedom1();
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RealType m = dist.degrees_of_freedom2();
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RealType l = dist.non_centrality();
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RealType r;
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if(!detail::check_df(
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function,
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n, &r, Policy())
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!detail::check_df(
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function,
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m, &r, Policy())
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!detail::check_non_centrality(
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function,
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l,
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&r,
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Policy()))
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return r;
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RealType guess = m > 2 ? RealType(m * (n + l) / (n * (m - 2))) : RealType(1);
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return detail::generic_find_mode(
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dist,
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guess,
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function);
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}
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template <class RealType, class Policy>
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inline RealType variance(const non_central_f_distribution<RealType, Policy>& dist)
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{ // variance.
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const char* function = "variance(non_central_f_distribution<%1%> const&)";
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RealType n = dist.degrees_of_freedom1();
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RealType m = dist.degrees_of_freedom2();
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RealType l = dist.non_centrality();
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RealType r;
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if(!detail::check_df(
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function,
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n, &r, Policy())
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!detail::check_df(
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function,
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m, &r, Policy())
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!detail::check_non_centrality(
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function,
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l,
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&r,
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Policy()))
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return r;
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if(m <= 4)
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return policies::raise_domain_error(
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function,
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"Second degrees of freedom parameter was %1%, but must be > 4 !",
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m, Policy());
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RealType result = 2 * m * m * ((n + l) * (n + l)
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+ (m - 2) * (n + 2 * l));
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result /= (m - 4) * (m - 2) * (m - 2) * n * n;
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return result;
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}
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// RealType standard_deviation(const non_central_f_distribution<RealType, Policy>& dist)
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// standard_deviation provided by derived accessors.
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template <class RealType, class Policy>
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inline RealType skewness(const non_central_f_distribution<RealType, Policy>& dist)
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{ // skewness = sqrt(l).
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const char* function = "skewness(non_central_f_distribution<%1%> const&)";
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BOOST_MATH_STD_USING
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RealType n = dist.degrees_of_freedom1();
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RealType m = dist.degrees_of_freedom2();
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RealType l = dist.non_centrality();
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RealType r;
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if(!detail::check_df(
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function,
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n, &r, Policy())
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!detail::check_df(
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function,
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m, &r, Policy())
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!detail::check_non_centrality(
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function,
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l,
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&r,
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Policy()))
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return r;
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if(m <= 6)
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return policies::raise_domain_error(
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function,
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"Second degrees of freedom parameter was %1%, but must be > 6 !",
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m, Policy());
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RealType result = 2 * constants::root_two<RealType>();
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result *= sqrt(m - 4);
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result *= (n * (m + n - 2) *(m + 2 * n - 2)
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+ 3 * (m + n - 2) * (m + 2 * n - 2) * l
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+ 6 * (m + n - 2) * l * l + 2 * l * l * l);
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result /= (m - 6) * pow(n * (m + n - 2) + 2 * (m + n - 2) * l + l * l, RealType(1.5f));
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return result;
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}
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template <class RealType, class Policy>
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inline RealType kurtosis_excess(const non_central_f_distribution<RealType, Policy>& dist)
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{
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const char* function = "kurtosis_excess(non_central_f_distribution<%1%> const&)";
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BOOST_MATH_STD_USING
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RealType n = dist.degrees_of_freedom1();
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RealType m = dist.degrees_of_freedom2();
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RealType l = dist.non_centrality();
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RealType r;
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if(!detail::check_df(
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function,
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n, &r, Policy())
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!detail::check_df(
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function,
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m, &r, Policy())
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!detail::check_non_centrality(
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function,
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l,
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&r,
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Policy()))
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return r;
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if(m <= 8)
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return policies::raise_domain_error(
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function,
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"Second degrees of freedom parameter was %1%, but must be > 8 !",
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m, Policy());
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RealType l2 = l * l;
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RealType l3 = l2 * l;
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RealType l4 = l2 * l2;
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RealType result = (3 * (m - 4) * (n * (m + n - 2)
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* (4 * (m - 2) * (m - 2)
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+ (m - 2) * (m + 10) * n
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+ (10 + m) * n * n)
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+ 4 * (m + n - 2) * (4 * (m - 2) * (m - 2)
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+ (m - 2) * (10 + m) * n
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+ (10 + m) * n * n) * l + 2 * (10 + m)
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* (m + n - 2) * (2 * m + 3 * n - 4) * l2
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+ 4 * (10 + m) * (-2 + m + n) * l3
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+ (10 + m) * l4))
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/
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((-8 + m) * (-6 + m) * boost::math::pow<2>(n * (-2 + m + n)
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+ 2 * (-2 + m + n) * l + l2));
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return result;
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} // kurtosis_excess
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template <class RealType, class Policy>
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inline RealType kurtosis(const non_central_f_distribution<RealType, Policy>& dist)
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{
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return kurtosis_excess(dist) + 3;
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}
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template <class RealType, class Policy>
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inline RealType pdf(const non_central_f_distribution<RealType, Policy>& dist, const RealType& x)
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{ // Probability Density/Mass Function.
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typedef typename policies::evaluation<RealType, Policy>::type value_type;
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typedef typename policies::normalise<
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Policy,
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policies::promote_float<false>,
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policies::promote_double<false>,
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policies::discrete_quantile<>,
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policies::assert_undefined<> >::type forwarding_policy;
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value_type alpha = dist.degrees_of_freedom1() / 2;
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value_type beta = dist.degrees_of_freedom2() / 2;
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value_type y = x * alpha / beta;
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value_type r = pdf(boost::math::non_central_beta_distribution<value_type, forwarding_policy>(alpha, beta, dist.non_centrality()), y / (1 + y));
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return policies::checked_narrowing_cast<RealType, forwarding_policy>(
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r * (dist.degrees_of_freedom1() / dist.degrees_of_freedom2()) / ((1 + y) * (1 + y)),
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"pdf(non_central_f_distribution<%1%>, %1%)");
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} // pdf
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template <class RealType, class Policy>
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RealType cdf(const non_central_f_distribution<RealType, Policy>& dist, const RealType& x)
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{
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const char* function = "cdf(const non_central_f_distribution<%1%>&, %1%)";
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RealType r;
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if(!detail::check_df(
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function,
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dist.degrees_of_freedom1(), &r, Policy())
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!detail::check_df(
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function,
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dist.degrees_of_freedom2(), &r, Policy())
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!detail::check_non_centrality(
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function,
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dist.non_centrality(),
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&r,
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Policy()))
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return r;
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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 alpha = dist.degrees_of_freedom1() / 2;
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RealType beta = dist.degrees_of_freedom2() / 2;
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RealType y = x * alpha / beta;
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RealType c = y / (1 + y);
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RealType cp = 1 / (1 + y);
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//
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// To ensure accuracy, we pass both x and 1-x to the
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// non-central beta cdf routine, this ensures accuracy
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// even when we compute x to be ~ 1:
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//
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r = detail::non_central_beta_cdf(c, cp, alpha, beta,
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dist.non_centrality(), false, Policy());
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return r;
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} // cdf
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template <class RealType, class Policy>
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RealType cdf(const complemented2_type<non_central_f_distribution<RealType, Policy>, RealType>& c)
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{ // Complemented Cumulative Distribution Function
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const char* function = "cdf(complement(const non_central_f_distribution<%1%>&, %1%))";
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RealType r;
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if(!detail::check_df(
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function,
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c.dist.degrees_of_freedom1(), &r, Policy())
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!detail::check_df(
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function,
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c.dist.degrees_of_freedom2(), &r, Policy())
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!detail::check_non_centrality(
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function,
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c.dist.non_centrality(),
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&r,
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Policy()))
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return r;
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if((c.param < 0) || !(boost::math::isfinite)(c.param))
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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 !", c.param, Policy());
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}
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RealType alpha = c.dist.degrees_of_freedom1() / 2;
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RealType beta = c.dist.degrees_of_freedom2() / 2;
|
||
|
|
RealType y = c.param * alpha / beta;
|
||
|
|
RealType x = y / (1 + y);
|
||
|
|
RealType cx = 1 / (1 + y);
|
||
|
|
//
|
||
|
|
// To ensure accuracy, we pass both x and 1-x to the
|
||
|
|
// non-central beta cdf routine, this ensures accuracy
|
||
|
|
// even when we compute x to be ~ 1:
|
||
|
|
//
|
||
|
|
r = detail::non_central_beta_cdf(x, cx, alpha, beta,
|
||
|
|
c.dist.non_centrality(), true, Policy());
|
||
|
|
return r;
|
||
|
|
} // ccdf
|
||
|
|
|
||
|
|
template <class RealType, class Policy>
|
||
|
|
inline RealType quantile(const non_central_f_distribution<RealType, Policy>& dist, const RealType& p)
|
||
|
|
{ // Quantile (or Percent Point) function.
|
||
|
|
RealType alpha = dist.degrees_of_freedom1() / 2;
|
||
|
|
RealType beta = dist.degrees_of_freedom2() / 2;
|
||
|
|
RealType x = quantile(boost::math::non_central_beta_distribution<RealType, Policy>(alpha, beta, dist.non_centrality()), p);
|
||
|
|
if(x == 1)
|
||
|
|
return policies::raise_overflow_error<RealType>(
|
||
|
|
"quantile(const non_central_f_distribution<%1%>&, %1%)",
|
||
|
|
"Result of non central F quantile is too large to represent.",
|
||
|
|
Policy());
|
||
|
|
return (x / (1 - x)) * (dist.degrees_of_freedom2() / dist.degrees_of_freedom1());
|
||
|
|
} // quantile
|
||
|
|
|
||
|
|
template <class RealType, class Policy>
|
||
|
|
inline RealType quantile(const complemented2_type<non_central_f_distribution<RealType, Policy>, RealType>& c)
|
||
|
|
{ // Quantile (or Percent Point) function.
|
||
|
|
RealType alpha = c.dist.degrees_of_freedom1() / 2;
|
||
|
|
RealType beta = c.dist.degrees_of_freedom2() / 2;
|
||
|
|
RealType x = quantile(complement(boost::math::non_central_beta_distribution<RealType, Policy>(alpha, beta, c.dist.non_centrality()), c.param));
|
||
|
|
if(x == 1)
|
||
|
|
return policies::raise_overflow_error<RealType>(
|
||
|
|
"quantile(complement(const non_central_f_distribution<%1%>&, %1%))",
|
||
|
|
"Result of non central F quantile is too large to represent.",
|
||
|
|
Policy());
|
||
|
|
return (x / (1 - x)) * (c.dist.degrees_of_freedom2() / c.dist.degrees_of_freedom1());
|
||
|
|
} // quantile complement.
|
||
|
|
|
||
|
|
} // 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_SPECIAL_NON_CENTRAL_F_HPP
|
||
|
|
|
||
|
|
|
||
|
|
|