| // boost\math\distributions\non_central_f.hpp
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|
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| // Copyright John Maddock 2008.
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|
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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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|
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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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|
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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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|
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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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|
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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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|
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| typedef non_central_f_distribution<double> non_central_f; // Reserved name of type double.
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|
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| // Non-member functions to give properties of the distribution.
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|
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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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|
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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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|
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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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| ||
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| !detail::check_df(
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| function,
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| v2, &r, Policy())
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| ||
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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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|
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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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|
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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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| ||
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| !detail::check_df(
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| function,
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| m, &r, Policy())
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| ||
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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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| return detail::generic_find_mode(
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| dist,
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| m * (n + l) / (n * (m - 2)),
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| function);
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| }
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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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| ||
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| !detail::check_df(
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| function,
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| m, &r, Policy())
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| ||
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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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|
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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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|
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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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| ||
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| !detail::check_df(
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| function,
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| m, &r, Policy())
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| ||
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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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|
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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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| ||
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| !detail::check_df(
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| function,
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| m, &r, Policy())
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| ||
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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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|
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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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|
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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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|
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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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|
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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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| ||
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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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| ||
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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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|
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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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|
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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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|
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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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| ||
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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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| ||
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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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|
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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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|
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| RealType alpha = c.dist.degrees_of_freedom1() / 2;
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| RealType beta = c.dist.degrees_of_freedom2() / 2;
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| RealType y = c.param * alpha / beta;
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| RealType x = y / (1 + y);
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| RealType cx = 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(x, cx, alpha, beta,
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| c.dist.non_centrality(), true, Policy());
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| return r;
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| } // ccdf
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|
|
| template <class RealType, class Policy>
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| inline RealType quantile(const non_central_f_distribution<RealType, Policy>& dist, const RealType& p)
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| { // Quantile (or Percent Point) function.
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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 x = quantile(boost::math::non_central_beta_distribution<RealType, Policy>(alpha, beta, dist.non_centrality()), p);
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| if(x == 1)
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| return policies::raise_overflow_error<RealType>(
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| "quantile(const non_central_f_distribution<%1%>&, %1%)",
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| "Result of non central F quantile is too large to represent.",
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| Policy());
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| return (x / (1 - x)) * (dist.degrees_of_freedom2() / dist.degrees_of_freedom1());
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| } // quantile
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|
|
| template <class RealType, class Policy>
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| inline RealType quantile(const complemented2_type<non_central_f_distribution<RealType, Policy>, RealType>& c)
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| { // Quantile (or Percent Point) function.
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| RealType alpha = c.dist.degrees_of_freedom1() / 2;
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| RealType beta = c.dist.degrees_of_freedom2() / 2;
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| RealType x = quantile(complement(boost::math::non_central_beta_distribution<RealType, Policy>(alpha, beta, c.dist.non_centrality()), c.param));
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| if(x == 1)
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| return policies::raise_overflow_error<RealType>(
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| "quantile(complement(const non_central_f_distribution<%1%>&, %1%))",
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| "Result of non central F quantile is too large to represent.",
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| Policy());
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| return (x / (1 - x)) * (c.dist.degrees_of_freedom2() / c.dist.degrees_of_freedom1());
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| } // quantile complement.
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|
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| } // namespace math
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| } // namespace boost
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|
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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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|
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| #endif // BOOST_MATH_SPECIAL_NON_CENTRAL_F_HPP
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