boost/math/distributions/non_central_f.hpp
// boost\math\distributions\non_central_f.hpp
// Copyright John Maddock 2008.
// 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_SPECIAL_NON_CENTRAL_F_HPP
#define BOOST_MATH_SPECIAL_NON_CENTRAL_F_HPP
#include <boost/math/distributions/non_central_beta.hpp>
#include <boost/math/distributions/detail/generic_mode.hpp>
#include <boost/math/special_functions/pow.hpp>
namespace boost
{
namespace math
{
template <class RealType = double, class Policy = policies::policy<> >
class non_central_f_distribution
{
public:
typedef RealType value_type;
typedef Policy policy_type;
non_central_f_distribution(RealType v1_, RealType v2_, RealType lambda) : v1(v1_), v2(v2_), ncp(lambda)
{
const char* function = "boost::math::non_central_f_distribution<%1%>::non_central_f_distribution(%1%,%1%)";
RealType r;
detail::check_df(
function,
v1, &r, Policy());
detail::check_df(
function,
v2, &r, Policy());
detail::check_non_centrality(
function,
lambda,
&r,
Policy());
} // non_central_f_distribution constructor.
RealType degrees_of_freedom1()const
{
return v1;
}
RealType degrees_of_freedom2()const
{
return v2;
}
RealType non_centrality() const
{ // Private data getter function.
return ncp;
}
private:
// Data member, initialized by constructor.
RealType v1; // alpha.
RealType v2; // beta.
RealType ncp; // non-centrality parameter
}; // template <class RealType, class Policy> class non_central_f_distribution
typedef non_central_f_distribution<double> non_central_f; // Reserved name of type double.
#ifdef __cpp_deduction_guides
template <class RealType>
non_central_f_distribution(RealType,RealType,RealType)->non_central_f_distribution<typename boost::math::tools::promote_args<RealType>::type>;
#endif
// Non-member functions to give properties of the distribution.
template <class RealType, class Policy>
inline const std::pair<RealType, RealType> range(const non_central_f_distribution<RealType, Policy>& /* dist */)
{ // Range of permissible values for random variable k.
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 non_central_f_distribution<RealType, Policy>& /* dist */)
{ // Range of supported values for random variable k.
// 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>
inline RealType mean(const non_central_f_distribution<RealType, Policy>& dist)
{
const char* function = "mean(non_central_f_distribution<%1%> const&)";
RealType v1 = dist.degrees_of_freedom1();
RealType v2 = dist.degrees_of_freedom2();
RealType l = dist.non_centrality();
RealType r;
if(!detail::check_df(
function,
v1, &r, Policy())
||
!detail::check_df(
function,
v2, &r, Policy())
||
!detail::check_non_centrality(
function,
l,
&r,
Policy()))
return r;
if(v2 <= 2)
return policies::raise_domain_error(
function,
"Second degrees of freedom parameter was %1%, but must be > 2 !",
v2, Policy());
return v2 * (v1 + l) / (v1 * (v2 - 2));
} // mean
template <class RealType, class Policy>
inline RealType mode(const non_central_f_distribution<RealType, Policy>& dist)
{ // mode.
static const char* function = "mode(non_central_chi_squared_distribution<%1%> const&)";
RealType n = dist.degrees_of_freedom1();
RealType m = dist.degrees_of_freedom2();
RealType l = dist.non_centrality();
RealType r;
if(!detail::check_df(
function,
n, &r, Policy())
||
!detail::check_df(
function,
m, &r, Policy())
||
!detail::check_non_centrality(
function,
l,
&r,
Policy()))
return r;
RealType guess = m > 2 ? RealType(m * (n + l) / (n * (m - 2))) : RealType(1);
return detail::generic_find_mode(
dist,
guess,
function);
}
template <class RealType, class Policy>
inline RealType variance(const non_central_f_distribution<RealType, Policy>& dist)
{ // variance.
const char* function = "variance(non_central_f_distribution<%1%> const&)";
RealType n = dist.degrees_of_freedom1();
RealType m = dist.degrees_of_freedom2();
RealType l = dist.non_centrality();
RealType r;
if(!detail::check_df(
function,
n, &r, Policy())
||
!detail::check_df(
function,
m, &r, Policy())
||
!detail::check_non_centrality(
function,
l,
&r,
Policy()))
return r;
if(m <= 4)
return policies::raise_domain_error(
function,
"Second degrees of freedom parameter was %1%, but must be > 4 !",
m, Policy());
RealType result = 2 * m * m * ((n + l) * (n + l)
+ (m - 2) * (n + 2 * l));
result /= (m - 4) * (m - 2) * (m - 2) * n * n;
return result;
}
// RealType standard_deviation(const non_central_f_distribution<RealType, Policy>& dist)
// standard_deviation provided by derived accessors.
template <class RealType, class Policy>
inline RealType skewness(const non_central_f_distribution<RealType, Policy>& dist)
{ // skewness = sqrt(l).
const char* function = "skewness(non_central_f_distribution<%1%> const&)";
BOOST_MATH_STD_USING
RealType n = dist.degrees_of_freedom1();
RealType m = dist.degrees_of_freedom2();
RealType l = dist.non_centrality();
RealType r;
if(!detail::check_df(
function,
n, &r, Policy())
||
!detail::check_df(
function,
m, &r, Policy())
||
!detail::check_non_centrality(
function,
l,
&r,
Policy()))
return r;
if(m <= 6)
return policies::raise_domain_error(
function,
"Second degrees of freedom parameter was %1%, but must be > 6 !",
m, Policy());
RealType result = 2 * constants::root_two<RealType>();
result *= sqrt(m - 4);
result *= (n * (m + n - 2) *(m + 2 * n - 2)
+ 3 * (m + n - 2) * (m + 2 * n - 2) * l
+ 6 * (m + n - 2) * l * l + 2 * l * l * l);
result /= (m - 6) * pow(n * (m + n - 2) + 2 * (m + n - 2) * l + l * l, RealType(1.5f));
return result;
}
template <class RealType, class Policy>
inline RealType kurtosis_excess(const non_central_f_distribution<RealType, Policy>& dist)
{
const char* function = "kurtosis_excess(non_central_f_distribution<%1%> const&)";
BOOST_MATH_STD_USING
RealType n = dist.degrees_of_freedom1();
RealType m = dist.degrees_of_freedom2();
RealType l = dist.non_centrality();
RealType r;
if(!detail::check_df(
function,
n, &r, Policy())
||
!detail::check_df(
function,
m, &r, Policy())
||
!detail::check_non_centrality(
function,
l,
&r,
Policy()))
return r;
if(m <= 8)
return policies::raise_domain_error(
function,
"Second degrees of freedom parameter was %1%, but must be > 8 !",
m, Policy());
RealType l2 = l * l;
RealType l3 = l2 * l;
RealType l4 = l2 * l2;
RealType result = (3 * (m - 4) * (n * (m + n - 2)
* (4 * (m - 2) * (m - 2)
+ (m - 2) * (m + 10) * n
+ (10 + m) * n * n)
+ 4 * (m + n - 2) * (4 * (m - 2) * (m - 2)
+ (m - 2) * (10 + m) * n
+ (10 + m) * n * n) * l + 2 * (10 + m)
* (m + n - 2) * (2 * m + 3 * n - 4) * l2
+ 4 * (10 + m) * (-2 + m + n) * l3
+ (10 + m) * l4))
/
((-8 + m) * (-6 + m) * boost::math::pow<2>(n * (-2 + m + n)
+ 2 * (-2 + m + n) * l + l2));
return result;
} // kurtosis_excess
template <class RealType, class Policy>
inline RealType kurtosis(const non_central_f_distribution<RealType, Policy>& dist)
{
return kurtosis_excess(dist) + 3;
}
template <class RealType, class Policy>
inline RealType pdf(const non_central_f_distribution<RealType, Policy>& dist, const RealType& x)
{ // Probability Density/Mass Function.
typedef typename policies::evaluation<RealType, Policy>::type value_type;
typedef typename policies::normalise<
Policy,
policies::promote_float<false>,
policies::promote_double<false>,
policies::discrete_quantile<>,
policies::assert_undefined<> >::type forwarding_policy;
value_type alpha = dist.degrees_of_freedom1() / 2;
value_type beta = dist.degrees_of_freedom2() / 2;
value_type y = x * alpha / beta;
value_type r = pdf(boost::math::non_central_beta_distribution<value_type, forwarding_policy>(alpha, beta, dist.non_centrality()), y / (1 + y));
return policies::checked_narrowing_cast<RealType, forwarding_policy>(
r * (dist.degrees_of_freedom1() / dist.degrees_of_freedom2()) / ((1 + y) * (1 + y)),
"pdf(non_central_f_distribution<%1%>, %1%)");
} // pdf
template <class RealType, class Policy>
RealType cdf(const non_central_f_distribution<RealType, Policy>& dist, const RealType& x)
{
const char* function = "cdf(const non_central_f_distribution<%1%>&, %1%)";
RealType r;
if(!detail::check_df(
function,
dist.degrees_of_freedom1(), &r, Policy())
||
!detail::check_df(
function,
dist.degrees_of_freedom2(), &r, Policy())
||
!detail::check_non_centrality(
function,
dist.non_centrality(),
&r,
Policy()))
return r;
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 alpha = dist.degrees_of_freedom1() / 2;
RealType beta = dist.degrees_of_freedom2() / 2;
RealType y = x * alpha / beta;
RealType c = y / (1 + y);
RealType cp = 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(c, cp, alpha, beta,
dist.non_centrality(), false, Policy());
return r;
} // cdf
template <class RealType, class Policy>
RealType cdf(const complemented2_type<non_central_f_distribution<RealType, Policy>, RealType>& c)
{ // Complemented Cumulative Distribution Function
const char* function = "cdf(complement(const non_central_f_distribution<%1%>&, %1%))";
RealType r;
if(!detail::check_df(
function,
c.dist.degrees_of_freedom1(), &r, Policy())
||
!detail::check_df(
function,
c.dist.degrees_of_freedom2(), &r, Policy())
||
!detail::check_non_centrality(
function,
c.dist.non_centrality(),
&r,
Policy()))
return r;
if((c.param < 0) || !(boost::math::isfinite)(c.param))
{
return policies::raise_domain_error<RealType>(
function, "Random Variable parameter was %1%, but must be > 0 !", c.param, Policy());
}
RealType alpha = c.dist.degrees_of_freedom1() / 2;
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