1203 lines
48 KiB
Plaintext
1203 lines
48 KiB
Plaintext
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// boost\math\distributions\non_central_t.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_T_HPP
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#define BOOST_MATH_SPECIAL_NON_CENTRAL_T_HPP
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#include <boost/math/distributions/fwd.hpp>
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#include <boost/math/distributions/non_central_beta.hpp> // for nc beta
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#include <boost/math/distributions/normal.hpp> // for normal CDF and quantile
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#include <boost/math/distributions/students_t.hpp>
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#include <boost/math/distributions/detail/generic_quantile.hpp> // quantile
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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, class Policy>
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class non_central_t_distribution;
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namespace detail{
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template <class T, class Policy>
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T non_central_t2_p(T v, T delta, T x, T y, const Policy& pol, T init_val)
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{
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BOOST_MATH_STD_USING
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//
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// Variables come first:
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//
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boost::uintmax_t max_iter = policies::get_max_series_iterations<Policy>();
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T errtol = policies::get_epsilon<T, Policy>();
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T d2 = delta * delta / 2;
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//
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// k is the starting point for iteration, and is the
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// maximum of the poisson weighting term, we don't
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// ever allow k == 0 as this can lead to catastrophic
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// cancellation errors later (test case is v = 1621286869049072.3
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// delta = 0.16212868690490723, x = 0.86987415482475994).
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//
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int k = itrunc(d2);
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T pois;
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if(k == 0) k = 1;
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// Starting Poisson weight:
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pois = gamma_p_derivative(T(k+1), d2, pol)
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* tgamma_delta_ratio(T(k + 1), T(0.5f))
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* delta / constants::root_two<T>();
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if(pois == 0)
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return init_val;
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T xterm, beta;
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// Recurrance & starting beta terms:
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beta = x < y
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? detail::ibeta_imp(T(k + 1), T(v / 2), x, pol, false, true, &xterm)
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: detail::ibeta_imp(T(v / 2), T(k + 1), y, pol, true, true, &xterm);
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xterm *= y / (v / 2 + k);
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T poisf(pois), betaf(beta), xtermf(xterm);
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T sum = init_val;
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if((xterm == 0) && (beta == 0))
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return init_val;
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//
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// Backwards recursion first, this is the stable
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// direction for recursion:
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//
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boost::uintmax_t count = 0;
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T last_term = 0;
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for(int i = k; i >= 0; --i)
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{
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T term = beta * pois;
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sum += term;
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// Don't terminate on first term in case we "fixed" k above:
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if((fabs(last_term) > fabs(term)) && fabs(term/sum) < errtol)
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break;
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last_term = term;
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pois *= (i + 0.5f) / d2;
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beta += xterm;
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xterm *= (i) / (x * (v / 2 + i - 1));
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++count;
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}
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last_term = 0;
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for(int i = k + 1; ; ++i)
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{
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poisf *= d2 / (i + 0.5f);
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xtermf *= (x * (v / 2 + i - 1)) / (i);
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betaf -= xtermf;
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T term = poisf * betaf;
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sum += term;
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if((fabs(last_term) >= fabs(term)) && (fabs(term/sum) < errtol))
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break;
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last_term = term;
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++count;
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if(count > max_iter)
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{
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return policies::raise_evaluation_error(
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"cdf(non_central_t_distribution<%1%>, %1%)",
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"Series did not converge, closest value was %1%", sum, pol);
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}
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}
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return sum;
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}
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template <class T, class Policy>
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T non_central_t2_q(T v, T delta, T x, T y, const Policy& pol, T init_val)
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{
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BOOST_MATH_STD_USING
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//
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// Variables come first:
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//
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boost::uintmax_t max_iter = policies::get_max_series_iterations<Policy>();
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T errtol = boost::math::policies::get_epsilon<T, Policy>();
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T d2 = delta * delta / 2;
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//
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// k is the starting point for iteration, and is the
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// maximum of the poisson weighting term, we don't allow
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// k == 0 as this can cause catastrophic cancellation errors
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// (test case is v = 561908036470413.25, delta = 0.056190803647041321,
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// x = 1.6155232703966216):
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//
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int k = itrunc(d2);
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if(k == 0) k = 1;
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// Starting Poisson weight:
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T pois;
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if((k < (int)(max_factorial<T>::value)) && (d2 < tools::log_max_value<T>()) && (log(d2) * k < tools::log_max_value<T>()))
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{
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//
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// For small k we can optimise this calculation by using
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// a simpler reduced formula:
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//
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pois = exp(-d2);
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pois *= pow(d2, static_cast<T>(k));
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pois /= boost::math::tgamma(T(k + 1 + 0.5), pol);
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pois *= delta / constants::root_two<T>();
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}
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else
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{
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pois = gamma_p_derivative(T(k+1), d2, pol)
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* tgamma_delta_ratio(T(k + 1), T(0.5f))
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* delta / constants::root_two<T>();
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}
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if(pois == 0)
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return init_val;
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// Recurance term:
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T xterm;
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T beta;
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// Starting beta term:
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if(k != 0)
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{
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beta = x < y
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? detail::ibeta_imp(T(k + 1), T(v / 2), x, pol, true, true, &xterm)
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: detail::ibeta_imp(T(v / 2), T(k + 1), y, pol, false, true, &xterm);
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xterm *= y / (v / 2 + k);
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}
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else
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{
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beta = pow(y, v / 2);
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xterm = beta;
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}
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T poisf(pois), betaf(beta), xtermf(xterm);
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T sum = init_val;
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if((xterm == 0) && (beta == 0))
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return init_val;
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//
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// Fused forward and backwards recursion:
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//
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boost::uintmax_t count = 0;
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T last_term = 0;
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for(int i = k + 1, j = k; ; ++i, --j)
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{
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poisf *= d2 / (i + 0.5f);
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xtermf *= (x * (v / 2 + i - 1)) / (i);
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betaf += xtermf;
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T term = poisf * betaf;
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if(j >= 0)
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{
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term += beta * pois;
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pois *= (j + 0.5f) / d2;
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beta -= xterm;
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xterm *= (j) / (x * (v / 2 + j - 1));
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}
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sum += term;
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// Don't terminate on first term in case we "fixed" the value of k above:
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if((fabs(last_term) > fabs(term)) && fabs(term/sum) < errtol)
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break;
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last_term = term;
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if(count > max_iter)
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{
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return policies::raise_evaluation_error(
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"cdf(non_central_t_distribution<%1%>, %1%)",
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"Series did not converge, closest value was %1%", sum, pol);
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}
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++count;
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}
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return sum;
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}
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template <class T, class Policy>
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T non_central_t_cdf(T v, T delta, T t, bool invert, const Policy& pol)
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{
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BOOST_MATH_STD_USING
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if ((boost::math::isinf)(v))
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{ // Infinite degrees of freedom, so use normal distribution located at delta.
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normal_distribution<T, Policy> n(delta, 1);
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return cdf(n, t);
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}
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//
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// Otherwise, for t < 0 we have to use the reflection formula:
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if(t < 0)
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{
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t = -t;
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delta = -delta;
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invert = !invert;
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}
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if(fabs(delta / (4 * v)) < policies::get_epsilon<T, Policy>())
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{
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// Approximate with a Student's T centred on delta,
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// the crossover point is based on eq 2.6 from
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// "A Comparison of Approximations To Percentiles of the
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// Noncentral t-Distribution". H. Sahai and M. M. Ojeda,
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// Revista Investigacion Operacional Vol 21, No 2, 2000.
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// Original sources referenced in the above are:
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// "Some Approximations to the Percentage Points of the Noncentral
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// t-Distribution". C. van Eeden. International Statistical Review, 29, 4-31.
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// "Continuous Univariate Distributions". N.L. Johnson, S. Kotz and
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// N. Balkrishnan. 1995. John Wiley and Sons New York.
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T result = cdf(students_t_distribution<T, Policy>(v), t - delta);
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return invert ? 1 - result : result;
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}
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//
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// x and y are the corresponding random
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// variables for the noncentral beta distribution,
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// with y = 1 - x:
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//
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T x = t * t / (v + t * t);
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T y = v / (v + t * t);
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T d2 = delta * delta;
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T a = 0.5f;
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T b = v / 2;
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T c = a + b + d2 / 2;
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//
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// Crossover point for calculating p or q is the same
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// as for the noncentral beta:
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//
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T cross = 1 - (b / c) * (1 + d2 / (2 * c * c));
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T result;
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if(x < cross)
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{
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//
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// Calculate p:
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//
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if(x != 0)
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{
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result = non_central_beta_p(a, b, d2, x, y, pol);
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result = non_central_t2_p(v, delta, x, y, pol, result);
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result /= 2;
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}
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else
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result = 0;
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result += cdf(boost::math::normal_distribution<T, Policy>(), -delta);
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}
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else
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{
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//
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// Calculate q:
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//
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invert = !invert;
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if(x != 0)
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{
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result = non_central_beta_q(a, b, d2, x, y, pol);
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result = non_central_t2_q(v, delta, x, y, pol, result);
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result /= 2;
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}
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else // x == 0
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result = cdf(complement(boost::math::normal_distribution<T, Policy>(), -delta));
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}
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if(invert)
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result = 1 - result;
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return result;
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}
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template <class T, class Policy>
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T non_central_t_quantile(const char* function, T v, T delta, T p, T q, const Policy&)
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{
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BOOST_MATH_STD_USING
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// static const char* function = "quantile(non_central_t_distribution<%1%>, %1%)";
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// now passed as function
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typedef typename policies::evaluation<T, 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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T r;
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if(!detail::check_df_gt0_to_inf(
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function,
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v, &r, Policy())
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!detail::check_finite(
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function,
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delta,
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&r,
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Policy())
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!detail::check_probability(
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function,
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p,
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&r,
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Policy()))
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return r;
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value_type guess = 0;
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if ( ((boost::math::isinf)(v)) || (v > 1 / boost::math::tools::epsilon<T>()) )
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{ // Infinite or very large degrees of freedom, so use normal distribution located at delta.
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normal_distribution<T, Policy> n(delta, 1);
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if (p < q)
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{
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return quantile(n, p);
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}
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else
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{
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return quantile(complement(n, q));
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}
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}
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else if(v > 3)
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{ // Use normal distribution to calculate guess.
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value_type mean = (v > 1 / policies::get_epsilon<T, Policy>()) ? delta : delta * sqrt(v / 2) * tgamma_delta_ratio((v - 1) * 0.5f, T(0.5f));
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value_type var = (v > 1 / policies::get_epsilon<T, Policy>()) ? value_type(1) : (((delta * delta + 1) * v) / (v - 2) - mean * mean);
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if(p < q)
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guess = quantile(normal_distribution<value_type, forwarding_policy>(mean, var), p);
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else
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guess = quantile(complement(normal_distribution<value_type, forwarding_policy>(mean, var), q));
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}
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//
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// We *must* get the sign of the initial guess correct,
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// or our root-finder will fail, so double check it now:
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//
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value_type pzero = non_central_t_cdf(
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static_cast<value_type>(v),
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static_cast<value_type>(delta),
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static_cast<value_type>(0),
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!(p < q),
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forwarding_policy());
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int s;
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if(p < q)
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s = boost::math::sign(p - pzero);
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else
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s = boost::math::sign(pzero - q);
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|
|
if(s != boost::math::sign(guess))
|
||
|
|
{
|
||
|
|
guess = static_cast<T>(s);
|
||
|
|
}
|
||
|
|
|
||
|
|
value_type result = detail::generic_quantile(
|
||
|
|
non_central_t_distribution<value_type, forwarding_policy>(v, delta),
|
||
|
|
(p < q ? p : q),
|
||
|
|
guess,
|
||
|
|
(p >= q),
|
||
|
|
function);
|
||
|
|
return policies::checked_narrowing_cast<T, forwarding_policy>(
|
||
|
|
result,
|
||
|
|
function);
|
||
|
|
}
|
||
|
|
|
||
|
|
template <class T, class Policy>
|
||
|
|
T non_central_t2_pdf(T n, T delta, T x, T y, const Policy& pol, T init_val)
|
||
|
|
{
|
||
|
|
BOOST_MATH_STD_USING
|
||
|
|
//
|
||
|
|
// Variables come first:
|
||
|
|
//
|
||
|
|
boost::uintmax_t max_iter = policies::get_max_series_iterations<Policy>();
|
||
|
|
T errtol = boost::math::policies::get_epsilon<T, Policy>();
|
||
|
|
T d2 = delta * delta / 2;
|
||
|
|
//
|
||
|
|
// k is the starting point for iteration, and is the
|
||
|
|
// maximum of the poisson weighting term:
|
||
|
|
//
|
||
|
|
int k = itrunc(d2);
|
||
|
|
T pois, xterm;
|
||
|
|
if(k == 0)
|
||
|
|
k = 1;
|
||
|
|
// Starting Poisson weight:
|
||
|
|
pois = gamma_p_derivative(T(k+1), d2, pol)
|
||
|
|
* tgamma_delta_ratio(T(k + 1), T(0.5f))
|
||
|
|
* delta / constants::root_two<T>();
|
||
|
|
// Starting beta term:
|
||
|
|
xterm = x < y
|
||
|
|
? ibeta_derivative(T(k + 1), n / 2, x, pol)
|
||
|
|
: ibeta_derivative(n / 2, T(k + 1), y, pol);
|
||
|
|
T poisf(pois), xtermf(xterm);
|
||
|
|
T sum = init_val;
|
||
|
|
if((pois == 0) || (xterm == 0))
|
||
|
|
return init_val;
|
||
|
|
|
||
|
|
//
|
||
|
|
// Backwards recursion first, this is the stable
|
||
|
|
// direction for recursion:
|
||
|
|
//
|
||
|
|
boost::uintmax_t count = 0;
|
||
|
|
for(int i = k; i >= 0; --i)
|
||
|
|
{
|
||
|
|
T term = xterm * pois;
|
||
|
|
sum += term;
|
||
|
|
if(((fabs(term/sum) < errtol) && (i != k)) || (term == 0))
|
||
|
|
break;
|
||
|
|
pois *= (i + 0.5f) / d2;
|
||
|
|
xterm *= (i) / (x * (n / 2 + i));
|
||
|
|
++count;
|
||
|
|
if(count > max_iter)
|
||
|
|
{
|
||
|
|
return policies::raise_evaluation_error(
|
||
|
|
"pdf(non_central_t_distribution<%1%>, %1%)",
|
||
|
|
"Series did not converge, closest value was %1%", sum, pol);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
for(int i = k + 1; ; ++i)
|
||
|
|
{
|
||
|
|
poisf *= d2 / (i + 0.5f);
|
||
|
|
xtermf *= (x * (n / 2 + i)) / (i);
|
||
|
|
T term = poisf * xtermf;
|
||
|
|
sum += term;
|
||
|
|
if((fabs(term/sum) < errtol) || (term == 0))
|
||
|
|
break;
|
||
|
|
++count;
|
||
|
|
if(count > max_iter)
|
||
|
|
{
|
||
|
|
return policies::raise_evaluation_error(
|
||
|
|
"pdf(non_central_t_distribution<%1%>, %1%)",
|
||
|
|
"Series did not converge, closest value was %1%", sum, pol);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
return sum;
|
||
|
|
}
|
||
|
|
|
||
|
|
template <class T, class Policy>
|
||
|
|
T non_central_t_pdf(T n, T delta, T t, const Policy& pol)
|
||
|
|
{
|
||
|
|
BOOST_MATH_STD_USING
|
||
|
|
if ((boost::math::isinf)(n))
|
||
|
|
{ // Infinite degrees of freedom, so use normal distribution located at delta.
|
||
|
|
normal_distribution<T, Policy> norm(delta, 1);
|
||
|
|
return pdf(norm, t);
|
||
|
|
}
|
||
|
|
//
|
||
|
|
// Otherwise, for t < 0 we have to use the reflection formula:
|
||
|
|
if(t < 0)
|
||
|
|
{
|
||
|
|
t = -t;
|
||
|
|
delta = -delta;
|
||
|
|
}
|
||
|
|
if(t == 0)
|
||
|
|
{
|
||
|
|
//
|
||
|
|
// Handle this as a special case, using the formula
|
||
|
|
// from Weisstein, Eric W.
|
||
|
|
// "Noncentral Student's t-Distribution."
|
||
|
|
// From MathWorld--A Wolfram Web Resource.
|
||
|
|
// http://mathworld.wolfram.com/NoncentralStudentst-Distribution.html
|
||
|
|
//
|
||
|
|
// The formula is simplified thanks to the relation
|
||
|
|
// 1F1(a,b,0) = 1.
|
||
|
|
//
|
||
|
|
return tgamma_delta_ratio(n / 2 + 0.5f, T(0.5f))
|
||
|
|
* sqrt(n / constants::pi<T>())
|
||
|
|
* exp(-delta * delta / 2) / 2;
|
||
|
|
}
|
||
|
|
if(fabs(delta / (4 * n)) < policies::get_epsilon<T, Policy>())
|
||
|
|
{
|
||
|
|
// Approximate with a Student's T centred on delta,
|
||
|
|
// the crossover point is based on eq 2.6 from
|
||
|
|
// "A Comparison of Approximations To Percentiles of the
|
||
|
|
// Noncentral t-Distribution". H. Sahai and M. M. Ojeda,
|
||
|
|
// Revista Investigacion Operacional Vol 21, No 2, 2000.
|
||
|
|
// Original sources referenced in the above are:
|
||
|
|
// "Some Approximations to the Percentage Points of the Noncentral
|
||
|
|
// t-Distribution". C. van Eeden. International Statistical Review, 29, 4-31.
|
||
|
|
// "Continuous Univariate Distributions". N.L. Johnson, S. Kotz and
|
||
|
|
// N. Balkrishnan. 1995. John Wiley and Sons New York.
|
||
|
|
return pdf(students_t_distribution<T, Policy>(n), t - delta);
|
||
|
|
}
|
||
|
|
//
|
||
|
|
// x and y are the corresponding random
|
||
|
|
// variables for the noncentral beta distribution,
|
||
|
|
// with y = 1 - x:
|
||
|
|
//
|
||
|
|
T x = t * t / (n + t * t);
|
||
|
|
T y = n / (n + t * t);
|
||
|
|
T a = 0.5f;
|
||
|
|
T b = n / 2;
|
||
|
|
T d2 = delta * delta;
|
||
|
|
//
|
||
|
|
// Calculate pdf:
|
||
|
|
//
|
||
|
|
T dt = n * t / (n * n + 2 * n * t * t + t * t * t * t);
|
||
|
|
T result = non_central_beta_pdf(a, b, d2, x, y, pol);
|
||
|
|
T tol = tools::epsilon<T>() * result * 500;
|
||
|
|
result = non_central_t2_pdf(n, delta, x, y, pol, result);
|
||
|
|
if(result <= tol)
|
||
|
|
result = 0;
|
||
|
|
result *= dt;
|
||
|
|
return result;
|
||
|
|
}
|
||
|
|
|
||
|
|
template <class T, class Policy>
|
||
|
|
T mean(T v, T delta, const Policy& pol)
|
||
|
|
{
|
||
|
|
if ((boost::math::isinf)(v))
|
||
|
|
{
|
||
|
|
return delta;
|
||
|
|
}
|
||
|
|
BOOST_MATH_STD_USING
|
||
|
|
if (v > 1 / boost::math::tools::epsilon<T>() )
|
||
|
|
{
|
||
|
|
//normal_distribution<T, Policy> n(delta, 1);
|
||
|
|
//return boost::math::mean(n);
|
||
|
|
return delta;
|
||
|
|
}
|
||
|
|
else
|
||
|
|
{
|
||
|
|
return delta * sqrt(v / 2) * tgamma_delta_ratio((v - 1) * 0.5f, T(0.5f), pol);
|
||
|
|
}
|
||
|
|
// Other moments use mean so using normal distribution is propagated.
|
||
|
|
}
|
||
|
|
|
||
|
|
template <class T, class Policy>
|
||
|
|
T variance(T v, T delta, const Policy& pol)
|
||
|
|
{
|
||
|
|
if ((boost::math::isinf)(v))
|
||
|
|
{
|
||
|
|
return 1;
|
||
|
|
}
|
||
|
|
if (delta == 0)
|
||
|
|
{ // == Student's t
|
||
|
|
return v / (v - 2);
|
||
|
|
}
|
||
|
|
T result = ((delta * delta + 1) * v) / (v - 2);
|
||
|
|
T m = mean(v, delta, pol);
|
||
|
|
result -= m * m;
|
||
|
|
return result;
|
||
|
|
}
|
||
|
|
|
||
|
|
template <class T, class Policy>
|
||
|
|
T skewness(T v, T delta, const Policy& pol)
|
||
|
|
{
|
||
|
|
BOOST_MATH_STD_USING
|
||
|
|
if ((boost::math::isinf)(v))
|
||
|
|
{
|
||
|
|
return 0;
|
||
|
|
}
|
||
|
|
if(delta == 0)
|
||
|
|
{ // == Student's t
|
||
|
|
return 0;
|
||
|
|
}
|
||
|
|
T mean = boost::math::detail::mean(v, delta, pol);
|
||
|
|
T l2 = delta * delta;
|
||
|
|
T var = ((l2 + 1) * v) / (v - 2) - mean * mean;
|
||
|
|
T result = -2 * var;
|
||
|
|
result += v * (l2 + 2 * v - 3) / ((v - 3) * (v - 2));
|
||
|
|
result *= mean;
|
||
|
|
result /= pow(var, T(1.5f));
|
||
|
|
return result;
|
||
|
|
}
|
||
|
|
|
||
|
|
template <class T, class Policy>
|
||
|
|
T kurtosis_excess(T v, T delta, const Policy& pol)
|
||
|
|
{
|
||
|
|
BOOST_MATH_STD_USING
|
||
|
|
if ((boost::math::isinf)(v))
|
||
|
|
{
|
||
|
|
return 3;
|
||
|
|
}
|
||
|
|
if (delta == 0)
|
||
|
|
{ // == Student's t
|
||
|
|
return 3;
|
||
|
|
}
|
||
|
|
T mean = boost::math::detail::mean(v, delta, pol);
|
||
|
|
T l2 = delta * delta;
|
||
|
|
T var = ((l2 + 1) * v) / (v - 2) - mean * mean;
|
||
|
|
T result = -3 * var;
|
||
|
|
result += v * (l2 * (v + 1) + 3 * (3 * v - 5)) / ((v - 3) * (v - 2));
|
||
|
|
result *= -mean * mean;
|
||
|
|
result += v * v * (l2 * l2 + 6 * l2 + 3) / ((v - 4) * (v - 2));
|
||
|
|
result /= var * var;
|
||
|
|
return result;
|
||
|
|
}
|
||
|
|
|
||
|
|
#if 0
|
||
|
|
//
|
||
|
|
// This code is disabled, since there can be multiple answers to the
|
||
|
|
// question, and it's not clear how to find the "right" one.
|
||
|
|
//
|
||
|
|
template <class RealType, class Policy>
|
||
|
|
struct t_degrees_of_freedom_finder
|
||
|
|
{
|
||
|
|
t_degrees_of_freedom_finder(
|
||
|
|
RealType delta_, RealType x_, RealType p_, bool c)
|
||
|
|
: delta(delta_), x(x_), p(p_), comp(c) {}
|
||
|
|
|
||
|
|
RealType operator()(const RealType& v)
|
||
|
|
{
|
||
|
|
non_central_t_distribution<RealType, Policy> d(v, delta);
|
||
|
|
return comp ?
|
||
|
|
p - cdf(complement(d, x))
|
||
|
|
: cdf(d, x) - p;
|
||
|
|
}
|
||
|
|
private:
|
||
|
|
RealType delta;
|
||
|
|
RealType x;
|
||
|
|
RealType p;
|
||
|
|
bool comp;
|
||
|
|
};
|
||
|
|
|
||
|
|
template <class RealType, class Policy>
|
||
|
|
inline RealType find_t_degrees_of_freedom(
|
||
|
|
RealType delta, RealType x, RealType p, RealType q, const Policy& pol)
|
||
|
|
{
|
||
|
|
const char* function = "non_central_t<%1%>::find_degrees_of_freedom";
|
||
|
|
if((p == 0) || (q == 0))
|
||
|
|
{
|
||
|
|
//
|
||
|
|
// Can't a thing if one of p and q is zero:
|
||
|
|
//
|
||
|
|
return policies::raise_evaluation_error<RealType>(function,
|
||
|
|
"Can't find degrees of freedom when the probability is 0 or 1, only possible answer is %1%",
|
||
|
|
RealType(std::numeric_limits<RealType>::quiet_NaN()), Policy());
|
||
|
|
}
|
||
|
|
t_degrees_of_freedom_finder<RealType, Policy> f(delta, x, p < q ? p : q, p < q ? false : true);
|
||
|
|
tools::eps_tolerance<RealType> tol(policies::digits<RealType, Policy>());
|
||
|
|
boost::uintmax_t max_iter = policies::get_max_root_iterations<Policy>();
|
||
|
|
//
|
||
|
|
// Pick an initial guess:
|
||
|
|
//
|
||
|
|
RealType guess = 200;
|
||
|
|
std::pair<RealType, RealType> ir = tools::bracket_and_solve_root(
|
||
|
|
f, guess, RealType(2), false, tol, max_iter, pol);
|
||
|
|
RealType result = ir.first + (ir.second - ir.first) / 2;
|
||
|
|
if(max_iter >= policies::get_max_root_iterations<Policy>())
|
||
|
|
{
|
||
|
|
return policies::raise_evaluation_error<RealType>(function, "Unable to locate solution in a reasonable time:"
|
||
|
|
" or there is no answer to problem. Current best guess is %1%", result, Policy());
|
||
|
|
}
|
||
|
|
return result;
|
||
|
|
}
|
||
|
|
|
||
|
|
template <class RealType, class Policy>
|
||
|
|
struct t_non_centrality_finder
|
||
|
|
{
|
||
|
|
t_non_centrality_finder(
|
||
|
|
RealType v_, RealType x_, RealType p_, bool c)
|
||
|
|
: v(v_), x(x_), p(p_), comp(c) {}
|
||
|
|
|
||
|
|
RealType operator()(const RealType& delta)
|
||
|
|
{
|
||
|
|
non_central_t_distribution<RealType, Policy> d(v, delta);
|
||
|
|
return comp ?
|
||
|
|
p - cdf(complement(d, x))
|
||
|
|
: cdf(d, x) - p;
|
||
|
|
}
|
||
|
|
private:
|
||
|
|
RealType v;
|
||
|
|
RealType x;
|
||
|
|
RealType p;
|
||
|
|
bool comp;
|
||
|
|
};
|
||
|
|
|
||
|
|
template <class RealType, class Policy>
|
||
|
|
inline RealType find_t_non_centrality(
|
||
|
|
RealType v, RealType x, RealType p, RealType q, const Policy& pol)
|
||
|
|
{
|
||
|
|
const char* function = "non_central_t<%1%>::find_t_non_centrality";
|
||
|
|
if((p == 0) || (q == 0))
|
||
|
|
{
|
||
|
|
//
|
||
|
|
// Can't do a thing if one of p and q is zero:
|
||
|
|
//
|
||
|
|
return policies::raise_evaluation_error<RealType>(function,
|
||
|
|
"Can't find non-centrality parameter when the probability is 0 or 1, only possible answer is %1%",
|
||
|
|
RealType(std::numeric_limits<RealType>::quiet_NaN()), Policy());
|
||
|
|
}
|
||
|
|
t_non_centrality_finder<RealType, Policy> f(v, x, p < q ? p : q, p < q ? false : true);
|
||
|
|
tools::eps_tolerance<RealType> tol(policies::digits<RealType, Policy>());
|
||
|
|
boost::uintmax_t max_iter = policies::get_max_root_iterations<Policy>();
|
||
|
|
//
|
||
|
|
// Pick an initial guess that we know is the right side of
|
||
|
|
// zero:
|
||
|
|
//
|
||
|
|
RealType guess;
|
||
|
|
if(f(0) < 0)
|
||
|
|
guess = 1;
|
||
|
|
else
|
||
|
|
guess = -1;
|
||
|
|
std::pair<RealType, RealType> ir = tools::bracket_and_solve_root(
|
||
|
|
f, guess, RealType(2), false, tol, max_iter, pol);
|
||
|
|
RealType result = ir.first + (ir.second - ir.first) / 2;
|
||
|
|
if(max_iter >= policies::get_max_root_iterations<Policy>())
|
||
|
|
{
|
||
|
|
return policies::raise_evaluation_error<RealType>(function, "Unable to locate solution in a reasonable time:"
|
||
|
|
" or there is no answer to problem. Current best guess is %1%", result, Policy());
|
||
|
|
}
|
||
|
|
return result;
|
||
|
|
}
|
||
|
|
#endif
|
||
|
|
} // namespace detail ======================================================================
|
||
|
|
|
||
|
|
template <class RealType = double, class Policy = policies::policy<> >
|
||
|
|
class non_central_t_distribution
|
||
|
|
{
|
||
|
|
public:
|
||
|
|
typedef RealType value_type;
|
||
|
|
typedef Policy policy_type;
|
||
|
|
|
||
|
|
non_central_t_distribution(RealType v_, RealType lambda) : v(v_), ncp(lambda)
|
||
|
|
{
|
||
|
|
const char* function = "boost::math::non_central_t_distribution<%1%>::non_central_t_distribution(%1%,%1%)";
|
||
|
|
RealType r;
|
||
|
|
detail::check_df_gt0_to_inf(
|
||
|
|
function,
|
||
|
|
v, &r, Policy());
|
||
|
|
detail::check_finite(
|
||
|
|
function,
|
||
|
|
lambda,
|
||
|
|
&r,
|
||
|
|
Policy());
|
||
|
|
} // non_central_t_distribution constructor.
|
||
|
|
|
||
|
|
RealType degrees_of_freedom() const
|
||
|
|
{ // Private data getter function.
|
||
|
|
return v;
|
||
|
|
}
|
||
|
|
RealType non_centrality() const
|
||
|
|
{ // Private data getter function.
|
||
|
|
return ncp;
|
||
|
|
}
|
||
|
|
#if 0
|
||
|
|
//
|
||
|
|
// This code is disabled, since there can be multiple answers to the
|
||
|
|
// question, and it's not clear how to find the "right" one.
|
||
|
|
//
|
||
|
|
static RealType find_degrees_of_freedom(RealType delta, RealType x, RealType p)
|
||
|
|
{
|
||
|
|
const char* function = "non_central_t<%1%>::find_degrees_of_freedom";
|
||
|
|
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 result = detail::find_t_degrees_of_freedom(
|
||
|
|
static_cast<value_type>(delta),
|
||
|
|
static_cast<value_type>(x),
|
||
|
|
static_cast<value_type>(p),
|
||
|
|
static_cast<value_type>(1-p),
|
||
|
|
forwarding_policy());
|
||
|
|
return policies::checked_narrowing_cast<RealType, forwarding_policy>(
|
||
|
|
result,
|
||
|
|
function);
|
||
|
|
}
|
||
|
|
template <class A, class B, class C>
|
||
|
|
static RealType find_degrees_of_freedom(const complemented3_type<A,B,C>& c)
|
||
|
|
{
|
||
|
|
const char* function = "non_central_t<%1%>::find_degrees_of_freedom";
|
||
|
|
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 result = detail::find_t_degrees_of_freedom(
|
||
|
|
static_cast<value_type>(c.dist),
|
||
|
|
static_cast<value_type>(c.param1),
|
||
|
|
static_cast<value_type>(1-c.param2),
|
||
|
|
static_cast<value_type>(c.param2),
|
||
|
|
forwarding_policy());
|
||
|
|
return policies::checked_narrowing_cast<RealType, forwarding_policy>(
|
||
|
|
result,
|
||
|
|
function);
|
||
|
|
}
|
||
|
|
static RealType find_non_centrality(RealType v, RealType x, RealType p)
|
||
|
|
{
|
||
|
|
const char* function = "non_central_t<%1%>::find_t_non_centrality";
|
||
|
|
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 result = detail::find_t_non_centrality(
|
||
|
|
static_cast<value_type>(v),
|
||
|
|
static_cast<value_type>(x),
|
||
|
|
static_cast<value_type>(p),
|
||
|
|
static_cast<value_type>(1-p),
|
||
|
|
forwarding_policy());
|
||
|
|
return policies::checked_narrowing_cast<RealType, forwarding_policy>(
|
||
|
|
result,
|
||
|
|
function);
|
||
|
|
}
|
||
|
|
template <class A, class B, class C>
|
||
|
|
static RealType find_non_centrality(const complemented3_type<A,B,C>& c)
|
||
|
|
{
|
||
|
|
const char* function = "non_central_t<%1%>::find_t_non_centrality";
|
||
|
|
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 result = detail::find_t_non_centrality(
|
||
|
|
static_cast<value_type>(c.dist),
|
||
|
|
static_cast<value_type>(c.param1),
|
||
|
|
static_cast<value_type>(1-c.param2),
|
||
|
|
static_cast<value_type>(c.param2),
|
||
|
|
forwarding_policy());
|
||
|
|
return policies::checked_narrowing_cast<RealType, forwarding_policy>(
|
||
|
|
result,
|
||
|
|
function);
|
||
|
|
}
|
||
|
|
#endif
|
||
|
|
private:
|
||
|
|
// Data member, initialized by constructor.
|
||
|
|
RealType v; // degrees of freedom
|
||
|
|
RealType ncp; // non-centrality parameter
|
||
|
|
}; // template <class RealType, class Policy> class non_central_t_distribution
|
||
|
|
|
||
|
|
typedef non_central_t_distribution<double> non_central_t; // Reserved name of type double.
|
||
|
|
|
||
|
|
// Non-member functions to give properties of the distribution.
|
||
|
|
|
||
|
|
template <class RealType, class Policy>
|
||
|
|
inline const std::pair<RealType, RealType> range(const non_central_t_distribution<RealType, Policy>& /* dist */)
|
||
|
|
{ // Range of permissible values for random variable k.
|
||
|
|
using boost::math::tools::max_value;
|
||
|
|
return std::pair<RealType, RealType>(-max_value<RealType>(), max_value<RealType>());
|
||
|
|
}
|
||
|
|
|
||
|
|
template <class RealType, class Policy>
|
||
|
|
inline const std::pair<RealType, RealType> support(const non_central_t_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>(-max_value<RealType>(), max_value<RealType>());
|
||
|
|
}
|
||
|
|
|
||
|
|
template <class RealType, class Policy>
|
||
|
|
inline RealType mode(const non_central_t_distribution<RealType, Policy>& dist)
|
||
|
|
{ // mode.
|
||
|
|
static const char* function = "mode(non_central_t_distribution<%1%> const&)";
|
||
|
|
RealType v = dist.degrees_of_freedom();
|
||
|
|
RealType l = dist.non_centrality();
|
||
|
|
RealType r;
|
||
|
|
if(!detail::check_df_gt0_to_inf(
|
||
|
|
function,
|
||
|
|
v, &r, Policy())
|
||
|
|
||
|
||
|
|
!detail::check_finite(
|
||
|
|
function,
|
||
|
|
l,
|
||
|
|
&r,
|
||
|
|
Policy()))
|
||
|
|
return (RealType)r;
|
||
|
|
|
||
|
|
BOOST_MATH_STD_USING
|
||
|
|
|
||
|
|
RealType m = v < 3 ? 0 : detail::mean(v, l, Policy());
|
||
|
|
RealType var = v < 4 ? 1 : detail::variance(v, l, Policy());
|
||
|
|
|
||
|
|
return detail::generic_find_mode(
|
||
|
|
dist,
|
||
|
|
m,
|
||
|
|
function,
|
||
|
|
sqrt(var));
|
||
|
|
}
|
||
|
|
|
||
|
|
template <class RealType, class Policy>
|
||
|
|
inline RealType mean(const non_central_t_distribution<RealType, Policy>& dist)
|
||
|
|
{
|
||
|
|
BOOST_MATH_STD_USING
|
||
|
|
const char* function = "mean(const non_central_t_distribution<%1%>&)";
|
||
|
|
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;
|
||
|
|
RealType v = dist.degrees_of_freedom();
|
||
|
|
RealType l = dist.non_centrality();
|
||
|
|
RealType r;
|
||
|
|
if(!detail::check_df_gt0_to_inf(
|
||
|
|
function,
|
||
|
|
v, &r, Policy())
|
||
|
|
||
|
||
|
|
!detail::check_finite(
|
||
|
|
function,
|
||
|
|
l,
|
||
|
|
&r,
|
||
|
|
Policy()))
|
||
|
|
return (RealType)r;
|
||
|
|
if(v <= 1)
|
||
|
|
return policies::raise_domain_error<RealType>(
|
||
|
|
function,
|
||
|
|
"The non-central t distribution has no defined mean for degrees of freedom <= 1: got v=%1%.", v, Policy());
|
||
|
|
// return l * sqrt(v / 2) * tgamma_delta_ratio((v - 1) * 0.5f, RealType(0.5f));
|
||
|
|
return policies::checked_narrowing_cast<RealType, forwarding_policy>(
|
||
|
|
detail::mean(static_cast<value_type>(v), static_cast<value_type>(l), forwarding_policy()), function);
|
||
|
|
|
||
|
|
} // mean
|
||
|
|
|
||
|
|
template <class RealType, class Policy>
|
||
|
|
inline RealType variance(const non_central_t_distribution<RealType, Policy>& dist)
|
||
|
|
{ // variance.
|
||
|
|
const char* function = "variance(const non_central_t_distribution<%1%>&)";
|
||
|
|
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;
|
||
|
|
BOOST_MATH_STD_USING
|
||
|
|
RealType v = dist.degrees_of_freedom();
|
||
|
|
RealType l = dist.non_centrality();
|
||
|
|
RealType r;
|
||
|
|
if(!detail::check_df_gt0_to_inf(
|
||
|
|
function,
|
||
|
|
v, &r, Policy())
|
||
|
|
||
|
||
|
|
!detail::check_finite(
|
||
|
|
function,
|
||
|
|
l,
|
||
|
|
&r,
|
||
|
|
Policy()))
|
||
|
|
return (RealType)r;
|
||
|
|
if(v <= 2)
|
||
|
|
return policies::raise_domain_error<RealType>(
|
||
|
|
function,
|
||
|
|
"The non-central t distribution has no defined variance for degrees of freedom <= 2: got v=%1%.", v, Policy());
|
||
|
|
return policies::checked_narrowing_cast<RealType, forwarding_policy>(
|
||
|
|
detail::variance(static_cast<value_type>(v), static_cast<value_type>(l), forwarding_policy()), function);
|
||
|
|
}
|
||
|
|
|
||
|
|
// RealType standard_deviation(const non_central_t_distribution<RealType, Policy>& dist)
|
||
|
|
// standard_deviation provided by derived accessors.
|
||
|
|
|
||
|
|
template <class RealType, class Policy>
|
||
|
|
inline RealType skewness(const non_central_t_distribution<RealType, Policy>& dist)
|
||
|
|
{ // skewness = sqrt(l).
|
||
|
|
const char* function = "skewness(const non_central_t_distribution<%1%>&)";
|
||
|
|
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;
|
||
|
|
RealType v = dist.degrees_of_freedom();
|
||
|
|
RealType l = dist.non_centrality();
|
||
|
|
RealType r;
|
||
|
|
if(!detail::check_df_gt0_to_inf(
|
||
|
|
function,
|
||
|
|
v, &r, Policy())
|
||
|
|
||
|
||
|
|
!detail::check_finite(
|
||
|
|
function,
|
||
|
|
l,
|
||
|
|
&r,
|
||
|
|
Policy()))
|
||
|
|
return (RealType)r;
|
||
|
|
if(v <= 3)
|
||
|
|
return policies::raise_domain_error<RealType>(
|
||
|
|
function,
|
||
|
|
"The non-central t distribution has no defined skewness for degrees of freedom <= 3: got v=%1%.", v, Policy());;
|
||
|
|
return policies::checked_narrowing_cast<RealType, forwarding_policy>(
|
||
|
|
detail::skewness(static_cast<value_type>(v), static_cast<value_type>(l), forwarding_policy()), function);
|
||
|
|
}
|
||
|
|
|
||
|
|
template <class RealType, class Policy>
|
||
|
|
inline RealType kurtosis_excess(const non_central_t_distribution<RealType, Policy>& dist)
|
||
|
|
{
|
||
|
|
const char* function = "kurtosis_excess(const non_central_t_distribution<%1%>&)";
|
||
|
|
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;
|
||
|
|
RealType v = dist.degrees_of_freedom();
|
||
|
|
RealType l = dist.non_centrality();
|
||
|
|
RealType r;
|
||
|
|
if(!detail::check_df_gt0_to_inf(
|
||
|
|
function,
|
||
|
|
v, &r, Policy())
|
||
|
|
||
|
||
|
|
!detail::check_finite(
|
||
|
|
function,
|
||
|
|
l,
|
||
|
|
&r,
|
||
|
|
Policy()))
|
||
|
|
return (RealType)r;
|
||
|
|
if(v <= 4)
|
||
|
|
return policies::raise_domain_error<RealType>(
|
||
|
|
function,
|
||
|
|
"The non-central t distribution has no defined kurtosis for degrees of freedom <= 4: got v=%1%.", v, Policy());;
|
||
|
|
return policies::checked_narrowing_cast<RealType, forwarding_policy>(
|
||
|
|
detail::kurtosis_excess(static_cast<value_type>(v), static_cast<value_type>(l), forwarding_policy()), function);
|
||
|
|
} // kurtosis_excess
|
||
|
|
|
||
|
|
template <class RealType, class Policy>
|
||
|
|
inline RealType kurtosis(const non_central_t_distribution<RealType, Policy>& dist)
|
||
|
|
{
|
||
|
|
return kurtosis_excess(dist) + 3;
|
||
|
|
}
|
||
|
|
|
||
|
|
template <class RealType, class Policy>
|
||
|
|
inline RealType pdf(const non_central_t_distribution<RealType, Policy>& dist, const RealType& t)
|
||
|
|
{ // Probability Density/Mass Function.
|
||
|
|
const char* function = "pdf(non_central_t_distribution<%1%>, %1%)";
|
||
|
|
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;
|
||
|
|
|
||
|
|
RealType v = dist.degrees_of_freedom();
|
||
|
|
RealType l = dist.non_centrality();
|
||
|
|
RealType r;
|
||
|
|
if(!detail::check_df_gt0_to_inf(
|
||
|
|
function,
|
||
|
|
v, &r, Policy())
|
||
|
|
||
|
||
|
|
!detail::check_finite(
|
||
|
|
function,
|
||
|
|
l,
|
||
|
|
&r,
|
||
|
|
Policy())
|
||
|
|
||
|
||
|
|
!detail::check_x(
|
||
|
|
function,
|
||
|
|
t,
|
||
|
|
&r,
|
||
|
|
Policy()))
|
||
|
|
return (RealType)r;
|
||
|
|
return policies::checked_narrowing_cast<RealType, forwarding_policy>(
|
||
|
|
detail::non_central_t_pdf(static_cast<value_type>(v),
|
||
|
|
static_cast<value_type>(l),
|
||
|
|
static_cast<value_type>(t),
|
||
|
|
Policy()),
|
||
|
|
function);
|
||
|
|
} // pdf
|
||
|
|
|
||
|
|
template <class RealType, class Policy>
|
||
|
|
RealType cdf(const non_central_t_distribution<RealType, Policy>& dist, const RealType& x)
|
||
|
|
{
|
||
|
|
const char* function = "boost::math::cdf(non_central_t_distribution<%1%>&, %1%)";
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|
// was const char* function = "boost::math::non_central_t_distribution<%1%>::cdf(%1%)";
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|
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typedef typename policies::evaluation<RealType, Policy>::type value_type;
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||
|
|
typedef typename policies::normalise<
|
||
|
|
Policy,
|
||
|
|
policies::promote_float<false>,
|
||
|
|
policies::promote_double<false>,
|
||
|
|
policies::discrete_quantile<>,
|
||
|
|
policies::assert_undefined<> >::type forwarding_policy;
|
||
|
|
|
||
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|
RealType v = dist.degrees_of_freedom();
|
||
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|
RealType l = dist.non_centrality();
|
||
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|
RealType r;
|
||
|
|
if(!detail::check_df_gt0_to_inf(
|
||
|
|
function,
|
||
|
|
v, &r, Policy())
|
||
|
|
||
|
||
|
|
!detail::check_finite(
|
||
|
|
function,
|
||
|
|
l,
|
||
|
|
&r,
|
||
|
|
Policy())
|
||
|
|
||
|
||
|
|
!detail::check_x(
|
||
|
|
function,
|
||
|
|
x,
|
||
|
|
&r,
|
||
|
|
Policy()))
|
||
|
|
return (RealType)r;
|
||
|
|
if ((boost::math::isinf)(v))
|
||
|
|
{ // Infinite degrees of freedom, so use normal distribution located at delta.
|
||
|
|
normal_distribution<RealType, Policy> n(l, 1);
|
||
|
|
cdf(n, x);
|
||
|
|
//return cdf(normal_distribution<RealType, Policy>(l, 1), x);
|
||
|
|
}
|
||
|
|
|
||
|
|
if(l == 0)
|
||
|
|
{ // NO non-centrality, so use Student's t instead.
|
||
|
|
return cdf(students_t_distribution<RealType, Policy>(v), x);
|
||
|
|
}
|
||
|
|
return policies::checked_narrowing_cast<RealType, forwarding_policy>(
|
||
|
|
detail::non_central_t_cdf(
|
||
|
|
static_cast<value_type>(v),
|
||
|
|
static_cast<value_type>(l),
|
||
|
|
static_cast<value_type>(x),
|
||
|
|
false, Policy()),
|
||
|
|
function);
|
||
|
|
} // cdf
|
||
|
|
|
||
|
|
template <class RealType, class Policy>
|
||
|
|
RealType cdf(const complemented2_type<non_central_t_distribution<RealType, Policy>, RealType>& c)
|
||
|
|
{ // Complemented Cumulative Distribution Function
|
||
|
|
// was const char* function = "boost::math::non_central_t_distribution<%1%>::cdf(%1%)";
|
||
|
|
const char* function = "boost::math::cdf(const complement(non_central_t_distribution<%1%>&), %1%)";
|
||
|
|
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;
|
||
|
|
|
||
|
|
non_central_t_distribution<RealType, Policy> const& dist = c.dist;
|
||
|
|
RealType x = c.param;
|
||
|
|
RealType v = dist.degrees_of_freedom();
|
||
|
|
RealType l = dist.non_centrality(); // aka delta
|
||
|
|
RealType r;
|
||
|
|
if(!detail::check_df_gt0_to_inf(
|
||
|
|
function,
|
||
|
|
v, &r, Policy())
|
||
|
|
||
|
||
|
|
!detail::check_finite(
|
||
|
|
function,
|
||
|
|
l,
|
||
|
|
&r,
|
||
|
|
Policy())
|
||
|
|
||
|
||
|
|
!detail::check_x(
|
||
|
|
function,
|
||
|
|
x,
|
||
|
|
&r,
|
||
|
|
Policy()))
|
||
|
|
return (RealType)r;
|
||
|
|
|
||
|
|
if ((boost::math::isinf)(v))
|
||
|
|
{ // Infinite degrees of freedom, so use normal distribution located at delta.
|
||
|
|
normal_distribution<RealType, Policy> n(l, 1);
|
||
|
|
return cdf(complement(n, x));
|
||
|
|
}
|
||
|
|
if(l == 0)
|
||
|
|
{ // zero non-centrality so use Student's t distribution.
|
||
|
|
return cdf(complement(students_t_distribution<RealType, Policy>(v), x));
|
||
|
|
}
|
||
|
|
return policies::checked_narrowing_cast<RealType, forwarding_policy>(
|
||
|
|
detail::non_central_t_cdf(
|
||
|
|
static_cast<value_type>(v),
|
||
|
|
static_cast<value_type>(l),
|
||
|
|
static_cast<value_type>(x),
|
||
|
|
true, Policy()),
|
||
|
|
function);
|
||
|
|
} // ccdf
|
||
|
|
|
||
|
|
template <class RealType, class Policy>
|
||
|
|
inline RealType quantile(const non_central_t_distribution<RealType, Policy>& dist, const RealType& p)
|
||
|
|
{ // Quantile (or Percent Point) function.
|
||
|
|
static const char* function = "quantile(const non_central_t_distribution<%1%>, %1%)";
|
||
|
|
RealType v = dist.degrees_of_freedom();
|
||
|
|
RealType l = dist.non_centrality();
|
||
|
|
return detail::non_central_t_quantile(function, v, l, p, RealType(1-p), Policy());
|
||
|
|
} // quantile
|
||
|
|
|
||
|
|
template <class RealType, class Policy>
|
||
|
|
inline RealType quantile(const complemented2_type<non_central_t_distribution<RealType, Policy>, RealType>& c)
|
||
|
|
{ // Quantile (or Percent Point) function.
|
||
|
|
static const char* function = "quantile(const complement(non_central_t_distribution<%1%>, %1%))";
|
||
|
|
non_central_t_distribution<RealType, Policy> const& dist = c.dist;
|
||
|
|
RealType q = c.param;
|
||
|
|
RealType v = dist.degrees_of_freedom();
|
||
|
|
RealType l = dist.non_centrality();
|
||
|
|
return detail::non_central_t_quantile(function, v, l, RealType(1-q), q, Policy());
|
||
|
|
} // 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_T_HPP
|
||
|
|
|