| // boost\math\distributions\non_central_beta.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_BETA_HPP
|
| #define BOOST_MATH_SPECIAL_NON_CENTRAL_BETA_HPP
|
|
|
| #include <boost/math/distributions/fwd.hpp>
|
| #include <boost/math/special_functions/beta.hpp> // for incomplete gamma. gamma_q
|
| #include <boost/math/distributions/complement.hpp> // complements
|
| #include <boost/math/distributions/beta.hpp> // central distribution
|
| #include <boost/math/distributions/detail/generic_mode.hpp>
|
| #include <boost/math/distributions/detail/common_error_handling.hpp> // error checks
|
| #include <boost/math/special_functions/fpclassify.hpp> // isnan.
|
| #include <boost/math/tools/roots.hpp> // for root finding.
|
| #include <boost/math/tools/series.hpp>
|
|
|
| namespace boost
|
| {
|
| namespace math
|
| {
|
|
|
| template <class RealType, class Policy>
|
| class non_central_beta_distribution;
|
|
|
| namespace detail{
|
|
|
| template <class T, class Policy>
|
| T non_central_beta_p(T a, T b, T lam, T x, T y, const Policy& pol, T init_val = 0)
|
| {
|
| BOOST_MATH_STD_USING
|
| using namespace boost::math;
|
| //
|
| // Variables come first:
|
| //
|
| boost::uintmax_t max_iter = policies::get_max_series_iterations<Policy>();
|
| T errtol = boost::math::policies::get_epsilon<T, Policy>();
|
| T l2 = lam / 2;
|
| //
|
| // k is the starting point for iteration, and is the
|
| // maximum of the poisson weighting term,
|
| // note that unlike other similar code, we do not set
|
| // k to zero, when l2 is small, as forward iteration
|
| // is unstable:
|
| //
|
| int k = itrunc(l2);
|
| if(k == 0)
|
| k = 1;
|
| T pois;
|
| if(k == 0)
|
| {
|
| // Starting Poisson weight:
|
| pois = exp(-l2);
|
| }
|
| else
|
| {
|
| // Starting Poisson weight:
|
| pois = gamma_p_derivative(T(k+1), l2, pol);
|
| }
|
| if(pois == 0)
|
| return init_val;
|
| // recurance term:
|
| T xterm;
|
| // Starting beta term:
|
| T beta = x < y
|
| ? detail::ibeta_imp(T(a + k), b, x, pol, false, true, &xterm)
|
| : detail::ibeta_imp(b, T(a + k), y, pol, true, true, &xterm);
|
|
|
| xterm *= y / (a + b + k - 1);
|
| T poisf(pois), betaf(beta), xtermf(xterm);
|
| T sum = init_val;
|
|
|
| if((beta == 0) && (xterm == 0))
|
| return init_val;
|
|
|
| //
|
| // Backwards recursion first, this is the stable
|
| // direction for recursion:
|
| //
|
| T last_term = 0;
|
| boost::uintmax_t count = k;
|
| for(int i = k; i >= 0; --i)
|
| {
|
| T term = beta * pois;
|
| sum += term;
|
| if(((fabs(term/sum) < errtol) && (last_term >= term)) || (term == 0))
|
| {
|
| count = k - i;
|
| break;
|
| }
|
| pois *= i / l2;
|
| beta += xterm;
|
| xterm *= (a + i - 1) / (x * (a + b + i - 2));
|
| last_term = term;
|
| }
|
| for(int i = k + 1; ; ++i)
|
| {
|
| poisf *= l2 / i;
|
| xtermf *= (x * (a + b + i - 2)) / (a + i - 1);
|
| betaf -= xtermf;
|
|
|
| T term = poisf * betaf;
|
| sum += term;
|
| if((fabs(term/sum) < errtol) || (term == 0))
|
| {
|
| break;
|
| }
|
| if(static_cast<boost::uintmax_t>(count + i - k) > max_iter)
|
| {
|
| return policies::raise_evaluation_error(
|
| "cdf(non_central_beta_distribution<%1%>, %1%)",
|
| "Series did not converge, closest value was %1%", sum, pol);
|
| }
|
| }
|
| return sum;
|
| }
|
|
|
| template <class T, class Policy>
|
| T non_central_beta_q(T a, T b, T lam, T x, T y, const Policy& pol, T init_val = 0)
|
| {
|
| BOOST_MATH_STD_USING
|
| using namespace boost::math;
|
| //
|
| // Variables come first:
|
| //
|
| boost::uintmax_t max_iter = policies::get_max_series_iterations<Policy>();
|
| T errtol = boost::math::policies::get_epsilon<T, Policy>();
|
| T l2 = lam / 2;
|
| //
|
| // k is the starting point for iteration, and is the
|
| // maximum of the poisson weighting term:
|
| //
|
| int k = itrunc(l2);
|
| T pois;
|
| if(k <= 30)
|
| {
|
| //
|
| // Might as well start at 0 since we'll likely have this number of terms anyway:
|
| //
|
| if(a + b > 1)
|
| k = 0;
|
| else if(k == 0)
|
| k = 1;
|
| }
|
| if(k == 0)
|
| {
|
| // Starting Poisson weight:
|
| pois = exp(-l2);
|
| }
|
| else
|
| {
|
| // Starting Poisson weight:
|
| pois = gamma_p_derivative(T(k+1), l2, pol);
|
| }
|
| if(pois == 0)
|
| return init_val;
|
| // recurance term:
|
| T xterm;
|
| // Starting beta term:
|
| T beta = x < y
|
| ? detail::ibeta_imp(T(a + k), b, x, pol, true, true, &xterm)
|
| : detail::ibeta_imp(b, T(a + k), y, pol, false, true, &xterm);
|
|
|
| xterm *= y / (a + b + k - 1);
|
| T poisf(pois), betaf(beta), xtermf(xterm);
|
| T sum = init_val;
|
| if((beta == 0) && (xterm == 0))
|
| return init_val;
|
| //
|
| // Forwards recursion first, this is the stable
|
| // direction for recursion, and the location
|
| // of the bulk of the sum:
|
| //
|
| T last_term = 0;
|
| boost::uintmax_t count = 0;
|
| for(int i = k + 1; ; ++i)
|
| {
|
| poisf *= l2 / i;
|
| xtermf *= (x * (a + b + i - 2)) / (a + i - 1);
|
| betaf += xtermf;
|
|
|
| T term = poisf * betaf;
|
| sum += term;
|
| if((fabs(term/sum) < errtol) && (last_term >= term))
|
| {
|
| count = i - k;
|
| break;
|
| }
|
| if(static_cast<boost::uintmax_t>(i - k) > max_iter)
|
| {
|
| return policies::raise_evaluation_error(
|
| "cdf(non_central_beta_distribution<%1%>, %1%)",
|
| "Series did not converge, closest value was %1%", sum, pol);
|
| }
|
| last_term = term;
|
| }
|
| for(int i = k; i >= 0; --i)
|
| {
|
| T term = beta * pois;
|
| sum += term;
|
| if(fabs(term/sum) < errtol)
|
| {
|
| break;
|
| }
|
| if(static_cast<boost::uintmax_t>(count + k - i) > max_iter)
|
| {
|
| return policies::raise_evaluation_error(
|
| "cdf(non_central_beta_distribution<%1%>, %1%)",
|
| "Series did not converge, closest value was %1%", sum, pol);
|
| }
|
| pois *= i / l2;
|
| beta -= xterm;
|
| xterm *= (a + i - 1) / (x * (a + b + i - 2));
|
| }
|
| return sum;
|
| }
|
|
|
| template <class RealType, class Policy>
|
| inline RealType non_central_beta_cdf(RealType x, RealType y, RealType a, RealType b, RealType l, bool invert, const Policy&)
|
| {
|
| 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
|
|
|
| if(x == 0)
|
| return invert ? 1.0f : 0.0f;
|
| if(y == 0)
|
| return invert ? 0.0f : 1.0f;
|
| value_type result;
|
| value_type c = a + b + l / 2;
|
| value_type cross = 1 - (b / c) * (1 + l / (2 * c * c));
|
| if(l == 0)
|
| result = cdf(boost::math::beta_distribution<RealType, Policy>(a, b), x);
|
| else if(x > cross)
|
| {
|
| // Complement is the smaller of the two:
|
| result = detail::non_central_beta_q(
|
| static_cast<value_type>(a),
|
| static_cast<value_type>(b),
|
| static_cast<value_type>(l),
|
| static_cast<value_type>(x),
|
| static_cast<value_type>(y),
|
| forwarding_policy(),
|
| static_cast<value_type>(invert ? 0 : -1));
|
| invert = !invert;
|
| }
|
| else
|
| {
|
| result = detail::non_central_beta_p(
|
| static_cast<value_type>(a),
|
| static_cast<value_type>(b),
|
| static_cast<value_type>(l),
|
| static_cast<value_type>(x),
|
| static_cast<value_type>(y),
|
| forwarding_policy(),
|
| static_cast<value_type>(invert ? -1 : 0));
|
| }
|
| if(invert)
|
| result = -result;
|
| return policies::checked_narrowing_cast<RealType, forwarding_policy>(
|
| result,
|
| "boost::math::non_central_beta_cdf<%1%>(%1%, %1%, %1%)");
|
| }
|
|
|
| template <class T, class Policy>
|
| struct nc_beta_quantile_functor
|
| {
|
| nc_beta_quantile_functor(const non_central_beta_distribution<T,Policy>& d, T t, bool c)
|
| : dist(d), target(t), comp(c) {}
|
|
|
| T operator()(const T& x)
|
| {
|
| return comp ?
|
| target - cdf(complement(dist, x))
|
| : cdf(dist, x) - target;
|
| }
|
|
|
| private:
|
| non_central_beta_distribution<T,Policy> dist;
|
| T target;
|
| bool comp;
|
| };
|
|
|
| //
|
| // This is more or less a copy of bracket_and_solve_root, but
|
| // modified to search only the interval [0,1] using similar
|
| // heuristics.
|
| //
|
| template <class F, class T, class Tol, class Policy>
|
| std::pair<T, T> bracket_and_solve_root_01(F f, const T& guess, T factor, bool rising, Tol tol, boost::uintmax_t& max_iter, const Policy& pol)
|
| {
|
| BOOST_MATH_STD_USING
|
| static const char* function = "boost::math::tools::bracket_and_solve_root_01<%1%>";
|
| //
|
| // Set up inital brackets:
|
| //
|
| T a = guess;
|
| T b = a;
|
| T fa = f(a);
|
| T fb = fa;
|
| //
|
| // Set up invocation count:
|
| //
|
| boost::uintmax_t count = max_iter - 1;
|
|
|
| if((fa < 0) == (guess < 0 ? !rising : rising))
|
| {
|
| //
|
| // Zero is to the right of b, so walk upwards
|
| // until we find it:
|
| //
|
| while((boost::math::sign)(fb) == (boost::math::sign)(fa))
|
| {
|
| if(count == 0)
|
| {
|
| b = policies::raise_evaluation_error(function, "Unable to bracket root, last nearest value was %1%", b, pol);
|
| return std::make_pair(a, b);
|
| }
|
| //
|
| // Heuristic: every 20 iterations we double the growth factor in case the
|
| // initial guess was *really* bad !
|
| //
|
| if((max_iter - count) % 20 == 0)
|
| factor *= 2;
|
| //
|
| // Now go ahead and move are guess by "factor",
|
| // we do this by reducing 1-guess by factor:
|
| //
|
| a = b;
|
| fa = fb;
|
| b = 1 - ((1 - b) / factor);
|
| fb = f(b);
|
| --count;
|
| BOOST_MATH_INSTRUMENT_CODE("a = " << a << " b = " << b << " fa = " << fa << " fb = " << fb << " count = " << count);
|
| }
|
| }
|
| else
|
| {
|
| //
|
| // Zero is to the left of a, so walk downwards
|
| // until we find it:
|
| //
|
| while((boost::math::sign)(fb) == (boost::math::sign)(fa))
|
| {
|
| if(fabs(a) < tools::min_value<T>())
|
| {
|
| // Escape route just in case the answer is zero!
|
| max_iter -= count;
|
| max_iter += 1;
|
| return a > 0 ? std::make_pair(T(0), T(a)) : std::make_pair(T(a), T(0));
|
| }
|
| if(count == 0)
|
| {
|
| a = policies::raise_evaluation_error(function, "Unable to bracket root, last nearest value was %1%", a, pol);
|
| return std::make_pair(a, b);
|
| }
|
| //
|
| // Heuristic: every 20 iterations we double the growth factor in case the
|
| // initial guess was *really* bad !
|
| //
|
| if((max_iter - count) % 20 == 0)
|
| factor *= 2;
|
| //
|
| // Now go ahead and move are guess by "factor":
|
| //
|
| b = a;
|
| fb = fa;
|
| a /= factor;
|
| fa = f(a);
|
| --count;
|
| BOOST_MATH_INSTRUMENT_CODE("a = " << a << " b = " << b << " fa = " << fa << " fb = " << fb << " count = " << count);
|
| }
|
| }
|
| max_iter -= count;
|
| max_iter += 1;
|
| std::pair<T, T> r = toms748_solve(
|
| f,
|
| (a < 0 ? b : a),
|
| (a < 0 ? a : b),
|
| (a < 0 ? fb : fa),
|
| (a < 0 ? fa : fb),
|
| tol,
|
| count,
|
| pol);
|
| max_iter += count;
|
| BOOST_MATH_INSTRUMENT_CODE("max_iter = " << max_iter << " count = " << count);
|
| return r;
|
| }
|
|
|
| template <class RealType, class Policy>
|
| RealType nc_beta_quantile(const non_central_beta_distribution<RealType, Policy>& dist, const RealType& p, bool comp)
|
| {
|
| static const char* function = "quantile(non_central_beta_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;
|
|
|
| value_type a = dist.alpha();
|
| value_type b = dist.beta();
|
| value_type l = dist.non_centrality();
|
| value_type r;
|
| if(!beta_detail::check_alpha(
|
| function,
|
| a, &r, Policy())
|
| ||
|
| !beta_detail::check_beta(
|
| function,
|
| b, &r, Policy())
|
| ||
|
| !detail::check_non_centrality(
|
| function,
|
| l,
|
| &r,
|
| Policy())
|
| ||
|
| !detail::check_probability(
|
| function,
|
| static_cast<value_type>(p),
|
| &r,
|
| Policy()))
|
| return (RealType)r;
|
| //
|
| // Special cases first:
|
| //
|
| if(p == 0)
|
| return comp
|
| ? 1.0f
|
| : 0.0f;
|
| if(p == 1)
|
| return !comp
|
| ? 1.0f
|
| : 0.0f;
|
|
|
| value_type c = a + b + l / 2;
|
| value_type mean = 1 - (b / c) * (1 + l / (2 * c * c));
|
| /*
|
| //
|
| // Calculate a normal approximation to the quantile,
|
| // uses mean and variance approximations from:
|
| // Algorithm AS 310:
|
| // Computing the Non-Central Beta Distribution Function
|
| // R. Chattamvelli; R. Shanmugam
|
| // Applied Statistics, Vol. 46, No. 1. (1997), pp. 146-156.
|
| //
|
| // Unfortunately, when this is wrong it tends to be *very*
|
| // wrong, so it's disabled for now, even though it often
|
| // gets the initial guess quite close. Probably we could
|
| // do much better by factoring in the skewness if only
|
| // we could calculate it....
|
| //
|
| value_type delta = l / 2;
|
| value_type delta2 = delta * delta;
|
| value_type delta3 = delta * delta2;
|
| value_type delta4 = delta2 * delta2;
|
| value_type G = c * (c + 1) + delta;
|
| value_type alpha = a + b;
|
| value_type alpha2 = alpha * alpha;
|
| value_type eta = (2 * alpha + 1) * (2 * alpha + 1) + 1;
|
| value_type H = 3 * alpha2 + 5 * alpha + 2;
|
| value_type F = alpha2 * (alpha + 1) + H * delta
|
| + (2 * alpha + 4) * delta2 + delta3;
|
| value_type P = (3 * alpha + 1) * (9 * alpha + 17)
|
| + 2 * alpha * (3 * alpha + 2) * (3 * alpha + 4) + 15;
|
| value_type Q = 54 * alpha2 + 162 * alpha + 130;
|
| value_type R = 6 * (6 * alpha + 11);
|
| value_type D = delta
|
| * (H * H + 2 * P * delta + Q * delta2 + R * delta3 + 9 * delta4);
|
| value_type variance = (b / G)
|
| * (1 + delta * (l * l + 3 * l + eta) / (G * G))
|
| - (b * b / F) * (1 + D / (F * F));
|
| value_type sd = sqrt(variance);
|
|
|
| value_type guess = comp
|
| ? quantile(complement(normal_distribution<RealType, Policy>(static_cast<RealType>(mean), static_cast<RealType>(sd)), p))
|
| : quantile(normal_distribution<RealType, Policy>(static_cast<RealType>(mean), static_cast<RealType>(sd)), p);
|
|
|
| if(guess >= 1)
|
| guess = mean;
|
| if(guess <= tools::min_value<value_type>())
|
| guess = mean;
|
| */
|
| value_type guess = mean;
|
| detail::nc_beta_quantile_functor<value_type, Policy>
|
| f(non_central_beta_distribution<value_type, Policy>(a, b, l), p, comp);
|
| tools::eps_tolerance<value_type> tol(policies::digits<RealType, Policy>());
|
| boost::uintmax_t max_iter = policies::get_max_root_iterations<Policy>();
|
|
|
| std::pair<value_type, value_type> ir
|
| = bracket_and_solve_root_01(
|
| f, guess, value_type(2.5), true, tol,
|
| max_iter, Policy());
|
| value_type 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:"
|
| " either there is no answer to quantile of the non central beta distribution"
|
| " or the answer is infinite. Current best guess is %1%",
|
| policies::checked_narrowing_cast<RealType, forwarding_policy>(
|
| result,
|
| function), Policy());
|
| }
|
| return policies::checked_narrowing_cast<RealType, forwarding_policy>(
|
| result,
|
| function);
|
| }
|
|
|
| template <class T, class Policy>
|
| T non_central_beta_pdf(T a, T b, T lam, T x, T y, const Policy& pol)
|
| {
|
| BOOST_MATH_STD_USING
|
| using namespace boost::math;
|
| //
|
| // Variables come first:
|
| //
|
| boost::uintmax_t max_iter = policies::get_max_series_iterations<Policy>();
|
| T errtol = boost::math::policies::get_epsilon<T, Policy>();
|
| T l2 = lam / 2;
|
| //
|
| // k is the starting point for iteration, and is the
|
| // maximum of the poisson weighting term:
|
| //
|
| int k = itrunc(l2);
|
| // Starting Poisson weight:
|
| T pois = gamma_p_derivative(T(k+1), l2, pol);
|
| // Starting beta term:
|
| T beta = x < y ?
|
| ibeta_derivative(a + k, b, x, pol)
|
| : ibeta_derivative(b, a + k, y, pol);
|
| T sum = 0;
|
| T poisf(pois);
|
| T betaf(beta);
|
|
|
| //
|
| // Stable backwards recursion first:
|
| //
|
| boost::uintmax_t count = k;
|
| for(int i = k; i >= 0; --i)
|
| {
|
| T term = beta * pois;
|
| sum += term;
|
| if((fabs(term/sum) < errtol) || (term == 0))
|
| {
|
| count = k - i;
|
| break;
|
| }
|
| pois *= i / l2;
|
| beta *= (a + i - 1) / (x * (a + i + b - 1));
|
| }
|
| for(int i = k + 1; ; ++i)
|
| {
|
| poisf *= l2 / i;
|
| betaf *= x * (a + b + i - 1) / (a + i - 1);
|
|
|
| T term = poisf * betaf;
|
| sum += term;
|
| if((fabs(term/sum) < errtol) || (term == 0))
|
| {
|
| break;
|
| }
|
| if(static_cast<boost::uintmax_t>(count + i - k) > max_iter)
|
| {
|
| return policies::raise_evaluation_error(
|
| "pdf(non_central_beta_distribution<%1%>, %1%)",
|
| "Series did not converge, closest value was %1%", sum, pol);
|
| }
|
| }
|
| return sum;
|
| }
|
|
|
| template <class RealType, class Policy>
|
| RealType nc_beta_pdf(const non_central_beta_distribution<RealType, Policy>& dist, const RealType& x)
|
| {
|
| BOOST_MATH_STD_USING
|
| static const char* function = "pdf(non_central_beta_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;
|
|
|
| value_type a = dist.alpha();
|
| value_type b = dist.beta();
|
| value_type l = dist.non_centrality();
|
| value_type r;
|
| if(!beta_detail::check_alpha(
|
| function,
|
| a, &r, Policy())
|
| ||
|
| !beta_detail::check_beta(
|
| function,
|
| b, &r, Policy())
|
| ||
|
| !detail::check_non_centrality(
|
| function,
|
| l,
|
| &r,
|
| Policy())
|
| ||
|
| !beta_detail::check_x(
|
| function,
|
| static_cast<value_type>(x),
|
| &r,
|
| Policy()))
|
| return (RealType)r;
|
|
|
| if(l == 0)
|
| return pdf(boost::math::beta_distribution<RealType, Policy>(dist.alpha(), dist.beta()), x);
|
| return policies::checked_narrowing_cast<RealType, forwarding_policy>(
|
| non_central_beta_pdf(a, b, l, static_cast<value_type>(x), value_type(1 - static_cast<value_type>(x)), forwarding_policy()),
|
| "function");
|
| }
|
|
|
| template <class T>
|
| struct hypergeometric_2F2_sum
|
| {
|
| typedef T result_type;
|
| hypergeometric_2F2_sum(T a1_, T a2_, T b1_, T b2_, T z_) : a1(a1_), a2(a2_), b1(b1_), b2(b2_), z(z_), term(1), k(0) {}
|
| T operator()()
|
| {
|
| T result = term;
|
| term *= a1 * a2 / (b1 * b2);
|
| a1 += 1;
|
| a2 += 1;
|
| b1 += 1;
|
| b2 += 1;
|
| k += 1;
|
| term /= k;
|
| term *= z;
|
| return result;
|
| }
|
| T a1, a2, b1, b2, z, term, k;
|
| };
|
|
|
| template <class T, class Policy>
|
| T hypergeometric_2F2(T a1, T a2, T b1, T b2, T z, const Policy& pol)
|
| {
|
| typedef typename policies::evaluation<T, Policy>::type value_type;
|
|
|
| const char* function = "boost::math::detail::hypergeometric_2F2<%1%>(%1%,%1%,%1%,%1%,%1%)";
|
|
|
| hypergeometric_2F2_sum<value_type> s(a1, a2, b1, b2, z);
|
| boost::uintmax_t max_iter = policies::get_max_series_iterations<Policy>();
|
| #if BOOST_WORKAROUND(__BORLANDC__, BOOST_TESTED_AT(0x582))
|
| value_type zero = 0;
|
| value_type result = boost::math::tools::sum_series(s, boost::math::policies::get_epsilon<value_type, Policy>(), max_iter, zero);
|
| #else
|
| value_type result = boost::math::tools::sum_series(s, boost::math::policies::get_epsilon<value_type, Policy>(), max_iter);
|
| #endif
|
| policies::check_series_iterations(function, max_iter, pol);
|
| return policies::checked_narrowing_cast<T, Policy>(result, function);
|
| }
|
|
|
| } // namespace detail
|
|
|
| template <class RealType = double, class Policy = policies::policy<> >
|
| class non_central_beta_distribution
|
| {
|
| public:
|
| typedef RealType value_type;
|
| typedef Policy policy_type;
|
|
|
| non_central_beta_distribution(RealType a_, RealType b_, RealType lambda) : a(a_), b(b_), ncp(lambda)
|
| {
|
| const char* function = "boost::math::non_central_beta_distribution<%1%>::non_central_beta_distribution(%1%,%1%)";
|
| RealType r;
|
| beta_detail::check_alpha(
|
| function,
|
| a, &r, Policy());
|
| beta_detail::check_beta(
|
| function,
|
| b, &r, Policy());
|
| detail::check_non_centrality(
|
| function,
|
| lambda,
|
| &r,
|
| Policy());
|
| } // non_central_beta_distribution constructor.
|
|
|
| RealType alpha() const
|
| { // Private data getter function.
|
| return a;
|
| }
|
| RealType beta() const
|
| { // Private data getter function.
|
| return b;
|
| }
|
| RealType non_centrality() const
|
| { // Private data getter function.
|
| return ncp;
|
| }
|
| private:
|
| // Data member, initialized by constructor.
|
| RealType a; // alpha.
|
| RealType b; // beta.
|
| RealType ncp; // non-centrality parameter
|
| }; // template <class RealType, class Policy> class non_central_beta_distribution
|
|
|
| typedef non_central_beta_distribution<double> non_central_beta; // 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_beta_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), static_cast<RealType>(1));
|
| }
|
|
|
| template <class RealType, class Policy>
|
| inline const std::pair<RealType, RealType> support(const non_central_beta_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), static_cast<RealType>(1));
|
| }
|
|
|
| template <class RealType, class Policy>
|
| inline RealType mode(const non_central_beta_distribution<RealType, Policy>& dist)
|
| { // mode.
|
| static const char* function = "mode(non_central_beta_distribution<%1%> const&)";
|
|
|
| RealType a = dist.alpha();
|
| RealType b = dist.beta();
|
| RealType l = dist.non_centrality();
|
| RealType r;
|
| if(!beta_detail::check_alpha(
|
| function,
|
| a, &r, Policy())
|
| ||
|
| !beta_detail::check_beta(
|
| function,
|
| b, &r, Policy())
|
| ||
|
| !detail::check_non_centrality(
|
| function,
|
| l,
|
| &r,
|
| Policy()))
|
| return (RealType)r;
|
| RealType c = a + b + l / 2;
|
| RealType mean = 1 - (b / c) * (1 + l / (2 * c * c));
|
| return detail::generic_find_mode_01(
|
| dist,
|
| mean,
|
| function);
|
| }
|
|
|
| //
|
| // We don't have the necessary information to implement
|
| // these at present. These are just disabled for now,
|
| // prototypes retained so we can fill in the blanks
|
| // later:
|
| //
|
| template <class RealType, class Policy>
|
| inline RealType mean(const non_central_beta_distribution<RealType, Policy>& dist)
|
| {
|
| BOOST_MATH_STD_USING
|
| RealType a = dist.alpha();
|
| RealType b = dist.beta();
|
| RealType d = dist.non_centrality();
|
| RealType apb = a + b;
|
| return exp(-d / 2) * a * detail::hypergeometric_2F2<RealType, Policy>(1 + a, apb, a, 1 + apb, d / 2, Policy()) / apb;
|
| } // mean
|
|
|
| template <class RealType, class Policy>
|
| inline RealType variance(const non_central_beta_distribution<RealType, Policy>& dist)
|
| {
|
| //
|
| // Relative error of this function may be arbitarily large... absolute
|
| // error will be small however... that's the best we can do for now.
|
| //
|
| BOOST_MATH_STD_USING
|
| RealType a = dist.alpha();
|
| RealType b = dist.beta();
|
| RealType d = dist.non_centrality();
|
| RealType apb = a + b;
|
| RealType result = detail::hypergeometric_2F2(RealType(1 + a), apb, a, RealType(1 + apb), RealType(d / 2), Policy());
|
| result *= result * -exp(-d) * a * a / (apb * apb);
|
| result += exp(-d / 2) * a * (1 + a) * detail::hypergeometric_2F2(RealType(2 + a), apb, a, RealType(2 + apb), RealType(d / 2), Policy()) / (apb * (1 + apb));
|
| return result;
|
| }
|
|
|
| // RealType standard_deviation(const non_central_beta_distribution<RealType, Policy>& dist)
|
| // standard_deviation provided by derived accessors.
|
| template <class RealType, class Policy>
|
| inline RealType skewness(const non_central_beta_distribution<RealType, Policy>& /*dist*/)
|
| { // skewness = sqrt(l).
|
| const char* function = "boost::math::non_central_beta_distribution<%1%>::skewness()";
|
| typedef typename Policy::assert_undefined_type assert_type;
|
| BOOST_STATIC_ASSERT(assert_type::value == 0);
|
|
|
| return policies::raise_evaluation_error<RealType>(
|
| function,
|
| "This function is not yet implemented, the only sensible result is %1%.",
|
| std::numeric_limits<RealType>::quiet_NaN(), Policy()); // infinity?
|
| }
|
|
|
| template <class RealType, class Policy>
|
| inline RealType kurtosis_excess(const non_central_beta_distribution<RealType, Policy>& /*dist*/)
|
| {
|
| const char* function = "boost::math::non_central_beta_distribution<%1%>::kurtosis_excess()";
|
| typedef typename Policy::assert_undefined_type assert_type;
|
| BOOST_STATIC_ASSERT(assert_type::value == 0);
|
|
|
| return policies::raise_evaluation_error<RealType>(
|
| function,
|
| "This function is not yet implemented, the only sensible result is %1%.",
|
| std::numeric_limits<RealType>::quiet_NaN(), Policy()); // infinity?
|
| } // kurtosis_excess
|
|
|
| template <class RealType, class Policy>
|
| inline RealType kurtosis(const non_central_beta_distribution<RealType, Policy>& dist)
|
| {
|
| return kurtosis_excess(dist) + 3;
|
| }
|
|
|
| template <class RealType, class Policy>
|
| inline RealType pdf(const non_central_beta_distribution<RealType, Policy>& dist, const RealType& x)
|
| { // Probability Density/Mass Function.
|
| return detail::nc_beta_pdf(dist, x);
|
| } // pdf
|
|
|
| template <class RealType, class Policy>
|
| RealType cdf(const non_central_beta_distribution<RealType, Policy>& dist, const RealType& x)
|
| {
|
| const char* function = "boost::math::non_central_beta_distribution<%1%>::cdf(%1%)";
|
| RealType a = dist.alpha();
|
| RealType b = dist.beta();
|
| RealType l = dist.non_centrality();
|
| RealType r;
|
| if(!beta_detail::check_alpha(
|
| function,
|
| a, &r, Policy())
|
| ||
|
| !beta_detail::check_beta(
|
| function,
|
| b, &r, Policy())
|
| ||
|
| !detail::check_non_centrality(
|
| function,
|
| l,
|
| &r,
|
| Policy())
|
| ||
|
| !beta_detail::check_x(
|
| function,
|
| x,
|
| &r,
|
| Policy()))
|
| return (RealType)r;
|
|
|
| if(l == 0)
|
| return cdf(beta_distribution<RealType, Policy>(a, b), x);
|
|
|
| return detail::non_central_beta_cdf(x, RealType(1 - x), a, b, l, false, Policy());
|
| } // cdf
|
|
|
| template <class RealType, class Policy>
|
| RealType cdf(const complemented2_type<non_central_beta_distribution<RealType, Policy>, RealType>& c)
|
| { // Complemented Cumulative Distribution Function
|
| const char* function = "boost::math::non_central_beta_distribution<%1%>::cdf(%1%)";
|
| non_central_beta_distribution<RealType, Policy> const& dist = c.dist;
|
| RealType a = dist.alpha();
|
| RealType b = dist.beta();
|
| RealType l = dist.non_centrality();
|
| RealType x = c.param;
|
| RealType r;
|
| if(!beta_detail::check_alpha(
|
| function,
|
| a, &r, Policy())
|
| ||
|
| !beta_detail::check_beta(
|
| function,
|
| b, &r, Policy())
|
| ||
|
| !detail::check_non_centrality(
|
| function,
|
| l,
|
| &r,
|
| Policy())
|
| ||
|
| !beta_detail::check_x(
|
| function,
|
| x,
|
| &r,
|
| Policy()))
|
| return (RealType)r;
|
|
|
| if(l == 0)
|
| return cdf(complement(beta_distribution<RealType, Policy>(a, b), x));
|
|
|
| return detail::non_central_beta_cdf(x, RealType(1 - x), a, b, l, true, Policy());
|
| } // ccdf
|
|
|
| template <class RealType, class Policy>
|
| inline RealType quantile(const non_central_beta_distribution<RealType, Policy>& dist, const RealType& p)
|
| { // Quantile (or Percent Point) function.
|
| return detail::nc_beta_quantile(dist, p, false);
|
| } // quantile
|
|
|
| template <class RealType, class Policy>
|
| inline RealType quantile(const complemented2_type<non_central_beta_distribution<RealType, Policy>, RealType>& c)
|
| { // Quantile (or Percent Point) function.
|
| return detail::nc_beta_quantile(c.dist, c.param, true);
|
| } // 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_BETA_HPP
|
|
|
