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Diffstat (limited to 'src/third_party/boost-1.56.0/boost/math/distributions/beta.hpp')
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diff --git a/src/third_party/boost-1.56.0/boost/math/distributions/beta.hpp b/src/third_party/boost-1.56.0/boost/math/distributions/beta.hpp deleted file mode 100644 index 5ecf902d990..00000000000 --- a/src/third_party/boost-1.56.0/boost/math/distributions/beta.hpp +++ /dev/null @@ -1,541 +0,0 @@ -// boost\math\distributions\beta.hpp - -// Copyright John Maddock 2006. -// Copyright Paul A. Bristow 2006. - -// 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) - -// http://en.wikipedia.org/wiki/Beta_distribution -// http://www.itl.nist.gov/div898/handbook/eda/section3/eda366h.htm -// http://mathworld.wolfram.com/BetaDistribution.html - -// The Beta Distribution is a continuous probability distribution. -// The beta distribution is used to model events which are constrained to take place -// within an interval defined by maxima and minima, -// so is used extensively in PERT and other project management systems -// to describe the time to completion. -// The cdf of the beta distribution is used as a convenient way -// of obtaining the sum over a set of binomial outcomes. -// The beta distribution is also used in Bayesian statistics. - -#ifndef BOOST_MATH_DIST_BETA_HPP -#define BOOST_MATH_DIST_BETA_HPP - -#include <boost/math/distributions/fwd.hpp> -#include <boost/math/special_functions/beta.hpp> // for beta. -#include <boost/math/distributions/complement.hpp> // complements. -#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. - -#if defined (BOOST_MSVC) -# pragma warning(push) -# pragma warning(disable: 4702) // unreachable code -// in domain_error_imp in error_handling -#endif - -#include <utility> - -namespace boost -{ - namespace math - { - namespace beta_detail - { - // Common error checking routines for beta distribution functions: - template <class RealType, class Policy> - inline bool check_alpha(const char* function, const RealType& alpha, RealType* result, const Policy& pol) - { - if(!(boost::math::isfinite)(alpha) || (alpha <= 0)) - { - *result = policies::raise_domain_error<RealType>( - function, - "Alpha argument is %1%, but must be > 0 !", alpha, pol); - return false; - } - return true; - } // bool check_alpha - - template <class RealType, class Policy> - inline bool check_beta(const char* function, const RealType& beta, RealType* result, const Policy& pol) - { - if(!(boost::math::isfinite)(beta) || (beta <= 0)) - { - *result = policies::raise_domain_error<RealType>( - function, - "Beta argument is %1%, but must be > 0 !", beta, pol); - return false; - } - return true; - } // bool check_beta - - template <class RealType, class Policy> - inline bool check_prob(const char* function, const RealType& p, RealType* result, const Policy& pol) - { - if((p < 0) || (p > 1) || !(boost::math::isfinite)(p)) - { - *result = policies::raise_domain_error<RealType>( - function, - "Probability argument is %1%, but must be >= 0 and <= 1 !", p, pol); - return false; - } - return true; - } // bool check_prob - - template <class RealType, class Policy> - inline bool check_x(const char* function, const RealType& x, RealType* result, const Policy& pol) - { - if(!(boost::math::isfinite)(x) || (x < 0) || (x > 1)) - { - *result = policies::raise_domain_error<RealType>( - function, - "x argument is %1%, but must be >= 0 and <= 1 !", x, pol); - return false; - } - return true; - } // bool check_x - - template <class RealType, class Policy> - inline bool check_dist(const char* function, const RealType& alpha, const RealType& beta, RealType* result, const Policy& pol) - { // Check both alpha and beta. - return check_alpha(function, alpha, result, pol) - && check_beta(function, beta, result, pol); - } // bool check_dist - - template <class RealType, class Policy> - inline bool check_dist_and_x(const char* function, const RealType& alpha, const RealType& beta, RealType x, RealType* result, const Policy& pol) - { - return check_dist(function, alpha, beta, result, pol) - && beta_detail::check_x(function, x, result, pol); - } // bool check_dist_and_x - - template <class RealType, class Policy> - inline bool check_dist_and_prob(const char* function, const RealType& alpha, const RealType& beta, RealType p, RealType* result, const Policy& pol) - { - return check_dist(function, alpha, beta, result, pol) - && check_prob(function, p, result, pol); - } // bool check_dist_and_prob - - template <class RealType, class Policy> - inline bool check_mean(const char* function, const RealType& mean, RealType* result, const Policy& pol) - { - if(!(boost::math::isfinite)(mean) || (mean <= 0)) - { - *result = policies::raise_domain_error<RealType>( - function, - "mean argument is %1%, but must be > 0 !", mean, pol); - return false; - } - return true; - } // bool check_mean - template <class RealType, class Policy> - inline bool check_variance(const char* function, const RealType& variance, RealType* result, const Policy& pol) - { - if(!(boost::math::isfinite)(variance) || (variance <= 0)) - { - *result = policies::raise_domain_error<RealType>( - function, - "variance argument is %1%, but must be > 0 !", variance, pol); - return false; - } - return true; - } // bool check_variance - } // namespace beta_detail - - // typedef beta_distribution<double> beta; - // is deliberately NOT included to avoid a name clash with the beta function. - // Use beta_distribution<> mybeta(...) to construct type double. - - template <class RealType = double, class Policy = policies::policy<> > - class beta_distribution - { - public: - typedef RealType value_type; - typedef Policy policy_type; - - beta_distribution(RealType l_alpha = 1, RealType l_beta = 1) : m_alpha(l_alpha), m_beta(l_beta) - { - RealType result; - beta_detail::check_dist( - "boost::math::beta_distribution<%1%>::beta_distribution", - m_alpha, - m_beta, - &result, Policy()); - } // beta_distribution constructor. - // Accessor functions: - RealType alpha() const - { - return m_alpha; - } - RealType beta() const - { // . - return m_beta; - } - - // Estimation of the alpha & beta parameters. - // http://en.wikipedia.org/wiki/Beta_distribution - // gives formulae in section on parameter estimation. - // Also NIST EDA page 3 & 4 give the same. - // http://www.itl.nist.gov/div898/handbook/eda/section3/eda366h.htm - // http://www.epi.ucdavis.edu/diagnostictests/betabuster.html - - static RealType find_alpha( - RealType mean, // Expected value of mean. - RealType variance) // Expected value of variance. - { - static const char* function = "boost::math::beta_distribution<%1%>::find_alpha"; - RealType result = 0; // of error checks. - if(false == - ( - beta_detail::check_mean(function, mean, &result, Policy()) - && beta_detail::check_variance(function, variance, &result, Policy()) - ) - ) - { - return result; - } - return mean * (( (mean * (1 - mean)) / variance)- 1); - } // RealType find_alpha - - static RealType find_beta( - RealType mean, // Expected value of mean. - RealType variance) // Expected value of variance. - { - static const char* function = "boost::math::beta_distribution<%1%>::find_beta"; - RealType result = 0; // of error checks. - if(false == - ( - beta_detail::check_mean(function, mean, &result, Policy()) - && - beta_detail::check_variance(function, variance, &result, Policy()) - ) - ) - { - return result; - } - return (1 - mean) * (((mean * (1 - mean)) /variance)-1); - } // RealType find_beta - - // Estimate alpha & beta from either alpha or beta, and x and probability. - // Uses for these parameter estimators are unclear. - - static RealType find_alpha( - RealType beta, // from beta. - RealType x, // x. - RealType probability) // cdf - { - static const char* function = "boost::math::beta_distribution<%1%>::find_alpha"; - RealType result = 0; // of error checks. - if(false == - ( - beta_detail::check_prob(function, probability, &result, Policy()) - && - beta_detail::check_beta(function, beta, &result, Policy()) - && - beta_detail::check_x(function, x, &result, Policy()) - ) - ) - { - return result; - } - return ibeta_inva(beta, x, probability, Policy()); - } // RealType find_alpha(beta, a, probability) - - static RealType find_beta( - // ibeta_invb(T b, T x, T p); (alpha, x, cdf,) - RealType alpha, // alpha. - RealType x, // probability x. - RealType probability) // probability cdf. - { - static const char* function = "boost::math::beta_distribution<%1%>::find_beta"; - RealType result = 0; // of error checks. - if(false == - ( - beta_detail::check_prob(function, probability, &result, Policy()) - && - beta_detail::check_alpha(function, alpha, &result, Policy()) - && - beta_detail::check_x(function, x, &result, Policy()) - ) - ) - { - return result; - } - return ibeta_invb(alpha, x, probability, Policy()); - } // RealType find_beta(alpha, x, probability) - - private: - RealType m_alpha; // Two parameters of the beta distribution. - RealType m_beta; - }; // template <class RealType, class Policy> class beta_distribution - - template <class RealType, class Policy> - inline const std::pair<RealType, RealType> range(const beta_distribution<RealType, Policy>& /* dist */) - { // Range of permissible values for random variable x. - 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 beta_distribution<RealType, Policy>& /* dist */) - { // Range of supported values for random variable x. - // This is range where cdf rises from 0 to 1, and outside it, the pdf is zero. - return std::pair<RealType, RealType>(static_cast<RealType>(0), static_cast<RealType>(1)); - } - - template <class RealType, class Policy> - inline RealType mean(const beta_distribution<RealType, Policy>& dist) - { // Mean of beta distribution = np. - return dist.alpha() / (dist.alpha() + dist.beta()); - } // mean - - template <class RealType, class Policy> - inline RealType variance(const beta_distribution<RealType, Policy>& dist) - { // Variance of beta distribution = np(1-p). - RealType a = dist.alpha(); - RealType b = dist.beta(); - return (a * b) / ((a + b ) * (a + b) * (a + b + 1)); - } // variance - - template <class RealType, class Policy> - inline RealType mode(const beta_distribution<RealType, Policy>& dist) - { - static const char* function = "boost::math::mode(beta_distribution<%1%> const&)"; - - RealType result; - if ((dist.alpha() <= 1)) - { - result = policies::raise_domain_error<RealType>( - function, - "mode undefined for alpha = %1%, must be > 1!", dist.alpha(), Policy()); - return result; - } - - if ((dist.beta() <= 1)) - { - result = policies::raise_domain_error<RealType>( - function, - "mode undefined for beta = %1%, must be > 1!", dist.beta(), Policy()); - return result; - } - RealType a = dist.alpha(); - RealType b = dist.beta(); - return (a-1) / (a + b - 2); - } // mode - - //template <class RealType, class Policy> - //inline RealType median(const beta_distribution<RealType, Policy>& dist) - //{ // Median of beta distribution is not defined. - // return tools::domain_error<RealType>(function, "Median is not implemented, result is %1%!", std::numeric_limits<RealType>::quiet_NaN()); - //} // median - - //But WILL be provided by the derived accessor as quantile(0.5). - - template <class RealType, class Policy> - inline RealType skewness(const beta_distribution<RealType, Policy>& dist) - { - BOOST_MATH_STD_USING // ADL of std functions. - RealType a = dist.alpha(); - RealType b = dist.beta(); - return (2 * (b-a) * sqrt(a + b + 1)) / ((a + b + 2) * sqrt(a * b)); - } // skewness - - template <class RealType, class Policy> - inline RealType kurtosis_excess(const beta_distribution<RealType, Policy>& dist) - { - RealType a = dist.alpha(); - RealType b = dist.beta(); - RealType a_2 = a * a; - RealType n = 6 * (a_2 * a - a_2 * (2 * b - 1) + b * b * (b + 1) - 2 * a * b * (b + 2)); - RealType d = a * b * (a + b + 2) * (a + b + 3); - return n / d; - } // kurtosis_excess - - template <class RealType, class Policy> - inline RealType kurtosis(const beta_distribution<RealType, Policy>& dist) - { - return 3 + kurtosis_excess(dist); - } // kurtosis - - template <class RealType, class Policy> - inline RealType pdf(const beta_distribution<RealType, Policy>& dist, const RealType& x) - { // Probability Density/Mass Function. - BOOST_FPU_EXCEPTION_GUARD - - static const char* function = "boost::math::pdf(beta_distribution<%1%> const&, %1%)"; - - BOOST_MATH_STD_USING // for ADL of std functions - - RealType a = dist.alpha(); - RealType b = dist.beta(); - - // Argument checks: - RealType result = 0; - if(false == beta_detail::check_dist_and_x( - function, - a, b, x, - &result, Policy())) - { - return result; - } - using boost::math::beta; - return ibeta_derivative(a, b, x, Policy()); - } // pdf - - template <class RealType, class Policy> - inline RealType cdf(const beta_distribution<RealType, Policy>& dist, const RealType& x) - { // Cumulative Distribution Function beta. - BOOST_MATH_STD_USING // for ADL of std functions - - static const char* function = "boost::math::cdf(beta_distribution<%1%> const&, %1%)"; - - RealType a = dist.alpha(); - RealType b = dist.beta(); - - // Argument checks: - RealType result = 0; - if(false == beta_detail::check_dist_and_x( - function, - a, b, x, - &result, Policy())) - { - return result; - } - // Special cases: - if (x == 0) - { - return 0; - } - else if (x == 1) - { - return 1; - } - return ibeta(a, b, x, Policy()); - } // beta cdf - - template <class RealType, class Policy> - inline RealType cdf(const complemented2_type<beta_distribution<RealType, Policy>, RealType>& c) - { // Complemented Cumulative Distribution Function beta. - - BOOST_MATH_STD_USING // for ADL of std functions - - static const char* function = "boost::math::cdf(beta_distribution<%1%> const&, %1%)"; - - RealType const& x = c.param; - beta_distribution<RealType, Policy> const& dist = c.dist; - RealType a = dist.alpha(); - RealType b = dist.beta(); - - // Argument checks: - RealType result = 0; - if(false == beta_detail::check_dist_and_x( - function, - a, b, x, - &result, Policy())) - { - return result; - } - if (x == 0) - { - return 1; - } - else if (x == 1) - { - return 0; - } - // Calculate cdf beta using the incomplete beta function. - // Use of ibeta here prevents cancellation errors in calculating - // 1 - x if x is very small, perhaps smaller than machine epsilon. - return ibetac(a, b, x, Policy()); - } // beta cdf - - template <class RealType, class Policy> - inline RealType quantile(const beta_distribution<RealType, Policy>& dist, const RealType& p) - { // Quantile or Percent Point beta function or - // Inverse Cumulative probability distribution function CDF. - // Return x (0 <= x <= 1), - // for a given probability p (0 <= p <= 1). - // These functions take a probability as an argument - // and return a value such that the probability that a random variable x - // will be less than or equal to that value - // is whatever probability you supplied as an argument. - - static const char* function = "boost::math::quantile(beta_distribution<%1%> const&, %1%)"; - - RealType result = 0; // of argument checks: - RealType a = dist.alpha(); - RealType b = dist.beta(); - if(false == beta_detail::check_dist_and_prob( - function, - a, b, p, - &result, Policy())) - { - return result; - } - // Special cases: - if (p == 0) - { - return 0; - } - if (p == 1) - { - return 1; - } - return ibeta_inv(a, b, p, static_cast<RealType*>(0), Policy()); - } // quantile - - template <class RealType, class Policy> - inline RealType quantile(const complemented2_type<beta_distribution<RealType, Policy>, RealType>& c) - { // Complement Quantile or Percent Point beta function . - // Return the number of expected x for a given - // complement of the probability q. - - static const char* function = "boost::math::quantile(beta_distribution<%1%> const&, %1%)"; - - // - // Error checks: - RealType q = c.param; - const beta_distribution<RealType, Policy>& dist = c.dist; - RealType result = 0; - RealType a = dist.alpha(); - RealType b = dist.beta(); - if(false == beta_detail::check_dist_and_prob( - function, - a, - b, - q, - &result, Policy())) - { - return result; - } - // Special cases: - if(q == 1) - { - return 0; - } - if(q == 0) - { - return 1; - } - - return ibetac_inv(a, b, q, static_cast<RealType*>(0), 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> - -#if defined (BOOST_MSVC) -# pragma warning(pop) -#endif - -#endif // BOOST_MATH_DIST_BETA_HPP - - |