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diff --git a/src/third_party/boost-1.69.0/boost/math/distributions/negative_binomial.hpp b/src/third_party/boost-1.69.0/boost/math/distributions/negative_binomial.hpp deleted file mode 100644 index 3b4de4062f7..00000000000 --- a/src/third_party/boost-1.69.0/boost/math/distributions/negative_binomial.hpp +++ /dev/null @@ -1,607 +0,0 @@ -// boost\math\special_functions\negative_binomial.hpp - -// Copyright Paul A. Bristow 2007. -// Copyright John Maddock 2007. - -// 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/negative_binomial_distribution -// http://mathworld.wolfram.com/NegativeBinomialDistribution.html -// http://documents.wolfram.com/teachersedition/Teacher/Statistics/DiscreteDistributions.html - -// The negative binomial distribution NegativeBinomialDistribution[n, p] -// is the distribution of the number (k) of failures that occur in a sequence of trials before -// r successes have occurred, where the probability of success in each trial is p. - -// In a sequence of Bernoulli trials or events -// (independent, yes or no, succeed or fail) with success_fraction probability p, -// negative_binomial is the probability that k or fewer failures -// preceed the r th trial's success. -// random variable k is the number of failures (NOT the probability). - -// Negative_binomial distribution is a discrete probability distribution. -// But note that the negative binomial distribution -// (like others including the binomial, Poisson & Bernoulli) -// is strictly defined as a discrete function: only integral values of k are envisaged. -// However because of the method of calculation using a continuous gamma function, -// it is convenient to treat it as if a continous function, -// and permit non-integral values of k. - -// However, by default the policy is to use discrete_quantile_policy. - -// To enforce the strict mathematical model, users should use conversion -// on k outside this function to ensure that k is integral. - -// MATHCAD cumulative negative binomial pnbinom(k, n, p) - -// Implementation note: much greater speed, and perhaps greater accuracy, -// might be achieved for extreme values by using a normal approximation. -// This is NOT been tested or implemented. - -#ifndef BOOST_MATH_SPECIAL_NEGATIVE_BINOMIAL_HPP -#define BOOST_MATH_SPECIAL_NEGATIVE_BINOMIAL_HPP - -#include <boost/math/distributions/fwd.hpp> -#include <boost/math/special_functions/beta.hpp> // for ibeta(a, b, x) == Ix(a, b). -#include <boost/math/distributions/complement.hpp> // complement. -#include <boost/math/distributions/detail/common_error_handling.hpp> // error checks domain_error & logic_error. -#include <boost/math/special_functions/fpclassify.hpp> // isnan. -#include <boost/math/tools/roots.hpp> // for root finding. -#include <boost/math/distributions/detail/inv_discrete_quantile.hpp> - -#include <boost/type_traits/is_floating_point.hpp> -#include <boost/type_traits/is_integral.hpp> -#include <boost/type_traits/is_same.hpp> -#include <boost/mpl/if.hpp> - -#include <limits> // using std::numeric_limits; -#include <utility> - -#if defined (BOOST_MSVC) -# pragma warning(push) -// This believed not now necessary, so commented out. -//# pragma warning(disable: 4702) // unreachable code. -// in domain_error_imp in error_handling. -#endif - -namespace boost -{ - namespace math - { - namespace negative_binomial_detail - { - // Common error checking routines for negative binomial distribution functions: - template <class RealType, class Policy> - inline bool check_successes(const char* function, const RealType& r, RealType* result, const Policy& pol) - { - if( !(boost::math::isfinite)(r) || (r <= 0) ) - { - *result = policies::raise_domain_error<RealType>( - function, - "Number of successes argument is %1%, but must be > 0 !", r, pol); - return false; - } - return true; - } - template <class RealType, class Policy> - inline bool check_success_fraction(const char* function, const RealType& p, RealType* result, const Policy& pol) - { - if( !(boost::math::isfinite)(p) || (p < 0) || (p > 1) ) - { - *result = policies::raise_domain_error<RealType>( - function, - "Success fraction argument is %1%, but must be >= 0 and <= 1 !", p, pol); - return false; - } - return true; - } - template <class RealType, class Policy> - inline bool check_dist(const char* function, const RealType& r, const RealType& p, RealType* result, const Policy& pol) - { - return check_success_fraction(function, p, result, pol) - && check_successes(function, r, result, pol); - } - template <class RealType, class Policy> - inline bool check_dist_and_k(const char* function, const RealType& r, const RealType& p, RealType k, RealType* result, const Policy& pol) - { - if(check_dist(function, r, p, result, pol) == false) - { - return false; - } - if( !(boost::math::isfinite)(k) || (k < 0) ) - { // Check k failures. - *result = policies::raise_domain_error<RealType>( - function, - "Number of failures argument is %1%, but must be >= 0 !", k, pol); - return false; - } - return true; - } // Check_dist_and_k - - template <class RealType, class Policy> - inline bool check_dist_and_prob(const char* function, const RealType& r, RealType p, RealType prob, RealType* result, const Policy& pol) - { - if((check_dist(function, r, p, result, pol) && detail::check_probability(function, prob, result, pol)) == false) - { - return false; - } - return true; - } // check_dist_and_prob - } // namespace negative_binomial_detail - - template <class RealType = double, class Policy = policies::policy<> > - class negative_binomial_distribution - { - public: - typedef RealType value_type; - typedef Policy policy_type; - - negative_binomial_distribution(RealType r, RealType p) : m_r(r), m_p(p) - { // Constructor. - RealType result; - negative_binomial_detail::check_dist( - "negative_binomial_distribution<%1%>::negative_binomial_distribution", - m_r, // Check successes r > 0. - m_p, // Check success_fraction 0 <= p <= 1. - &result, Policy()); - } // negative_binomial_distribution constructor. - - // Private data getter class member functions. - RealType success_fraction() const - { // Probability of success as fraction in range 0 to 1. - return m_p; - } - RealType successes() const - { // Total number of successes r. - return m_r; - } - - static RealType find_lower_bound_on_p( - RealType trials, - RealType successes, - RealType alpha) // alpha 0.05 equivalent to 95% for one-sided test. - { - static const char* function = "boost::math::negative_binomial<%1%>::find_lower_bound_on_p"; - RealType result = 0; // of error checks. - RealType failures = trials - successes; - if(false == detail::check_probability(function, alpha, &result, Policy()) - && negative_binomial_detail::check_dist_and_k( - function, successes, RealType(0), failures, &result, Policy())) - { - return result; - } - // Use complement ibeta_inv function for lower bound. - // This is adapted from the corresponding binomial formula - // here: http://www.itl.nist.gov/div898/handbook/prc/section2/prc241.htm - // This is a Clopper-Pearson interval, and may be overly conservative, - // see also "A Simple Improved Inferential Method for Some - // Discrete Distributions" Yong CAI and K. KRISHNAMOORTHY - // http://www.ucs.louisiana.edu/~kxk4695/Discrete_new.pdf - // - return ibeta_inv(successes, failures + 1, alpha, static_cast<RealType*>(0), Policy()); - } // find_lower_bound_on_p - - static RealType find_upper_bound_on_p( - RealType trials, - RealType successes, - RealType alpha) // alpha 0.05 equivalent to 95% for one-sided test. - { - static const char* function = "boost::math::negative_binomial<%1%>::find_upper_bound_on_p"; - RealType result = 0; // of error checks. - RealType failures = trials - successes; - if(false == negative_binomial_detail::check_dist_and_k( - function, successes, RealType(0), failures, &result, Policy()) - && detail::check_probability(function, alpha, &result, Policy())) - { - return result; - } - if(failures == 0) - return 1; - // Use complement ibetac_inv function for upper bound. - // Note adjusted failures value: *not* failures+1 as usual. - // This is adapted from the corresponding binomial formula - // here: http://www.itl.nist.gov/div898/handbook/prc/section2/prc241.htm - // This is a Clopper-Pearson interval, and may be overly conservative, - // see also "A Simple Improved Inferential Method for Some - // Discrete Distributions" Yong CAI and K. KRISHNAMOORTHY - // http://www.ucs.louisiana.edu/~kxk4695/Discrete_new.pdf - // - return ibetac_inv(successes, failures, alpha, static_cast<RealType*>(0), Policy()); - } // find_upper_bound_on_p - - // Estimate number of trials : - // "How many trials do I need to be P% sure of seeing k or fewer failures?" - - static RealType find_minimum_number_of_trials( - RealType k, // number of failures (k >= 0). - RealType p, // success fraction 0 <= p <= 1. - RealType alpha) // risk level threshold 0 <= alpha <= 1. - { - static const char* function = "boost::math::negative_binomial<%1%>::find_minimum_number_of_trials"; - // Error checks: - RealType result = 0; - if(false == negative_binomial_detail::check_dist_and_k( - function, RealType(1), p, k, &result, Policy()) - && detail::check_probability(function, alpha, &result, Policy())) - { return result; } - - result = ibeta_inva(k + 1, p, alpha, Policy()); // returns n - k - return result + k; - } // RealType find_number_of_failures - - static RealType find_maximum_number_of_trials( - RealType k, // number of failures (k >= 0). - RealType p, // success fraction 0 <= p <= 1. - RealType alpha) // risk level threshold 0 <= alpha <= 1. - { - static const char* function = "boost::math::negative_binomial<%1%>::find_maximum_number_of_trials"; - // Error checks: - RealType result = 0; - if(false == negative_binomial_detail::check_dist_and_k( - function, RealType(1), p, k, &result, Policy()) - && detail::check_probability(function, alpha, &result, Policy())) - { return result; } - - result = ibetac_inva(k + 1, p, alpha, Policy()); // returns n - k - return result + k; - } // RealType find_number_of_trials complemented - - private: - RealType m_r; // successes. - RealType m_p; // success_fraction - }; // template <class RealType, class Policy> class negative_binomial_distribution - - typedef negative_binomial_distribution<double> negative_binomial; // Reserved name of type double. - - template <class RealType, class Policy> - inline const std::pair<RealType, RealType> range(const negative_binomial_distribution<RealType, Policy>& /* dist */) - { // Range of permissible values for random variable k. - using boost::math::tools::max_value; - return std::pair<RealType, RealType>(static_cast<RealType>(0), max_value<RealType>()); // max_integer? - } - - template <class RealType, class Policy> - inline const std::pair<RealType, RealType> support(const negative_binomial_distribution<RealType, Policy>& /* dist */) - { // Range of supported values for random variable k. - // This is range where cdf rises from 0 to 1, and outside it, the pdf is zero. - using boost::math::tools::max_value; - return std::pair<RealType, RealType>(static_cast<RealType>(0), max_value<RealType>()); // max_integer? - } - - template <class RealType, class Policy> - inline RealType mean(const negative_binomial_distribution<RealType, Policy>& dist) - { // Mean of Negative Binomial distribution = r(1-p)/p. - return dist.successes() * (1 - dist.success_fraction() ) / dist.success_fraction(); - } // mean - - //template <class RealType, class Policy> - //inline RealType median(const negative_binomial_distribution<RealType, Policy>& dist) - //{ // Median of negative_binomial_distribution is not defined. - // return policies::raise_domain_error<RealType>(BOOST_CURRENT_FUNCTION, "Median is not implemented, result is %1%!", std::numeric_limits<RealType>::quiet_NaN()); - //} // median - // Now implemented via quantile(half) in derived accessors. - - template <class RealType, class Policy> - inline RealType mode(const negative_binomial_distribution<RealType, Policy>& dist) - { // Mode of Negative Binomial distribution = floor[(r-1) * (1 - p)/p] - BOOST_MATH_STD_USING // ADL of std functions. - return floor((dist.successes() -1) * (1 - dist.success_fraction()) / dist.success_fraction()); - } // mode - - template <class RealType, class Policy> - inline RealType skewness(const negative_binomial_distribution<RealType, Policy>& dist) - { // skewness of Negative Binomial distribution = 2-p / (sqrt(r(1-p)) - BOOST_MATH_STD_USING // ADL of std functions. - RealType p = dist.success_fraction(); - RealType r = dist.successes(); - - return (2 - p) / - sqrt(r * (1 - p)); - } // skewness - - template <class RealType, class Policy> - inline RealType kurtosis(const negative_binomial_distribution<RealType, Policy>& dist) - { // kurtosis of Negative Binomial distribution - // http://en.wikipedia.org/wiki/Negative_binomial is kurtosis_excess so add 3 - RealType p = dist.success_fraction(); - RealType r = dist.successes(); - return 3 + (6 / r) + ((p * p) / (r * (1 - p))); - } // kurtosis - - template <class RealType, class Policy> - inline RealType kurtosis_excess(const negative_binomial_distribution<RealType, Policy>& dist) - { // kurtosis excess of Negative Binomial distribution - // http://mathworld.wolfram.com/Kurtosis.html table of kurtosis_excess - RealType p = dist.success_fraction(); - RealType r = dist.successes(); - return (6 - p * (6-p)) / (r * (1-p)); - } // kurtosis_excess - - template <class RealType, class Policy> - inline RealType variance(const negative_binomial_distribution<RealType, Policy>& dist) - { // Variance of Binomial distribution = r (1-p) / p^2. - return dist.successes() * (1 - dist.success_fraction()) - / (dist.success_fraction() * dist.success_fraction()); - } // variance - - // RealType standard_deviation(const negative_binomial_distribution<RealType, Policy>& dist) - // standard_deviation provided by derived accessors. - // RealType hazard(const negative_binomial_distribution<RealType, Policy>& dist) - // hazard of Negative Binomial distribution provided by derived accessors. - // RealType chf(const negative_binomial_distribution<RealType, Policy>& dist) - // chf of Negative Binomial distribution provided by derived accessors. - - template <class RealType, class Policy> - inline RealType pdf(const negative_binomial_distribution<RealType, Policy>& dist, const RealType& k) - { // Probability Density/Mass Function. - BOOST_FPU_EXCEPTION_GUARD - - static const char* function = "boost::math::pdf(const negative_binomial_distribution<%1%>&, %1%)"; - - RealType r = dist.successes(); - RealType p = dist.success_fraction(); - RealType result = 0; - if(false == negative_binomial_detail::check_dist_and_k( - function, - r, - dist.success_fraction(), - k, - &result, Policy())) - { - return result; - } - - result = (p/(r + k)) * ibeta_derivative(r, static_cast<RealType>(k+1), p, Policy()); - // Equivalent to: - // return exp(lgamma(r + k) - lgamma(r) - lgamma(k+1)) * pow(p, r) * pow((1-p), k); - return result; - } // negative_binomial_pdf - - template <class RealType, class Policy> - inline RealType cdf(const negative_binomial_distribution<RealType, Policy>& dist, const RealType& k) - { // Cumulative Distribution Function of Negative Binomial. - static const char* function = "boost::math::cdf(const negative_binomial_distribution<%1%>&, %1%)"; - using boost::math::ibeta; // Regularized incomplete beta function. - // k argument may be integral, signed, or unsigned, or floating point. - // If necessary, it has already been promoted from an integral type. - RealType p = dist.success_fraction(); - RealType r = dist.successes(); - // Error check: - RealType result = 0; - if(false == negative_binomial_detail::check_dist_and_k( - function, - r, - dist.success_fraction(), - k, - &result, Policy())) - { - return result; - } - - RealType probability = ibeta(r, static_cast<RealType>(k+1), p, Policy()); - // Ip(r, k+1) = ibeta(r, k+1, p) - return probability; - } // cdf Cumulative Distribution Function Negative Binomial. - - template <class RealType, class Policy> - inline RealType cdf(const complemented2_type<negative_binomial_distribution<RealType, Policy>, RealType>& c) - { // Complemented Cumulative Distribution Function Negative Binomial. - - static const char* function = "boost::math::cdf(const negative_binomial_distribution<%1%>&, %1%)"; - using boost::math::ibetac; // Regularized incomplete beta function complement. - // k argument may be integral, signed, or unsigned, or floating point. - // If necessary, it has already been promoted from an integral type. - RealType const& k = c.param; - negative_binomial_distribution<RealType, Policy> const& dist = c.dist; - RealType p = dist.success_fraction(); - RealType r = dist.successes(); - // Error check: - RealType result = 0; - if(false == negative_binomial_detail::check_dist_and_k( - function, - r, - p, - k, - &result, Policy())) - { - return result; - } - // Calculate cdf negative binomial using the incomplete beta function. - // Use of ibeta here prevents cancellation errors in calculating - // 1-p if p is very small, perhaps smaller than machine epsilon. - // Ip(k+1, r) = ibetac(r, k+1, p) - // constrain_probability here? - RealType probability = ibetac(r, static_cast<RealType>(k+1), p, Policy()); - // Numerical errors might cause probability to be slightly outside the range < 0 or > 1. - // This might cause trouble downstream, so warn, possibly throw exception, but constrain to the limits. - return probability; - } // cdf Cumulative Distribution Function Negative Binomial. - - template <class RealType, class Policy> - inline RealType quantile(const negative_binomial_distribution<RealType, Policy>& dist, const RealType& P) - { // Quantile, percentile/100 or Percent Point Negative Binomial function. - // Return the number of expected failures k for a given probability p. - - // Inverse cumulative Distribution Function or Quantile (percentile / 100) of negative_binomial Probability. - // MAthCAD pnbinom return smallest k such that negative_binomial(k, n, p) >= probability. - // k argument may be integral, signed, or unsigned, or floating point. - // BUT Cephes/CodeCogs says: finds argument p (0 to 1) such that cdf(k, n, p) = y - static const char* function = "boost::math::quantile(const negative_binomial_distribution<%1%>&, %1%)"; - BOOST_MATH_STD_USING // ADL of std functions. - - RealType p = dist.success_fraction(); - RealType r = dist.successes(); - // Check dist and P. - RealType result = 0; - if(false == negative_binomial_detail::check_dist_and_prob - (function, r, p, P, &result, Policy())) - { - return result; - } - - // Special cases. - if (P == 1) - { // Would need +infinity failures for total confidence. - result = policies::raise_overflow_error<RealType>( - function, - "Probability argument is 1, which implies infinite failures !", Policy()); - return result; - // usually means return +std::numeric_limits<RealType>::infinity(); - // unless #define BOOST_MATH_THROW_ON_OVERFLOW_ERROR - } - if (P == 0) - { // No failures are expected if P = 0. - return 0; // Total trials will be just dist.successes. - } - if (P <= pow(dist.success_fraction(), dist.successes())) - { // p <= pdf(dist, 0) == cdf(dist, 0) - return 0; - } - if(p == 0) - { // Would need +infinity failures for total confidence. - result = policies::raise_overflow_error<RealType>( - function, - "Success fraction is 0, which implies infinite failures !", Policy()); - return result; - // usually means return +std::numeric_limits<RealType>::infinity(); - // unless #define BOOST_MATH_THROW_ON_OVERFLOW_ERROR - } - /* - // Calculate quantile of negative_binomial using the inverse incomplete beta function. - using boost::math::ibeta_invb; - return ibeta_invb(r, p, P, Policy()) - 1; // - */ - RealType guess = 0; - RealType factor = 5; - if(r * r * r * P * p > 0.005) - guess = detail::inverse_negative_binomial_cornish_fisher(r, p, RealType(1-p), P, RealType(1-P), Policy()); - - if(guess < 10) - { - // - // Cornish-Fisher Negative binomial approximation not accurate in this area: - // - guess = (std::min)(RealType(r * 2), RealType(10)); - } - else - factor = (1-P < sqrt(tools::epsilon<RealType>())) ? 2 : (guess < 20 ? 1.2f : 1.1f); - BOOST_MATH_INSTRUMENT_CODE("guess = " << guess); - // - // Max iterations permitted: - // - boost::uintmax_t max_iter = policies::get_max_root_iterations<Policy>(); - typedef typename Policy::discrete_quantile_type discrete_type; - return detail::inverse_discrete_quantile( - dist, - P, - false, - guess, - factor, - RealType(1), - discrete_type(), - max_iter); - } // RealType quantile(const negative_binomial_distribution dist, p) - - template <class RealType, class Policy> - inline RealType quantile(const complemented2_type<negative_binomial_distribution<RealType, Policy>, RealType>& c) - { // Quantile or Percent Point Binomial function. - // Return the number of expected failures k for a given - // complement of the probability Q = 1 - P. - static const char* function = "boost::math::quantile(const negative_binomial_distribution<%1%>&, %1%)"; - BOOST_MATH_STD_USING - - // Error checks: - RealType Q = c.param; - const negative_binomial_distribution<RealType, Policy>& dist = c.dist; - RealType p = dist.success_fraction(); - RealType r = dist.successes(); - RealType result = 0; - if(false == negative_binomial_detail::check_dist_and_prob( - function, - r, - p, - Q, - &result, Policy())) - { - return result; - } - - // Special cases: - // - if(Q == 1) - { // There may actually be no answer to this question, - // since the probability of zero failures may be non-zero, - return 0; // but zero is the best we can do: - } - if(Q == 0) - { // Probability 1 - Q == 1 so infinite failures to achieve certainty. - // Would need +infinity failures for total confidence. - result = policies::raise_overflow_error<RealType>( - function, - "Probability argument complement is 0, which implies infinite failures !", Policy()); - return result; - // usually means return +std::numeric_limits<RealType>::infinity(); - // unless #define BOOST_MATH_THROW_ON_OVERFLOW_ERROR - } - if (-Q <= boost::math::powm1(dist.success_fraction(), dist.successes(), Policy())) - { // q <= cdf(complement(dist, 0)) == pdf(dist, 0) - return 0; // - } - if(p == 0) - { // Success fraction is 0 so infinite failures to achieve certainty. - // Would need +infinity failures for total confidence. - result = policies::raise_overflow_error<RealType>( - function, - "Success fraction is 0, which implies infinite failures !", Policy()); - return result; - // usually means return +std::numeric_limits<RealType>::infinity(); - // unless #define BOOST_MATH_THROW_ON_OVERFLOW_ERROR - } - //return ibetac_invb(r, p, Q, Policy()) -1; - RealType guess = 0; - RealType factor = 5; - if(r * r * r * (1-Q) * p > 0.005) - guess = detail::inverse_negative_binomial_cornish_fisher(r, p, RealType(1-p), RealType(1-Q), Q, Policy()); - - if(guess < 10) - { - // - // Cornish-Fisher Negative binomial approximation not accurate in this area: - // - guess = (std::min)(RealType(r * 2), RealType(10)); - } - else - factor = (Q < sqrt(tools::epsilon<RealType>())) ? 2 : (guess < 20 ? 1.2f : 1.1f); - BOOST_MATH_INSTRUMENT_CODE("guess = " << guess); - // - // Max iterations permitted: - // - boost::uintmax_t max_iter = policies::get_max_root_iterations<Policy>(); - typedef typename Policy::discrete_quantile_type discrete_type; - return detail::inverse_discrete_quantile( - dist, - Q, - true, - guess, - factor, - RealType(1), - discrete_type(), - max_iter); - } // 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_SPECIAL_NEGATIVE_BINOMIAL_HPP |