| // boost\math\distributions\bernoulli.hpp |
| |
| // Copyright John Maddock 2006. |
| // Copyright Paul A. Bristow 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/bernoulli_distribution |
| // http://mathworld.wolfram.com/BernoulliDistribution.html |
| |
| // bernoulli distribution is the discrete probability distribution of |
| // the number (k) of successes, in a single Bernoulli trials. |
| // It is a version of the binomial distribution when n = 1. |
| |
| // But note that the bernoulli distribution |
| // (like others including the poisson, binomial & negative binomial) |
| // 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. |
| // To enforce the strict mathematical model, users should use floor or ceil functions |
| // on k outside this function to ensure that k is integral. |
| |
| #ifndef BOOST_MATH_SPECIAL_BERNOULLI_HPP |
| #define BOOST_MATH_SPECIAL_BERNOULLI_HPP |
| |
| #include <boost/math/distributions/fwd.hpp> |
| #include <boost/math/tools/config.hpp> |
| #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 <utility> |
| |
| namespace boost |
| { |
| namespace math |
| { |
| namespace bernoulli_detail |
| { |
| // Common error checking routines for bernoulli distribution functions: |
| 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, Policy()); |
| return false; |
| } |
| return true; |
| } |
| template <class RealType, class Policy> |
| inline bool check_dist(const char* function, const RealType& p, RealType* result, const Policy& /* pol */) |
| { |
| return check_success_fraction(function, p, result, Policy()); |
| } |
| template <class RealType, class Policy> |
| inline bool check_dist_and_k(const char* function, const RealType& p, RealType k, RealType* result, const Policy& pol) |
| { |
| if(check_dist(function, p, result, Policy()) == false) |
| { |
| return false; |
| } |
| if(!(boost::math::isfinite)(k) || !((k == 0) || (k == 1))) |
| { |
| *result = policies::raise_domain_error<RealType>( |
| function, |
| "Number of successes argument is %1%, but must be 0 or 1 !", k, pol); |
| return false; |
| } |
| return true; |
| } |
| template <class RealType, class Policy> |
| inline bool check_dist_and_prob(const char* function, RealType p, RealType prob, RealType* result, const Policy& /* pol */) |
| { |
| if(check_dist(function, p, result, Policy()) && detail::check_probability(function, prob, result, Policy()) == false) |
| { |
| return false; |
| } |
| return true; |
| } |
| } // namespace bernoulli_detail |
| |
| |
| template <class RealType = double, class Policy = policies::policy<> > |
| class bernoulli_distribution |
| { |
| public: |
| typedef RealType value_type; |
| typedef Policy policy_type; |
| |
| bernoulli_distribution(RealType p = 0.5) : m_p(p) |
| { // Default probability = half suits 'fair' coin tossing |
| // where probability of heads == probability of tails. |
| RealType result; // of checks. |
| bernoulli_detail::check_dist( |
| "boost::math::bernoulli_distribution<%1%>::bernoulli_distribution", |
| m_p, |
| &result, Policy()); |
| } // bernoulli_distribution constructor. |
| |
| RealType success_fraction() const |
| { // Probability. |
| return m_p; |
| } |
| |
| private: |
| RealType m_p; // success_fraction |
| }; // template <class RealType> class bernoulli_distribution |
| |
| typedef bernoulli_distribution<double> bernoulli; |
| |
| template <class RealType, class Policy> |
| inline const std::pair<RealType, RealType> range(const bernoulli_distribution<RealType, Policy>& /* dist */) |
| { // Range of permissible values for random variable k = {0, 1}. |
| 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 bernoulli_distribution<RealType, Policy>& /* dist */) |
| { // Range of supported values for random variable k = {0, 1}. |
| // 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 bernoulli_distribution<RealType, Policy>& dist) |
| { // Mean of bernoulli distribution = p (n = 1). |
| return dist.success_fraction(); |
| } // mean |
| |
| // Rely on dereived_accessors quantile(half) |
| //template <class RealType> |
| //inline RealType median(const bernoulli_distribution<RealType, Policy>& dist) |
| //{ // Median of bernoulli distribution is not defined. |
| // return tools::domain_error<RealType>(BOOST_CURRENT_FUNCTION, "Median is not implemented, result is %1%!", std::numeric_limits<RealType>::quiet_NaN()); |
| //} // median |
| |
| template <class RealType, class Policy> |
| inline RealType variance(const bernoulli_distribution<RealType, Policy>& dist) |
| { // Variance of bernoulli distribution =p * q. |
| return dist.success_fraction() * (1 - dist.success_fraction()); |
| } // variance |
| |
| template <class RealType, class Policy> |
| RealType pdf(const bernoulli_distribution<RealType, Policy>& dist, const RealType& k) |
| { // Probability Density/Mass Function. |
| BOOST_FPU_EXCEPTION_GUARD |
| // Error check: |
| RealType result; // of checks. |
| if(false == bernoulli_detail::check_dist_and_k( |
| "boost::math::pdf(bernoulli_distribution<%1%>, %1%)", |
| dist.success_fraction(), // 0 to 1 |
| k, // 0 or 1 |
| &result, Policy())) |
| { |
| return result; |
| } |
| // Assume k is integral. |
| if (k == 0) |
| { |
| return 1 - dist.success_fraction(); // 1 - p |
| } |
| else // k == 1 |
| { |
| return dist.success_fraction(); // p |
| } |
| } // pdf |
| |
| template <class RealType, class Policy> |
| inline RealType cdf(const bernoulli_distribution<RealType, Policy>& dist, const RealType& k) |
| { // Cumulative Distribution Function Bernoulli. |
| RealType p = dist.success_fraction(); |
| // Error check: |
| RealType result; |
| if(false == bernoulli_detail::check_dist_and_k( |
| "boost::math::cdf(bernoulli_distribution<%1%>, %1%)", |
| p, |
| k, |
| &result, Policy())) |
| { |
| return result; |
| } |
| if (k == 0) |
| { |
| return 1 - p; |
| } |
| else |
| { // k == 1 |
| return 1; |
| } |
| } // bernoulli cdf |
| |
| template <class RealType, class Policy> |
| inline RealType cdf(const complemented2_type<bernoulli_distribution<RealType, Policy>, RealType>& c) |
| { // Complemented Cumulative Distribution Function bernoulli. |
| RealType const& k = c.param; |
| bernoulli_distribution<RealType, Policy> const& dist = c.dist; |
| RealType p = dist.success_fraction(); |
| // Error checks: |
| RealType result; |
| if(false == bernoulli_detail::check_dist_and_k( |
| "boost::math::cdf(bernoulli_distribution<%1%>, %1%)", |
| p, |
| k, |
| &result, Policy())) |
| { |
| return result; |
| } |
| if (k == 0) |
| { |
| return p; |
| } |
| else |
| { // k == 1 |
| return 0; |
| } |
| } // bernoulli cdf complement |
| |
| template <class RealType, class Policy> |
| inline RealType quantile(const bernoulli_distribution<RealType, Policy>& dist, const RealType& p) |
| { // Quantile or Percent Point Bernoulli function. |
| // Return the number of expected successes k either 0 or 1. |
| // for a given probability p. |
| |
| RealType result; // of error checks: |
| if(false == bernoulli_detail::check_dist_and_prob( |
| "boost::math::quantile(bernoulli_distribution<%1%>, %1%)", |
| dist.success_fraction(), |
| p, |
| &result, Policy())) |
| { |
| return result; |
| } |
| if (p <= (1 - dist.success_fraction())) |
| { // p <= pdf(dist, 0) == cdf(dist, 0) |
| return 0; |
| } |
| else |
| { |
| return 1; |
| } |
| } // quantile |
| |
| template <class RealType, class Policy> |
| inline RealType quantile(const complemented2_type<bernoulli_distribution<RealType, Policy>, RealType>& c) |
| { // Quantile or Percent Point bernoulli function. |
| // Return the number of expected successes k for a given |
| // complement of the probability q. |
| // |
| // Error checks: |
| RealType q = c.param; |
| const bernoulli_distribution<RealType, Policy>& dist = c.dist; |
| RealType result; |
| if(false == bernoulli_detail::check_dist_and_prob( |
| "boost::math::quantile(bernoulli_distribution<%1%>, %1%)", |
| dist.success_fraction(), |
| q, |
| &result, Policy())) |
| { |
| return result; |
| } |
| |
| if (q <= 1 - dist.success_fraction()) |
| { // // q <= cdf(complement(dist, 0)) == pdf(dist, 0) |
| return 1; |
| } |
| else |
| { |
| return 0; |
| } |
| } // quantile complemented. |
| |
| template <class RealType, class Policy> |
| inline RealType mode(const bernoulli_distribution<RealType, Policy>& dist) |
| { |
| return static_cast<RealType>((dist.success_fraction() <= 0.5) ? 0 : 1); // p = 0.5 can be 0 or 1 |
| } |
| |
| template <class RealType, class Policy> |
| inline RealType skewness(const bernoulli_distribution<RealType, Policy>& dist) |
| { |
| BOOST_MATH_STD_USING; // Aid ADL for sqrt. |
| RealType p = dist.success_fraction(); |
| return (1 - 2 * p) / sqrt(p * (1 - p)); |
| } |
| |
| template <class RealType, class Policy> |
| inline RealType kurtosis_excess(const bernoulli_distribution<RealType, Policy>& dist) |
| { |
| RealType p = dist.success_fraction(); |
| // Note Wolfram says this is kurtosis in text, but gamma2 is the kurtosis excess, |
| // and Wikipedia also says this is the kurtosis excess formula. |
| // return (6 * p * p - 6 * p + 1) / (p * (1 - p)); |
| // But Wolfram kurtosis article gives this simpler formula for kurtosis excess: |
| return 1 / (1 - p) + 1/p -6; |
| } |
| |
| template <class RealType, class Policy> |
| inline RealType kurtosis(const bernoulli_distribution<RealType, Policy>& dist) |
| { |
| RealType p = dist.success_fraction(); |
| return 1 / (1 - p) + 1/p -6 + 3; |
| // Simpler than: |
| // return (6 * p * p - 6 * p + 1) / (p * (1 - p)) + 3; |
| } |
| |
| } // 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_BERNOULLI_HPP |
| |
| |
| |