337 lines
12 KiB
C++
337 lines
12 KiB
C++
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// boost\math\distributions\bernoulli.hpp
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// Copyright John Maddock 2006.
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// Copyright Paul A. Bristow 2007.
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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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// http://en.wikipedia.org/wiki/bernoulli_distribution
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// http://mathworld.wolfram.com/BernoulliDistribution.html
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// bernoulli distribution is the discrete probability distribution of
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// the number (k) of successes, in a single Bernoulli trials.
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// It is a version of the binomial distribution when n = 1.
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// But note that the bernoulli distribution
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// (like others including the poisson, binomial & negative binomial)
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// is strictly defined as a discrete function: only integral values of k are envisaged.
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// However because of the method of calculation using a continuous gamma function,
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// it is convenient to treat it as if a continous function,
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// and permit non-integral values of k.
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// To enforce the strict mathematical model, users should use floor or ceil functions
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// on k outside this function to ensure that k is integral.
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#ifndef BOOST_MATH_SPECIAL_BERNOULLI_HPP
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#define BOOST_MATH_SPECIAL_BERNOULLI_HPP
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#include <boost/math/distributions/fwd.hpp>
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#include <boost/math/tools/config.hpp>
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#include <boost/math/distributions/complement.hpp> // complements
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#include <boost/math/distributions/detail/common_error_handling.hpp> // error checks
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#include <boost/math/special_functions/fpclassify.hpp> // isnan.
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#include <utility>
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namespace boost
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{
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namespace math
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{
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namespace bernoulli_detail
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{
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// Common error checking routines for bernoulli distribution functions:
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template <class RealType, class Policy>
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inline bool check_success_fraction(const char* function, const RealType& p, RealType* result, const Policy& /* pol */)
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{
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if(!(boost::math::isfinite)(p) || (p < 0) || (p > 1))
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{
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*result = policies::raise_domain_error<RealType>(
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function,
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"Success fraction argument is %1%, but must be >= 0 and <= 1 !", p, Policy());
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return false;
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}
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return true;
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}
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template <class RealType, class Policy>
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inline bool check_dist(const char* function, const RealType& p, RealType* result, const Policy& /* pol */, const mpl::true_&)
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{
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return check_success_fraction(function, p, result, Policy());
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}
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template <class RealType, class Policy>
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inline bool check_dist(const char* , const RealType& , RealType* , const Policy& /* pol */, const mpl::false_&)
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{
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return true;
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}
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template <class RealType, class Policy>
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inline bool check_dist(const char* function, const RealType& p, RealType* result, const Policy& /* pol */)
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{
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return check_dist(function, p, result, Policy(), typename policies::constructor_error_check<Policy>::type());
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}
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template <class RealType, class Policy>
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inline bool check_dist_and_k(const char* function, const RealType& p, RealType k, RealType* result, const Policy& pol)
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{
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if(check_dist(function, p, result, Policy(), typename policies::method_error_check<Policy>::type()) == false)
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{
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return false;
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}
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if(!(boost::math::isfinite)(k) || !((k == 0) || (k == 1)))
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{
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*result = policies::raise_domain_error<RealType>(
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function,
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"Number of successes argument is %1%, but must be 0 or 1 !", k, pol);
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return false;
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}
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return true;
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}
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template <class RealType, class Policy>
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inline bool check_dist_and_prob(const char* function, RealType p, RealType prob, RealType* result, const Policy& /* pol */)
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{
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if((check_dist(function, p, result, Policy(), typename policies::method_error_check<Policy>::type()) && detail::check_probability(function, prob, result, Policy())) == false)
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{
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return false;
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}
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return true;
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}
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} // namespace bernoulli_detail
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template <class RealType = double, class Policy = policies::policy<> >
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class bernoulli_distribution
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{
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public:
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typedef RealType value_type;
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typedef Policy policy_type;
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bernoulli_distribution(RealType p = 0.5) : m_p(p)
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{ // Default probability = half suits 'fair' coin tossing
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// where probability of heads == probability of tails.
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RealType result; // of checks.
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bernoulli_detail::check_dist(
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"boost::math::bernoulli_distribution<%1%>::bernoulli_distribution",
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m_p,
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&result, Policy());
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} // bernoulli_distribution constructor.
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RealType success_fraction() const
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{ // Probability.
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return m_p;
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}
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private:
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RealType m_p; // success_fraction
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}; // template <class RealType> class bernoulli_distribution
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typedef bernoulli_distribution<double> bernoulli;
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template <class RealType, class Policy>
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inline const std::pair<RealType, RealType> range(const bernoulli_distribution<RealType, Policy>& /* dist */)
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{ // Range of permissible values for random variable k = {0, 1}.
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using boost::math::tools::max_value;
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return std::pair<RealType, RealType>(static_cast<RealType>(0), static_cast<RealType>(1));
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}
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template <class RealType, class Policy>
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inline const std::pair<RealType, RealType> support(const bernoulli_distribution<RealType, Policy>& /* dist */)
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{ // Range of supported values for random variable k = {0, 1}.
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// This is range where cdf rises from 0 to 1, and outside it, the pdf is zero.
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return std::pair<RealType, RealType>(static_cast<RealType>(0), static_cast<RealType>(1));
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}
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template <class RealType, class Policy>
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inline RealType mean(const bernoulli_distribution<RealType, Policy>& dist)
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{ // Mean of bernoulli distribution = p (n = 1).
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return dist.success_fraction();
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} // mean
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// Rely on dereived_accessors quantile(half)
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//template <class RealType>
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//inline RealType median(const bernoulli_distribution<RealType, Policy>& dist)
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//{ // Median of bernoulli distribution is not defined.
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// return tools::domain_error<RealType>(BOOST_CURRENT_FUNCTION, "Median is not implemented, result is %1%!", std::numeric_limits<RealType>::quiet_NaN());
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//} // median
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template <class RealType, class Policy>
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inline RealType variance(const bernoulli_distribution<RealType, Policy>& dist)
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{ // Variance of bernoulli distribution =p * q.
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return dist.success_fraction() * (1 - dist.success_fraction());
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} // variance
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template <class RealType, class Policy>
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RealType pdf(const bernoulli_distribution<RealType, Policy>& dist, const RealType& k)
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{ // Probability Density/Mass Function.
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BOOST_FPU_EXCEPTION_GUARD
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// Error check:
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RealType result = 0; // of checks.
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if(false == bernoulli_detail::check_dist_and_k(
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"boost::math::pdf(bernoulli_distribution<%1%>, %1%)",
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dist.success_fraction(), // 0 to 1
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k, // 0 or 1
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&result, Policy()))
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{
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return result;
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}
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// Assume k is integral.
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if (k == 0)
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{
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return 1 - dist.success_fraction(); // 1 - p
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}
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else // k == 1
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{
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return dist.success_fraction(); // p
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}
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} // pdf
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template <class RealType, class Policy>
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inline RealType cdf(const bernoulli_distribution<RealType, Policy>& dist, const RealType& k)
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{ // Cumulative Distribution Function Bernoulli.
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RealType p = dist.success_fraction();
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// Error check:
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RealType result = 0;
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if(false == bernoulli_detail::check_dist_and_k(
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"boost::math::cdf(bernoulli_distribution<%1%>, %1%)",
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p,
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k,
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&result, Policy()))
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{
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return result;
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}
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if (k == 0)
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{
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return 1 - p;
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}
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else
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{ // k == 1
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return 1;
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}
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} // bernoulli cdf
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template <class RealType, class Policy>
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inline RealType cdf(const complemented2_type<bernoulli_distribution<RealType, Policy>, RealType>& c)
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{ // Complemented Cumulative Distribution Function bernoulli.
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RealType const& k = c.param;
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bernoulli_distribution<RealType, Policy> const& dist = c.dist;
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RealType p = dist.success_fraction();
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// Error checks:
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RealType result = 0;
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if(false == bernoulli_detail::check_dist_and_k(
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"boost::math::cdf(bernoulli_distribution<%1%>, %1%)",
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p,
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k,
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&result, Policy()))
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{
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return result;
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}
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if (k == 0)
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{
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return p;
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}
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else
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{ // k == 1
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return 0;
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}
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} // bernoulli cdf complement
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template <class RealType, class Policy>
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inline RealType quantile(const bernoulli_distribution<RealType, Policy>& dist, const RealType& p)
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{ // Quantile or Percent Point Bernoulli function.
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// Return the number of expected successes k either 0 or 1.
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// for a given probability p.
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RealType result = 0; // of error checks:
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if(false == bernoulli_detail::check_dist_and_prob(
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"boost::math::quantile(bernoulli_distribution<%1%>, %1%)",
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dist.success_fraction(),
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p,
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&result, Policy()))
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{
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return result;
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}
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if (p <= (1 - dist.success_fraction()))
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{ // p <= pdf(dist, 0) == cdf(dist, 0)
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return 0;
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}
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else
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{
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return 1;
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}
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} // quantile
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template <class RealType, class Policy>
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inline RealType quantile(const complemented2_type<bernoulli_distribution<RealType, Policy>, RealType>& c)
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{ // Quantile or Percent Point bernoulli function.
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// Return the number of expected successes k for a given
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// complement of the probability q.
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//
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// Error checks:
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RealType q = c.param;
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const bernoulli_distribution<RealType, Policy>& dist = c.dist;
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RealType result = 0;
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if(false == bernoulli_detail::check_dist_and_prob(
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"boost::math::quantile(bernoulli_distribution<%1%>, %1%)",
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dist.success_fraction(),
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q,
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&result, Policy()))
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{
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return result;
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}
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if (q <= 1 - dist.success_fraction())
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{ // // q <= cdf(complement(dist, 0)) == pdf(dist, 0)
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return 1;
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}
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else
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{
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return 0;
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}
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} // quantile complemented.
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template <class RealType, class Policy>
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inline RealType mode(const bernoulli_distribution<RealType, Policy>& dist)
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{
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return static_cast<RealType>((dist.success_fraction() <= 0.5) ? 0 : 1); // p = 0.5 can be 0 or 1
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}
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template <class RealType, class Policy>
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inline RealType skewness(const bernoulli_distribution<RealType, Policy>& dist)
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{
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BOOST_MATH_STD_USING; // Aid ADL for sqrt.
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RealType p = dist.success_fraction();
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return (1 - 2 * p) / sqrt(p * (1 - p));
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}
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template <class RealType, class Policy>
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inline RealType kurtosis_excess(const bernoulli_distribution<RealType, Policy>& dist)
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{
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RealType p = dist.success_fraction();
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// Note Wolfram says this is kurtosis in text, but gamma2 is the kurtosis excess,
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// and Wikipedia also says this is the kurtosis excess formula.
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// return (6 * p * p - 6 * p + 1) / (p * (1 - p));
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// But Wolfram kurtosis article gives this simpler formula for kurtosis excess:
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return 1 / (1 - p) + 1/p -6;
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}
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template <class RealType, class Policy>
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inline RealType kurtosis(const bernoulli_distribution<RealType, Policy>& dist)
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{
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RealType p = dist.success_fraction();
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return 1 / (1 - p) + 1/p -6 + 3;
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// Simpler than:
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// return (6 * p * p - 6 * p + 1) / (p * (1 - p)) + 3;
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}
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} // namespace math
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} // namespace boost
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// This include must be at the end, *after* the accessors
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// for this distribution have been defined, in order to
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// keep compilers that support two-phase lookup happy.
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#include <boost/math/distributions/detail/derived_accessors.hpp>
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#endif // BOOST_MATH_SPECIAL_BERNOULLI_HPP
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