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Name	Size	Mode	Actions
detail/	-	0755	rm
arcsine.hpp	18797	0644	edit dl rm
bernoulli.hpp	12143	0644	edit dl rm
beta.hpp	18807	0644	edit dl rm
binomial.hpp	28654	0644	edit dl rm
cauchy.hpp	12310	0644	edit dl rm
chi_squared.hpp	12242	0644	edit dl rm
complement.hpp	5978	0644	edit dl rm
empirical_cumulative_distribution_function.hpp	1886	0644	edit dl rm
exponential.hpp	8944	0644	edit dl rm
extreme_value.hpp	10491	0644	edit dl rm
find_location.hpp	6713	0644	edit dl rm
find_scale.hpp	9674	0644	edit dl rm
fisher_f.hpp	14391	0644	edit dl rm
fwd.hpp	5461	0644	edit dl rm
gamma.hpp	10660	0644	edit dl rm
geometric.hpp	21156	0644	edit dl rm
hyperexponential.hpp	21887	0644	edit dl rm
hypergeometric.hpp	12220	0644	edit dl rm
inverse_chi_squared.hpp	15202	0644	edit dl rm
inverse_gamma.hpp	15389	0644	edit dl rm
inverse_gaussian.hpp	19760	0644	edit dl rm
laplace.hpp	10580	0644	edit dl rm
logistic.hpp	11273	0644	edit dl rm
lognormal.hpp	11714	0644	edit dl rm
negative_binomial.hpp	26139	0644	edit dl rm
non_central_beta.hpp	35837	0644	edit dl rm
non_central_chi_squared.hpp	40704	0644	edit dl rm
non_central_f.hpp	15848	0644	edit dl rm
non_central_t.hpp	47973	0644	edit dl rm
normal.hpp	10768	0644	edit dl rm
pareto.hpp	15516	0644	edit dl rm
poisson.hpp	20267	0644	edit dl rm
rayleigh.hpp	10344	0644	edit dl rm
skew_normal.hpp	25646	0644	edit dl rm
students_t.hpp	18476	0644	edit dl rm
triangular.hpp	18407	0644	edit dl rm
uniform.hpp	12963	0644	edit dl rm
weibull.hpp	12081	0644	edit dl rm

Edit: /usr/include/boost/math/distributions/bernoulli.hpp (12143B)

// 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 continuous 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 */, const boost::true_type&)
      {
        return check_success_fraction(function, p, result, Policy());
      }
      template <class RealType, class Policy>
      inline bool check_dist(const char* , const RealType& , RealType* , const Policy& /* pol */, const boost::false_type&)
      {
         return true;
      }
      template <class RealType, class Policy>
      inline bool check_dist(const char* function, const RealType& p, RealType* result, const Policy& /* pol */)
      {
         return check_dist(function, p, result, Policy(), typename policies::constructor_error_check<Policy>::type());
      }

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(), typename policies::method_error_check<Policy>::type()) == 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(), typename policies::method_error_check<Policy>::type()) && 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 = 0; // 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 = 0;
      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 = 0;
      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 = 0; // 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 = 0;
      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

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