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/usr/include/boost/math/distributions

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/normal.hpp (10768B)

//  Copyright John Maddock 2006, 2007.
//  Copyright Paul A. Bristow 2006, 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)

#ifndef BOOST_STATS_NORMAL_HPP
#define BOOST_STATS_NORMAL_HPP

// http://en.wikipedia.org/wiki/Normal_distribution
// http://www.itl.nist.gov/div898/handbook/eda/section3/eda3661.htm
// Also:
// Weisstein, Eric W. "Normal Distribution."
// From MathWorld--A Wolfram Web Resource.
// http://mathworld.wolfram.com/NormalDistribution.html

#include <boost/math/distributions/fwd.hpp>
#include <boost/math/special_functions/erf.hpp> // for erf/erfc.
#include <boost/math/distributions/complement.hpp>
#include <boost/math/distributions/detail/common_error_handling.hpp>

#include <utility>

namespace boost{ namespace math{

template <class RealType = double, class Policy = policies::policy<> >
class normal_distribution
{
public:
   typedef RealType value_type;
   typedef Policy policy_type;

normal_distribution(RealType l_mean = 0, RealType sd = 1)
      : m_mean(l_mean), m_sd(sd)
   { // Default is a 'standard' normal distribution N01.
     static const char* function = "boost::math::normal_distribution<%1%>::normal_distribution";

RealType result;
     detail::check_scale(function, sd, &result, Policy());
     detail::check_location(function, l_mean, &result, Policy());
   }

RealType mean()const
   { // alias for location.
      return m_mean;
   }

RealType standard_deviation()const
   { // alias for scale.
      return m_sd;
   }

// Synonyms, provided to allow generic use of find_location and find_scale.
   RealType location()const
   { // location.
      return m_mean;
   }
   RealType scale()const
   { // scale.
      return m_sd;
   }

private:
   //
   // Data members:
   //
   RealType m_mean;  // distribution mean or location.
   RealType m_sd;    // distribution standard deviation or scale.
}; // class normal_distribution

typedef normal_distribution<double> normal;

#ifdef BOOST_MSVC
#pragma warning(push)
#pragma warning(disable:4127)
#endif

template <class RealType, class Policy>
inline const std::pair<RealType, RealType> range(const normal_distribution<RealType, Policy>& /*dist*/)
{ // Range of permissible values for random variable x.
  if (std::numeric_limits<RealType>::has_infinity)
  { 
     return std::pair<RealType, RealType>(-std::numeric_limits<RealType>::infinity(), std::numeric_limits<RealType>::infinity()); // - to + infinity.
  }
  else
  { // Can only use max_value.
    using boost::math::tools::max_value;
    return std::pair<RealType, RealType>(-max_value<RealType>(), max_value<RealType>()); // - to + max value.
  }
}

template <class RealType, class Policy>
inline const std::pair<RealType, RealType> support(const normal_distribution<RealType, Policy>& /*dist*/)
{ // This is range values for random variable x where cdf rises from 0 to 1, and outside it, the pdf is zero.
  if (std::numeric_limits<RealType>::has_infinity)
  { 
     return std::pair<RealType, RealType>(-std::numeric_limits<RealType>::infinity(), std::numeric_limits<RealType>::infinity()); // - to + infinity.
  }
  else
  { // Can only use max_value.
   using boost::math::tools::max_value;
   return std::pair<RealType, RealType>(-max_value<RealType>(),  max_value<RealType>()); // - to + max value.
  }
}

#ifdef BOOST_MSVC
#pragma warning(pop)
#endif

template <class RealType, class Policy>
inline RealType pdf(const normal_distribution<RealType, Policy>& dist, const RealType& x)
{
   BOOST_MATH_STD_USING  // for ADL of std functions

RealType sd = dist.standard_deviation();
   RealType mean = dist.mean();

static const char* function = "boost::math::pdf(const normal_distribution<%1%>&, %1%)";

RealType result = 0;
   if(false == detail::check_scale(function, sd, &result, Policy()))
   {
      return result;
   }
   if(false == detail::check_location(function, mean, &result, Policy()))
   {
      return result;
   }
   if((boost::math::isinf)(x))
   {
     return 0; // pdf + and - infinity is zero.
   }
   // Below produces MSVC 4127 warnings, so the above used instead.
   //if(std::numeric_limits<RealType>::has_infinity && abs(x) == std::numeric_limits<RealType>::infinity())
   //{ // pdf + and - infinity is zero.
   //  return 0;
   //}
   if(false == detail::check_x(function, x, &result, Policy()))
   {
      return result;
   }

RealType exponent = x - mean;
   exponent *= -exponent;
   exponent /= 2 * sd * sd;

result = exp(exponent);
   result /= sd * sqrt(2 * constants::pi<RealType>());

return result;
} // pdf

template <class RealType, class Policy>
inline RealType cdf(const normal_distribution<RealType, Policy>& dist, const RealType& x)
{
   BOOST_MATH_STD_USING  // for ADL of std functions

RealType sd = dist.standard_deviation();
   RealType mean = dist.mean();
   static const char* function = "boost::math::cdf(const normal_distribution<%1%>&, %1%)";
   RealType result = 0;
   if(false == detail::check_scale(function, sd, &result, Policy()))
   {
      return result;
   }
   if(false == detail::check_location(function, mean, &result, Policy()))
   {
      return result;
   }
   if((boost::math::isinf)(x))
   {
     if(x < 0) return 0; // -infinity
     return 1; // + infinity
   }
   // These produce MSVC 4127 warnings, so the above used instead.
   //if(std::numeric_limits<RealType>::has_infinity && x == std::numeric_limits<RealType>::infinity())
   //{ // cdf +infinity is unity.
   //  return 1;
   //}
   //if(std::numeric_limits<RealType>::has_infinity && x == -std::numeric_limits<RealType>::infinity())
   //{ // cdf -infinity is zero.
   //  return 0;
   //}
   if(false == detail::check_x(function, x, &result, Policy()))
   {
     return result;
   }
   RealType diff = (x - mean) / (sd * constants::root_two<RealType>());
   result = boost::math::erfc(-diff, Policy()) / 2;
   return result;
} // cdf

template <class RealType, class Policy>
inline RealType quantile(const normal_distribution<RealType, Policy>& dist, const RealType& p)
{
   BOOST_MATH_STD_USING  // for ADL of std functions

RealType sd = dist.standard_deviation();
   RealType mean = dist.mean();
   static const char* function = "boost::math::quantile(const normal_distribution<%1%>&, %1%)";

result= boost::math::erfc_inv(2 * p, Policy());
   result = -result;
   result *= sd * constants::root_two<RealType>();
   result += mean;
   return result;
} // quantile

template <class RealType, class Policy>
inline RealType cdf(const complemented2_type<normal_distribution<RealType, Policy>, RealType>& c)
{
   BOOST_MATH_STD_USING  // for ADL of std functions

RealType sd = c.dist.standard_deviation();
   RealType mean = c.dist.mean();
   RealType x = c.param;
   static const char* function = "boost::math::cdf(const complement(normal_distribution<%1%>&), %1%)";

RealType result = 0;
   if(false == detail::check_scale(function, sd, &result, Policy()))
      return result;
   if(false == detail::check_location(function, mean, &result, Policy()))
      return result;
   if((boost::math::isinf)(x))
   {
     if(x < 0) return 1; // cdf complement -infinity is unity.
     return 0; // cdf complement +infinity is zero
   }
   // These produce MSVC 4127 warnings, so the above used instead.
   //if(std::numeric_limits<RealType>::has_infinity && x == std::numeric_limits<RealType>::infinity())
   //{ // cdf complement +infinity is zero.
   //  return 0;
   //}
   //if(std::numeric_limits<RealType>::has_infinity && x == -std::numeric_limits<RealType>::infinity())
   //{ // cdf complement -infinity is unity.
   //  return 1;
   //}
   if(false == detail::check_x(function, x, &result, Policy()))
      return result;

RealType diff = (x - mean) / (sd * constants::root_two<RealType>());
   result = boost::math::erfc(diff, Policy()) / 2;
   return result;
} // cdf complement

template <class RealType, class Policy>
inline RealType quantile(const complemented2_type<normal_distribution<RealType, Policy>, RealType>& c)
{
   BOOST_MATH_STD_USING  // for ADL of std functions

RealType sd = c.dist.standard_deviation();
   RealType mean = c.dist.mean();
   static const char* function = "boost::math::quantile(const complement(normal_distribution<%1%>&), %1%)";
   RealType result = 0;
   if(false == detail::check_scale(function, sd, &result, Policy()))
      return result;
   if(false == detail::check_location(function, mean, &result, Policy()))
      return result;
   RealType q = c.param;
   if(false == detail::check_probability(function, q, &result, Policy()))
      return result;
   result = boost::math::erfc_inv(2 * q, Policy());
   result *= sd * constants::root_two<RealType>();
   result += mean;
   return result;
} // quantile

template <class RealType, class Policy>
inline RealType mean(const normal_distribution<RealType, Policy>& dist)
{
   return dist.mean();
}

template <class RealType, class Policy>
inline RealType standard_deviation(const normal_distribution<RealType, Policy>& dist)
{
   return dist.standard_deviation();
}

template <class RealType, class Policy>
inline RealType mode(const normal_distribution<RealType, Policy>& dist)
{
   return dist.mean();
}

template <class RealType, class Policy>
inline RealType median(const normal_distribution<RealType, Policy>& dist)
{
   return dist.mean();
}

template <class RealType, class Policy>
inline RealType skewness(const normal_distribution<RealType, Policy>& /*dist*/)
{
   return 0;
}

template <class RealType, class Policy>
inline RealType kurtosis(const normal_distribution<RealType, Policy>& /*dist*/)
{
   return 3;
}

template <class RealType, class Policy>
inline RealType kurtosis_excess(const normal_distribution<RealType, Policy>& /*dist*/)
{
   return 0;
}

template <class RealType, class Policy>
inline RealType entropy(const normal_distribution<RealType, Policy> & dist)
{
   using std::log;
   RealType arg = constants::two_pi<RealType>()*constants::e<RealType>()*dist.standard_deviation()*dist.standard_deviation();
   return log(arg)/2;
}

} // 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_STATS_NORMAL_HPP

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