/usr/include/boost/math/distributions/normal.hpp is in libboost1.55-dev 1.55.0+dfsg-3.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
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// 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;
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*/)
{ // Range of supported values for random variable x.
// This is range 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.
}
}
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%)";
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(false == detail::check_probability(function, p, &result, Policy()))
return result;
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;
}
} // 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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