| // Copyright John Maddock 2006, 2007.
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| // Copyright Paul A. Bristow 2006, 2007.
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|
|
| // Use, modification and distribution are subject to the
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| // Boost Software License, Version 1.0. (See accompanying file
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| // LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
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|
|
| #ifndef BOOST_STATS_NORMAL_HPP
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| #define BOOST_STATS_NORMAL_HPP
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|
|
| // http://en.wikipedia.org/wiki/Normal_distribution
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| // http://www.itl.nist.gov/div898/handbook/eda/section3/eda3661.htm
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| // Also:
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| // Weisstein, Eric W. "Normal Distribution."
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| // From MathWorld--A Wolfram Web Resource.
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| // http://mathworld.wolfram.com/NormalDistribution.html
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|
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| #include <boost/math/distributions/fwd.hpp>
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| #include <boost/math/special_functions/erf.hpp> // for erf/erfc.
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| #include <boost/math/distributions/complement.hpp>
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| #include <boost/math/distributions/detail/common_error_handling.hpp>
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|
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| #include <utility>
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|
|
| namespace boost{ namespace math{
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|
|
| template <class RealType = double, class Policy = policies::policy<> >
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| class normal_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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|
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| normal_distribution(RealType mean = 0, RealType sd = 1)
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| : m_mean(mean), m_sd(sd)
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| { // Default is a 'standard' normal distribution N01.
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| static const char* function = "boost::math::normal_distribution<%1%>::normal_distribution";
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|
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| RealType result;
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| detail::check_scale(function, sd, &result, Policy());
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| detail::check_location(function, mean, &result, Policy());
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| }
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|
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| RealType mean()const
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| { // alias for location.
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| return m_mean;
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| }
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|
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| RealType standard_deviation()const
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| { // alias for scale.
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| return m_sd;
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| }
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|
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| // Synonyms, provided to allow generic use of find_location and find_scale.
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| RealType location()const
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| { // location.
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| return m_mean;
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| }
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| RealType scale()const
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| { // scale.
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| return m_sd;
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| }
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|
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| private:
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| //
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| // Data members:
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| //
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| RealType m_mean; // distribution mean or location.
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| RealType m_sd; // distribution standard deviation or scale.
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| }; // class normal_distribution
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|
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| typedef normal_distribution<double> normal;
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|
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| template <class RealType, class Policy>
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| inline const std::pair<RealType, RealType> range(const normal_distribution<RealType, Policy>& /*dist*/)
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| { // Range of permissible values for random variable x.
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| using boost::math::tools::max_value;
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| return std::pair<RealType, RealType>(-max_value<RealType>(), max_value<RealType>()); // - to + max value.
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| }
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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 normal_distribution<RealType, Policy>& /*dist*/)
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| { // Range of supported values for random variable x.
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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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|
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| using boost::math::tools::max_value;
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| return std::pair<RealType, RealType>(-max_value<RealType>(), max_value<RealType>()); // - to + max value.
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| }
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|
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| template <class RealType, class Policy>
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| inline RealType pdf(const normal_distribution<RealType, Policy>& dist, const RealType& x)
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| {
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| BOOST_MATH_STD_USING // for ADL of std functions
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|
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| RealType sd = dist.standard_deviation();
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| RealType mean = dist.mean();
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|
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| static const char* function = "boost::math::pdf(const normal_distribution<%1%>&, %1%)";
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| if((boost::math::isinf)(x))
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| {
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| return 0; // pdf + and - infinity is zero.
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| }
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| // Below produces MSVC 4127 warnings, so the above used instead.
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| //if(std::numeric_limits<RealType>::has_infinity && abs(x) == std::numeric_limits<RealType>::infinity())
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| //{ // pdf + and - infinity is zero.
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| // return 0;
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| //}
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|
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| RealType result;
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| if(false == detail::check_scale(function, sd, &result, Policy()))
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| {
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| return result;
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| }
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| if(false == detail::check_location(function, mean, &result, Policy()))
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| {
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| return result;
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| }
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| if(false == detail::check_x(function, x, &result, Policy()))
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| {
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| return result;
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| }
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|
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| RealType exponent = x - mean;
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| exponent *= -exponent;
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| exponent /= 2 * sd * sd;
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|
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| result = exp(exponent);
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| result /= sd * sqrt(2 * constants::pi<RealType>());
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|
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| return result;
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| } // pdf
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|
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| template <class RealType, class Policy>
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| inline RealType cdf(const normal_distribution<RealType, Policy>& dist, const RealType& x)
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| {
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| BOOST_MATH_STD_USING // for ADL of std functions
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|
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| RealType sd = dist.standard_deviation();
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| RealType mean = dist.mean();
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| static const char* function = "boost::math::cdf(const normal_distribution<%1%>&, %1%)";
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| RealType result;
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| if(false == detail::check_scale(function, sd, &result, Policy()))
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| {
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| return result;
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| }
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| if(false == detail::check_location(function, mean, &result, Policy()))
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| {
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| return result;
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| }
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| if((boost::math::isinf)(x))
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| {
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| if(x < 0) return 0; // -infinity
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| return 1; // + infinity
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| }
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| // These produce MSVC 4127 warnings, so the above used instead.
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| //if(std::numeric_limits<RealType>::has_infinity && x == std::numeric_limits<RealType>::infinity())
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| //{ // cdf +infinity is unity.
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| // return 1;
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| //}
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| //if(std::numeric_limits<RealType>::has_infinity && x == -std::numeric_limits<RealType>::infinity())
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| //{ // cdf -infinity is zero.
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| // return 0;
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| //}
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| if(false == detail::check_x(function, x, &result, Policy()))
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| {
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| return result;
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| }
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| RealType diff = (x - mean) / (sd * constants::root_two<RealType>());
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| result = boost::math::erfc(-diff, Policy()) / 2;
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| return result;
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| } // cdf
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|
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| template <class RealType, class Policy>
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| inline RealType quantile(const normal_distribution<RealType, Policy>& dist, const RealType& p)
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| {
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| BOOST_MATH_STD_USING // for ADL of std functions
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|
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| RealType sd = dist.standard_deviation();
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| RealType mean = dist.mean();
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| static const char* function = "boost::math::quantile(const normal_distribution<%1%>&, %1%)";
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|
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| RealType result;
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| if(false == detail::check_scale(function, sd, &result, Policy()))
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| return result;
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| if(false == detail::check_location(function, mean, &result, Policy()))
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| return result;
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| if(false == detail::check_probability(function, p, &result, Policy()))
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| return result;
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|
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| result= boost::math::erfc_inv(2 * p, Policy());
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| result = -result;
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| result *= sd * constants::root_two<RealType>();
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| result += mean;
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| return result;
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| } // quantile
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|
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| template <class RealType, class Policy>
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| inline RealType cdf(const complemented2_type<normal_distribution<RealType, Policy>, RealType>& c)
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| {
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| BOOST_MATH_STD_USING // for ADL of std functions
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|
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| RealType sd = c.dist.standard_deviation();
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| RealType mean = c.dist.mean();
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| RealType x = c.param;
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| static const char* function = "boost::math::cdf(const complement(normal_distribution<%1%>&), %1%)";
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|
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| if((boost::math::isinf)(x))
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| {
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| if(x < 0) return 1; // cdf complement -infinity is unity.
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| return 0; // cdf complement +infinity is zero
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| }
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| // These produce MSVC 4127 warnings, so the above used instead.
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| //if(std::numeric_limits<RealType>::has_infinity && x == std::numeric_limits<RealType>::infinity())
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| //{ // cdf complement +infinity is zero.
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| // return 0;
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| //}
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| //if(std::numeric_limits<RealType>::has_infinity && x == -std::numeric_limits<RealType>::infinity())
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| //{ // cdf complement -infinity is unity.
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| // return 1;
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| //}
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| RealType result;
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| if(false == detail::check_scale(function, sd, &result, Policy()))
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| return result;
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| if(false == detail::check_location(function, mean, &result, Policy()))
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| return result;
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| if(false == detail::check_x(function, x, &result, Policy()))
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| return result;
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|
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| RealType diff = (x - mean) / (sd * constants::root_two<RealType>());
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| result = boost::math::erfc(diff, Policy()) / 2;
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| return result;
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| } // cdf complement
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|
|
| template <class RealType, class Policy>
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| inline RealType quantile(const complemented2_type<normal_distribution<RealType, Policy>, RealType>& c)
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| {
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| BOOST_MATH_STD_USING // for ADL of std functions
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|
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| RealType sd = c.dist.standard_deviation();
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| RealType mean = c.dist.mean();
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| static const char* function = "boost::math::quantile(const complement(normal_distribution<%1%>&), %1%)";
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| RealType result;
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| if(false == detail::check_scale(function, sd, &result, Policy()))
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| return result;
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| if(false == detail::check_location(function, mean, &result, Policy()))
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| return result;
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| RealType q = c.param;
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| if(false == detail::check_probability(function, q, &result, Policy()))
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| return result;
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| result = boost::math::erfc_inv(2 * q, Policy());
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| result *= sd * constants::root_two<RealType>();
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| result += mean;
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| return result;
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| } // quantile
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|
|
| template <class RealType, class Policy>
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| inline RealType mean(const normal_distribution<RealType, Policy>& dist)
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| {
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| return dist.mean();
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| }
|
|
|
| template <class RealType, class Policy>
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| inline RealType standard_deviation(const normal_distribution<RealType, Policy>& dist)
|
| {
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| return dist.standard_deviation();
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| }
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|
|
| template <class RealType, class Policy>
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| inline RealType mode(const normal_distribution<RealType, Policy>& dist)
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| {
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| return dist.mean();
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| }
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|
|
| template <class RealType, class Policy>
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| inline RealType median(const normal_distribution<RealType, Policy>& dist)
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| {
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| return dist.mean();
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| }
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|
|
| template <class RealType, class Policy>
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| inline RealType skewness(const normal_distribution<RealType, Policy>& /*dist*/)
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| {
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| return 0;
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| }
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|
|
| template <class RealType, class Policy>
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| inline RealType kurtosis(const normal_distribution<RealType, Policy>& /*dist*/)
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| {
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| return 3;
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| }
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|
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| template <class RealType, class Policy>
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| inline RealType kurtosis_excess(const normal_distribution<RealType, Policy>& /*dist*/)
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| {
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| return 0;
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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_STATS_NORMAL_HPP
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|
|
|
|
