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// Copyright John Maddock 2006, 2007. // Copyright Paul A. Bristow 2006, 2007. // Copyright Matt Borland 2024. // 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 #include #include #include #include #include // for erf/erfc. #include #include #include #include namespace boost{ namespace math{ template > class normal_distribution { public: using value_type = RealType; using policy_type = Policy; BOOST_MATH_GPU_ENABLED explicit normal_distribution(RealType l_mean = 0, RealType sd = 1) : m_mean(l_mean), m_sd(sd) { // Default is a 'standard' normal distribution N01. constexpr auto 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()); } BOOST_MATH_GPU_ENABLED RealType mean()const { // alias for location. return m_mean; } BOOST_MATH_GPU_ENABLED RealType standard_deviation()const { // alias for scale. return m_sd; } // Synonyms, provided to allow generic use of find_location and find_scale. BOOST_MATH_GPU_ENABLED RealType location()const { // location. return m_mean; } BOOST_MATH_GPU_ENABLED 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 using normal = normal_distribution; // // Deduction guides, note we don't check the // value of __cpp_deduction_guides, just assume // they work as advertised, even if this is pre-final C++17. // #ifdef __cpp_deduction_guides template normal_distribution(RealType, RealType)->normal_distribution::type>; template normal_distribution(RealType)->normal_distribution::type>; #endif #ifdef _MSC_VER #pragma warning(push) #pragma warning(disable:4127) #endif template BOOST_MATH_GPU_ENABLED inline boost::math::pair range(const normal_distribution& /*dist*/) { // Range of permissible values for random variable x. BOOST_MATH_IF_CONSTEXPR (boost::math::numeric_limits::has_infinity) { return boost::math::pair(-boost::math::numeric_limits::infinity(), boost::math::numeric_limits::infinity()); // - to + infinity. } else { // Can only use max_value. using boost::math::tools::max_value; return boost::math::pair(-max_value(), max_value()); // - to + max value. } } template BOOST_MATH_GPU_ENABLED inline boost::math::pair support(const normal_distribution& /*dist*/) { // This is range values for random variable x where cdf rises from 0 to 1, and outside it, the pdf is zero. BOOST_MATH_IF_CONSTEXPR (boost::math::numeric_limits::has_infinity) { return boost::math::pair(-boost::math::numeric_limits::infinity(), boost::math::numeric_limits::infinity()); // - to + infinity. } else { // Can only use max_value. using boost::math::tools::max_value; return boost::math::pair(-max_value(), max_value()); // - to + max value. } } #ifdef _MSC_VER #pragma warning(pop) #endif template BOOST_MATH_GPU_ENABLED inline RealType pdf(const normal_distribution& dist, const RealType& x) { BOOST_MATH_STD_USING // for ADL of std functions RealType sd = dist.standard_deviation(); RealType mean = dist.mean(); constexpr auto 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. } 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()); return result; } // pdf template BOOST_MATH_GPU_ENABLED inline RealType logpdf(const normal_distribution& dist, const RealType& x) { BOOST_MATH_STD_USING // for ADL of std functions const RealType sd = dist.standard_deviation(); const RealType mean = dist.mean(); constexpr auto function = "boost::math::logpdf(const normal_distribution<%1%>&, %1%)"; RealType result = -boost::math::numeric_limits::infinity(); 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 result; // pdf + and - infinity is zero so logpdf is -inf } if(false == detail::check_x(function, x, &result, Policy())) { return result; } const RealType pi = boost::math::constants::pi(); const RealType half = boost::math::constants::half(); result = -log(sd) - half*log(2*pi) - (x-mean)*(x-mean)/(2*sd*sd); return result; } template BOOST_MATH_GPU_ENABLED inline RealType cdf(const normal_distribution& dist, const RealType& x) { BOOST_MATH_STD_USING // for ADL of std functions RealType sd = dist.standard_deviation(); RealType mean = dist.mean(); constexpr auto 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 } if(false == detail::check_x(function, x, &result, Policy())) { return result; } RealType diff = (x - mean) / (sd * constants::root_two()); result = boost::math::erfc(-diff, Policy()) / 2; return result; } // cdf template BOOST_MATH_GPU_ENABLED inline RealType quantile(const normal_distribution& dist, const RealType& p) { BOOST_MATH_STD_USING // for ADL of std functions RealType sd = dist.standard_deviation(); RealType mean = dist.mean(); constexpr auto 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(); result += mean; return result; } // quantile template BOOST_MATH_GPU_ENABLED inline RealType cdf(const complemented2_type, 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; constexpr auto 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 } if(false == detail::check_x(function, x, &result, Policy())) return result; RealType diff = (x - mean) / (sd * constants::root_two()); result = boost::math::erfc(diff, Policy()) / 2; return result; } // cdf complement template BOOST_MATH_GPU_ENABLED inline RealType quantile(const complemented2_type, RealType>& c) { BOOST_MATH_STD_USING // for ADL of std functions RealType sd = c.dist.standard_deviation(); RealType mean = c.dist.mean(); constexpr auto 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(); result += mean; return result; } // quantile template BOOST_MATH_GPU_ENABLED inline RealType mean(const normal_distribution& dist) { return dist.mean(); } template BOOST_MATH_GPU_ENABLED inline RealType standard_deviation(const normal_distribution& dist) { return dist.standard_deviation(); } template BOOST_MATH_GPU_ENABLED inline RealType mode(const normal_distribution& dist) { return dist.mean(); } template BOOST_MATH_GPU_ENABLED inline RealType median(const normal_distribution& dist) { return dist.mean(); } template BOOST_MATH_GPU_ENABLED inline RealType skewness(const normal_distribution& /*dist*/) { return 0; } template BOOST_MATH_GPU_ENABLED inline RealType kurtosis(const normal_distribution& /*dist*/) { return 3; } template BOOST_MATH_GPU_ENABLED inline RealType kurtosis_excess(const normal_distribution& /*dist*/) { return 0; } template BOOST_MATH_GPU_ENABLED inline RealType entropy(const normal_distribution & dist) { BOOST_MATH_STD_USING RealType arg = constants::two_pi()*constants::e()*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 #endif // BOOST_STATS_NORMAL_HPP