math/distributions/normal.hpp

0001 //  Copyright John Maddock 2006, 2007.
0002 //  Copyright Paul A. Bristow 2006, 2007.
0003 //  Copyright Matt Borland 2024.
0004 //  Use, modification and distribution are subject to the
0005 //  Boost Software License, Version 1.0. (See accompanying file
0006 //  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
0007
0008 #ifndef BOOST_STATS_NORMAL_HPP
0009 #define BOOST_STATS_NORMAL_HPP
0010
0011 // http://en.wikipedia.org/wiki/Normal_distribution
0012 // http://www.itl.nist.gov/div898/handbook/eda/section3/eda3661.htm
0013 // Also:
0014 // Weisstein, Eric W. "Normal Distribution."
0015 // From MathWorld--A Wolfram Web Resource.
0016 // http://mathworld.wolfram.com/NormalDistribution.html
0017
0018 #include <boost/math/tools/config.hpp>
0019 #include <boost/math/tools/tuple.hpp>
0020 #include <boost/math/tools/numeric_limits.hpp>
0021 #include <boost/math/distributions/fwd.hpp>
0022 #include <boost/math/special_functions/erf.hpp> // for erf/erfc.
0023 #include <boost/math/distributions/complement.hpp>
0024 #include <boost/math/distributions/detail/common_error_handling.hpp>
0025 #include <boost/math/constants/constants.hpp>
0026 #include <boost/math/policies/policy.hpp>
0027
0028 namespace boost{ namespace math{
0029
0030 template <class RealType = double, class Policy = policies::policy<> >
0031 class normal_distribution
0032 {
0033 public:
0034    using value_type = RealType;
0035    using policy_type = Policy;
0036
0037    BOOST_MATH_GPU_ENABLED explicit normal_distribution(RealType l_mean = 0, RealType sd = 1)
0038       : m_mean(l_mean), m_sd(sd)
0039    { // Default is a 'standard' normal distribution N01.
0040      constexpr auto function = "boost::math::normal_distribution<%1%>::normal_distribution";
0041
0042      RealType result;
0043      detail::check_scale(function, sd, &result, Policy());
0044      detail::check_location(function, l_mean, &result, Policy());
0045    }
0046
0047    BOOST_MATH_GPU_ENABLED RealType mean()const
0048    { // alias for location.
0049       return m_mean;
0050    }
0051
0052    BOOST_MATH_GPU_ENABLED RealType standard_deviation()const
0053    { // alias for scale.
0054       return m_sd;
0055    }
0056
0057    // Synonyms, provided to allow generic use of find_location and find_scale.
0058    BOOST_MATH_GPU_ENABLED RealType location()const
0059    { // location.
0060       return m_mean;
0061    }
0062    BOOST_MATH_GPU_ENABLED RealType scale()const
0063    { // scale.
0064       return m_sd;
0065    }
0066
0067 private:
0068    //
0069    // Data members:
0070    //
0071    RealType m_mean;  // distribution mean or location.
0072    RealType m_sd;    // distribution standard deviation or scale.
0073 }; // class normal_distribution
0074
0075 using normal = normal_distribution<double>;
0076
0077 //
0078 // Deduction guides, note we don't check the
0079 // value of __cpp_deduction_guides, just assume
0080 // they work as advertised, even if this is pre-final C++17.
0081 //
0082 #ifdef __cpp_deduction_guides
0083
0084 template <class RealType>
0085 normal_distribution(RealType, RealType)->normal_distribution<typename boost::math::tools::promote_args<RealType>::type>;
0086 template <class RealType>
0087 normal_distribution(RealType)->normal_distribution<typename boost::math::tools::promote_args<RealType>::type>;
0088
0089 #endif
0090
0091 #ifdef _MSC_VER
0092 #pragma warning(push)
0093 #pragma warning(disable:4127)
0094 #endif
0095
0096 template <class RealType, class Policy>
0097 BOOST_MATH_GPU_ENABLED inline boost::math::pair<RealType, RealType> range(const normal_distribution<RealType, Policy>& /*dist*/)
0098 { // Range of permissible values for random variable x.
0099   BOOST_MATH_IF_CONSTEXPR (boost::math::numeric_limits<RealType>::has_infinity)
0100   {
0101      return boost::math::pair<RealType, RealType>(-boost::math::numeric_limits<RealType>::infinity(), boost::math::numeric_limits<RealType>::infinity()); // - to + infinity.
0102   }
0103   else
0104   { // Can only use max_value.
0105     using boost::math::tools::max_value;
0106     return boost::math::pair<RealType, RealType>(-max_value<RealType>(), max_value<RealType>()); // - to + max value.
0107   }
0108 }
0109
0110 template <class RealType, class Policy>
0111 BOOST_MATH_GPU_ENABLED inline boost::math::pair<RealType, RealType> support(const normal_distribution<RealType, Policy>& /*dist*/)
0112 { // This is range values for random variable x where cdf rises from 0 to 1, and outside it, the pdf is zero.
0113   BOOST_MATH_IF_CONSTEXPR (boost::math::numeric_limits<RealType>::has_infinity)
0114   {
0115      return boost::math::pair<RealType, RealType>(-boost::math::numeric_limits<RealType>::infinity(), boost::math::numeric_limits<RealType>::infinity()); // - to + infinity.
0116   }
0117   else
0118   { // Can only use max_value.
0119    using boost::math::tools::max_value;
0120    return boost::math::pair<RealType, RealType>(-max_value<RealType>(),  max_value<RealType>()); // - to + max value.
0121   }
0122 }
0123
0124 #ifdef _MSC_VER
0125 #pragma warning(pop)
0126 #endif
0127
0128 template <class RealType, class Policy>
0129 BOOST_MATH_GPU_ENABLED inline RealType pdf(const normal_distribution<RealType, Policy>& dist, const RealType& x)
0130 {
0131    BOOST_MATH_STD_USING  // for ADL of std functions
0132
0133    RealType sd = dist.standard_deviation();
0134    RealType mean = dist.mean();
0135
0136    constexpr auto function = "boost::math::pdf(const normal_distribution<%1%>&, %1%)";
0137
0138    RealType result = 0;
0139    if(false == detail::check_scale(function, sd, &result, Policy()))
0140    {
0141       return result;
0142    }
0143    if(false == detail::check_location(function, mean, &result, Policy()))
0144    {
0145       return result;
0146    }
0147    if((boost::math::isinf)(x))
0148    {
0149      return 0; // pdf + and - infinity is zero.
0150    }
0151    if(false == detail::check_x(function, x, &result, Policy()))
0152    {
0153       return result;
0154    }
0155
0156    RealType exponent = x - mean;
0157    exponent *= -exponent;
0158    exponent /= 2 * sd * sd;
0159
0160    result = exp(exponent);
0161    result /= sd * sqrt(2 * constants::pi<RealType>());
0162
0163    return result;
0164 } // pdf
0165
0166 template <class RealType, class Policy>
0167 BOOST_MATH_GPU_ENABLED inline RealType logpdf(const normal_distribution<RealType, Policy>& dist, const RealType& x)
0168 {
0169    BOOST_MATH_STD_USING  // for ADL of std functions
0170
0171    const RealType sd = dist.standard_deviation();
0172    const RealType mean = dist.mean();
0173
0174    constexpr auto function = "boost::math::logpdf(const normal_distribution<%1%>&, %1%)";
0175
0176    RealType result = -boost::math::numeric_limits<RealType>::infinity();
0177    if(false == detail::check_scale(function, sd, &result, Policy()))
0178    {
0179       return result;
0180    }
0181    if(false == detail::check_location(function, mean, &result, Policy()))
0182    {
0183       return result;
0184    }
0185    if((boost::math::isinf)(x))
0186    {
0187       return result; // pdf + and - infinity is zero so logpdf is -inf
0188    }
0189    if(false == detail::check_x(function, x, &result, Policy()))
0190    {
0191       return result;
0192    }
0193
0194    const RealType pi = boost::math::constants::pi<RealType>();
0195    const RealType half = boost::math::constants::half<RealType>();
0196
0197    result = -log(sd) - half*log(2*pi) - (x-mean)*(x-mean)/(2*sd*sd);
0198
0199    return result;
0200 }
0201
0202 template <class RealType, class Policy>
0203 BOOST_MATH_GPU_ENABLED inline RealType cdf(const normal_distribution<RealType, Policy>& dist, const RealType& x)
0204 {
0205    BOOST_MATH_STD_USING  // for ADL of std functions
0206
0207    RealType sd = dist.standard_deviation();
0208    RealType mean = dist.mean();
0209    constexpr auto function = "boost::math::cdf(const normal_distribution<%1%>&, %1%)";
0210    RealType result = 0;
0211    if(false == detail::check_scale(function, sd, &result, Policy()))
0212    {
0213       return result;
0214    }
0215    if(false == detail::check_location(function, mean, &result, Policy()))
0216    {
0217       return result;
0218    }
0219    if((boost::math::isinf)(x))
0220    {
0221      if(x < 0) return 0; // -infinity
0222      return 1; // + infinity
0223    }
0224    if(false == detail::check_x(function, x, &result, Policy()))
0225    {
0226      return result;
0227    }
0228    RealType diff = (x - mean) / (sd * constants::root_two<RealType>());
0229    result = boost::math::erfc(-diff, Policy()) / 2;
0230    return result;
0231 } // cdf
0232
0233 template <class RealType, class Policy>
0234 BOOST_MATH_GPU_ENABLED inline RealType quantile(const normal_distribution<RealType, Policy>& dist, const RealType& p)
0235 {
0236    BOOST_MATH_STD_USING  // for ADL of std functions
0237
0238    RealType sd = dist.standard_deviation();
0239    RealType mean = dist.mean();
0240    constexpr auto function = "boost::math::quantile(const normal_distribution<%1%>&, %1%)";
0241
0242    RealType result = 0;
0243    if(false == detail::check_scale(function, sd, &result, Policy()))
0244       return result;
0245    if(false == detail::check_location(function, mean, &result, Policy()))
0246       return result;
0247    if(false == detail::check_probability(function, p, &result, Policy()))
0248       return result;
0249
0250    result= boost::math::erfc_inv(2 * p, Policy());
0251    result = -result;
0252    result *= sd * constants::root_two<RealType>();
0253    result += mean;
0254    return result;
0255 } // quantile
0256
0257 template <class RealType, class Policy>
0258 BOOST_MATH_GPU_ENABLED inline RealType cdf(const complemented2_type<normal_distribution<RealType, Policy>, RealType>& c)
0259 {
0260    BOOST_MATH_STD_USING  // for ADL of std functions
0261
0262    RealType sd = c.dist.standard_deviation();
0263    RealType mean = c.dist.mean();
0264    RealType x = c.param;
0265    constexpr auto function = "boost::math::cdf(const complement(normal_distribution<%1%>&), %1%)";
0266
0267    RealType result = 0;
0268    if(false == detail::check_scale(function, sd, &result, Policy()))
0269       return result;
0270    if(false == detail::check_location(function, mean, &result, Policy()))
0271       return result;
0272    if((boost::math::isinf)(x))
0273    {
0274      if(x < 0) return 1; // cdf complement -infinity is unity.
0275      return 0; // cdf complement +infinity is zero
0276    }
0277    if(false == detail::check_x(function, x, &result, Policy()))
0278       return result;
0279
0280    RealType diff = (x - mean) / (sd * constants::root_two<RealType>());
0281    result = boost::math::erfc(diff, Policy()) / 2;
0282    return result;
0283 } // cdf complement
0284
0285 template <class RealType, class Policy>
0286 BOOST_MATH_GPU_ENABLED inline RealType quantile(const complemented2_type<normal_distribution<RealType, Policy>, RealType>& c)
0287 {
0288    BOOST_MATH_STD_USING  // for ADL of std functions
0289
0290    RealType sd = c.dist.standard_deviation();
0291    RealType mean = c.dist.mean();
0292    constexpr auto function = "boost::math::quantile(const complement(normal_distribution<%1%>&), %1%)";
0293    RealType result = 0;
0294    if(false == detail::check_scale(function, sd, &result, Policy()))
0295       return result;
0296    if(false == detail::check_location(function, mean, &result, Policy()))
0297       return result;
0298    RealType q = c.param;
0299    if(false == detail::check_probability(function, q, &result, Policy()))
0300       return result;
0301    result = boost::math::erfc_inv(2 * q, Policy());
0302    result *= sd * constants::root_two<RealType>();
0303    result += mean;
0304    return result;
0305 } // quantile
0306
0307 template <class RealType, class Policy>
0308 BOOST_MATH_GPU_ENABLED inline RealType mean(const normal_distribution<RealType, Policy>& dist)
0309 {
0310    return dist.mean();
0311 }
0312
0313 template <class RealType, class Policy>
0314 BOOST_MATH_GPU_ENABLED inline RealType standard_deviation(const normal_distribution<RealType, Policy>& dist)
0315 {
0316    return dist.standard_deviation();
0317 }
0318
0319 template <class RealType, class Policy>
0320 BOOST_MATH_GPU_ENABLED inline RealType mode(const normal_distribution<RealType, Policy>& dist)
0321 {
0322    return dist.mean();
0323 }
0324
0325 template <class RealType, class Policy>
0326 BOOST_MATH_GPU_ENABLED inline RealType median(const normal_distribution<RealType, Policy>& dist)
0327 {
0328    return dist.mean();
0329 }
0330
0331 template <class RealType, class Policy>
0332 BOOST_MATH_GPU_ENABLED inline RealType skewness(const normal_distribution<RealType, Policy>& /*dist*/)
0333 {
0334    return 0;
0335 }
0336
0337 template <class RealType, class Policy>
0338 BOOST_MATH_GPU_ENABLED inline RealType kurtosis(const normal_distribution<RealType, Policy>& /*dist*/)
0339 {
0340    return 3;
0341 }
0342
0343 template <class RealType, class Policy>
0344 BOOST_MATH_GPU_ENABLED inline RealType kurtosis_excess(const normal_distribution<RealType, Policy>& /*dist*/)
0345 {
0346    return 0;
0347 }
0348
0349 template <class RealType, class Policy>
0350 BOOST_MATH_GPU_ENABLED inline RealType entropy(const normal_distribution<RealType, Policy> & dist)
0351 {
0352    BOOST_MATH_STD_USING
0353    RealType arg = constants::two_pi<RealType>()*constants::e<RealType>()*dist.standard_deviation()*dist.standard_deviation();
0354    return log(arg)/2;
0355 }
0356
0357 } // namespace math
0358 } // namespace boost
0359
0360 // This include must be at the end, *after* the accessors
0361 // for this distribution have been defined, in order to
0362 // keep compilers that support two-phase lookup happy.
0363 #include <boost/math/distributions/detail/derived_accessors.hpp>
0364
0365 #endif // BOOST_STATS_NORMAL_HPP
0366
0367