math/distributions/normal.hpp

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