// Copyright John Maddock 2006. | |
// 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_LOGNORMAL_HPP | |
#define BOOST_STATS_LOGNORMAL_HPP | |
// http://www.itl.nist.gov/div898/handbook/eda/section3/eda3669.htm | |
// http://mathworld.wolfram.com/LogNormalDistribution.html | |
// http://en.wikipedia.org/wiki/Lognormal_distribution | |
#include <boost/math/distributions/fwd.hpp> | |
#include <boost/math/distributions/normal.hpp> | |
#include <boost/math/special_functions/expm1.hpp> | |
#include <boost/math/distributions/detail/common_error_handling.hpp> | |
#include <utility> | |
namespace boost{ namespace math | |
{ | |
namespace detail | |
{ | |
template <class RealType, class Policy> | |
inline bool check_lognormal_x( | |
const char* function, | |
RealType const& x, | |
RealType* result, const Policy& pol) | |
{ | |
if((x < 0) || !(boost::math::isfinite)(x)) | |
{ | |
*result = policies::raise_domain_error<RealType>( | |
function, | |
"Random variate is %1% but must be >= 0 !", x, pol); | |
return false; | |
} | |
return true; | |
} | |
} // namespace detail | |
template <class RealType = double, class Policy = policies::policy<> > | |
class lognormal_distribution | |
{ | |
public: | |
typedef RealType value_type; | |
typedef Policy policy_type; | |
lognormal_distribution(RealType location = 0, RealType scale = 1) | |
: m_location(location), m_scale(scale) | |
{ | |
RealType result; | |
detail::check_scale("boost::math::lognormal_distribution<%1%>::lognormal_distribution", scale, &result, Policy()); | |
} | |
RealType location()const | |
{ | |
return m_location; | |
} | |
RealType scale()const | |
{ | |
return m_scale; | |
} | |
private: | |
// | |
// Data members: | |
// | |
RealType m_location; // distribution location. | |
RealType m_scale; // distribution scale. | |
}; | |
typedef lognormal_distribution<double> lognormal; | |
template <class RealType, class Policy> | |
inline const std::pair<RealType, RealType> range(const lognormal_distribution<RealType, Policy>& /*dist*/) | |
{ // Range of permissible values for random variable x is >0 to +infinity. | |
using boost::math::tools::max_value; | |
return std::pair<RealType, RealType>(static_cast<RealType>(0), max_value<RealType>()); | |
} | |
template <class RealType, class Policy> | |
inline const std::pair<RealType, RealType> support(const lognormal_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. | |
using boost::math::tools::max_value; | |
return std::pair<RealType, RealType>(static_cast<RealType>(0), max_value<RealType>()); | |
} | |
template <class RealType, class Policy> | |
RealType pdf(const lognormal_distribution<RealType, Policy>& dist, const RealType& x) | |
{ | |
BOOST_MATH_STD_USING // for ADL of std functions | |
RealType mu = dist.location(); | |
RealType sigma = dist.scale(); | |
static const char* function = "boost::math::pdf(const lognormal_distribution<%1%>&, %1%)"; | |
RealType result; | |
if(0 == detail::check_scale(function, sigma, &result, Policy())) | |
return result; | |
if(0 == detail::check_lognormal_x(function, x, &result, Policy())) | |
return result; | |
if(x == 0) | |
return 0; | |
RealType exponent = log(x) - mu; | |
exponent *= -exponent; | |
exponent /= 2 * sigma * sigma; | |
result = exp(exponent); | |
result /= sigma * sqrt(2 * constants::pi<RealType>()) * x; | |
return result; | |
} | |
template <class RealType, class Policy> | |
inline RealType cdf(const lognormal_distribution<RealType, Policy>& dist, const RealType& x) | |
{ | |
BOOST_MATH_STD_USING // for ADL of std functions | |
static const char* function = "boost::math::cdf(const lognormal_distribution<%1%>&, %1%)"; | |
RealType result; | |
if(0 == detail::check_lognormal_x(function, x, &result, Policy())) | |
return result; | |
if(x == 0) | |
return 0; | |
normal_distribution<RealType, Policy> norm(dist.location(), dist.scale()); | |
return cdf(norm, log(x)); | |
} | |
template <class RealType, class Policy> | |
inline RealType quantile(const lognormal_distribution<RealType, Policy>& dist, const RealType& p) | |
{ | |
BOOST_MATH_STD_USING // for ADL of std functions | |
static const char* function = "boost::math::quantile(const lognormal_distribution<%1%>&, %1%)"; | |
RealType result; | |
if(0 == detail::check_probability(function, p, &result, Policy())) | |
return result; | |
if(p == 0) | |
return 0; | |
if(p == 1) | |
return policies::raise_overflow_error<RealType>(function, 0, Policy()); | |
normal_distribution<RealType, Policy> norm(dist.location(), dist.scale()); | |
return exp(quantile(norm, p)); | |
} | |
template <class RealType, class Policy> | |
inline RealType cdf(const complemented2_type<lognormal_distribution<RealType, Policy>, RealType>& c) | |
{ | |
BOOST_MATH_STD_USING // for ADL of std functions | |
static const char* function = "boost::math::cdf(const lognormal_distribution<%1%>&, %1%)"; | |
RealType result; | |
if(0 == detail::check_lognormal_x(function, c.param, &result, Policy())) | |
return result; | |
if(c.param == 0) | |
return 1; | |
normal_distribution<RealType, Policy> norm(c.dist.location(), c.dist.scale()); | |
return cdf(complement(norm, log(c.param))); | |
} | |
template <class RealType, class Policy> | |
inline RealType quantile(const complemented2_type<lognormal_distribution<RealType, Policy>, RealType>& c) | |
{ | |
BOOST_MATH_STD_USING // for ADL of std functions | |
static const char* function = "boost::math::quantile(const lognormal_distribution<%1%>&, %1%)"; | |
RealType result; | |
if(0 == detail::check_probability(function, c.param, &result, Policy())) | |
return result; | |
if(c.param == 1) | |
return 0; | |
if(c.param == 0) | |
return policies::raise_overflow_error<RealType>(function, 0, Policy()); | |
normal_distribution<RealType, Policy> norm(c.dist.location(), c.dist.scale()); | |
return exp(quantile(complement(norm, c.param))); | |
} | |
template <class RealType, class Policy> | |
inline RealType mean(const lognormal_distribution<RealType, Policy>& dist) | |
{ | |
BOOST_MATH_STD_USING // for ADL of std functions | |
RealType mu = dist.location(); | |
RealType sigma = dist.scale(); | |
RealType result; | |
if(0 == detail::check_scale("boost::math::mean(const lognormal_distribution<%1%>&)", sigma, &result, Policy())) | |
return result; | |
return exp(mu + sigma * sigma / 2); | |
} | |
template <class RealType, class Policy> | |
inline RealType variance(const lognormal_distribution<RealType, Policy>& dist) | |
{ | |
BOOST_MATH_STD_USING // for ADL of std functions | |
RealType mu = dist.location(); | |
RealType sigma = dist.scale(); | |
RealType result; | |
if(0 == detail::check_scale("boost::math::variance(const lognormal_distribution<%1%>&)", sigma, &result, Policy())) | |
return result; | |
return boost::math::expm1(sigma * sigma, Policy()) * exp(2 * mu + sigma * sigma); | |
} | |
template <class RealType, class Policy> | |
inline RealType mode(const lognormal_distribution<RealType, Policy>& dist) | |
{ | |
BOOST_MATH_STD_USING // for ADL of std functions | |
RealType mu = dist.location(); | |
RealType sigma = dist.scale(); | |
RealType result; | |
if(0 == detail::check_scale("boost::math::mode(const lognormal_distribution<%1%>&)", sigma, &result, Policy())) | |
return result; | |
return exp(mu - sigma * sigma); | |
} | |
template <class RealType, class Policy> | |
inline RealType median(const lognormal_distribution<RealType, Policy>& dist) | |
{ | |
BOOST_MATH_STD_USING // for ADL of std functions | |
RealType mu = dist.location(); | |
return exp(mu); // e^mu | |
} | |
template <class RealType, class Policy> | |
inline RealType skewness(const lognormal_distribution<RealType, Policy>& dist) | |
{ | |
BOOST_MATH_STD_USING // for ADL of std functions | |
//RealType mu = dist.location(); | |
RealType sigma = dist.scale(); | |
RealType ss = sigma * sigma; | |
RealType ess = exp(ss); | |
RealType result; | |
if(0 == detail::check_scale("boost::math::skewness(const lognormal_distribution<%1%>&)", sigma, &result, Policy())) | |
return result; | |
return (ess + 2) * sqrt(boost::math::expm1(ss, Policy())); | |
} | |
template <class RealType, class Policy> | |
inline RealType kurtosis(const lognormal_distribution<RealType, Policy>& dist) | |
{ | |
BOOST_MATH_STD_USING // for ADL of std functions | |
//RealType mu = dist.location(); | |
RealType sigma = dist.scale(); | |
RealType ss = sigma * sigma; | |
RealType result; | |
if(0 == detail::check_scale("boost::math::kurtosis(const lognormal_distribution<%1%>&)", sigma, &result, Policy())) | |
return result; | |
return exp(4 * ss) + 2 * exp(3 * ss) + 3 * exp(2 * ss) - 3; | |
} | |
template <class RealType, class Policy> | |
inline RealType kurtosis_excess(const lognormal_distribution<RealType, Policy>& dist) | |
{ | |
BOOST_MATH_STD_USING // for ADL of std functions | |
// RealType mu = dist.location(); | |
RealType sigma = dist.scale(); | |
RealType ss = sigma * sigma; | |
RealType result; | |
if(0 == detail::check_scale("boost::math::kurtosis_excess(const lognormal_distribution<%1%>&)", sigma, &result, Policy())) | |
return result; | |
return exp(4 * ss) + 2 * exp(3 * ss) + 3 * exp(2 * ss) - 6; | |
} | |
} // 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_STUDENTS_T_HPP | |