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