Chris@16: //  Copyright John Maddock 2006.
Chris@16: //  Use, modification and distribution are subject to the
Chris@16: //  Boost Software License, Version 1.0. (See accompanying file
Chris@16: //  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
Chris@16: 
Chris@16: #ifndef BOOST_STATS_LOGNORMAL_HPP
Chris@16: #define BOOST_STATS_LOGNORMAL_HPP
Chris@16: 
Chris@16: // http://www.itl.nist.gov/div898/handbook/eda/section3/eda3669.htm
Chris@16: // http://mathworld.wolfram.com/LogNormalDistribution.html
Chris@16: // http://en.wikipedia.org/wiki/Lognormal_distribution
Chris@16: 
Chris@16: #include <boost/math/distributions/fwd.hpp>
Chris@16: #include <boost/math/distributions/normal.hpp>
Chris@16: #include <boost/math/special_functions/expm1.hpp>
Chris@16: #include <boost/math/distributions/detail/common_error_handling.hpp>
Chris@16: 
Chris@16: #include <utility>
Chris@16: 
Chris@16: namespace boost{ namespace math
Chris@16: {
Chris@16: namespace detail
Chris@16: {
Chris@16: 
Chris@16:   template <class RealType, class Policy>
Chris@16:   inline bool check_lognormal_x(
Chris@16:         const char* function,
Chris@16:         RealType const& x,
Chris@16:         RealType* result, const Policy& pol)
Chris@16:   {
Chris@16:      if((x < 0) || !(boost::math::isfinite)(x))
Chris@16:      {
Chris@16:         *result = policies::raise_domain_error<RealType>(
Chris@16:            function,
Chris@16:            "Random variate is %1% but must be >= 0 !", x, pol);
Chris@16:         return false;
Chris@16:      }
Chris@16:      return true;
Chris@16:   }
Chris@16: 
Chris@16: } // namespace detail
Chris@16: 
Chris@16: 
Chris@16: template <class RealType = double, class Policy = policies::policy<> >
Chris@16: class lognormal_distribution
Chris@16: {
Chris@16: public:
Chris@16:    typedef RealType value_type;
Chris@16:    typedef Policy policy_type;
Chris@16: 
Chris@16:    lognormal_distribution(RealType l_location = 0, RealType l_scale = 1)
Chris@16:       : m_location(l_location), m_scale(l_scale)
Chris@16:    {
Chris@16:       RealType result;
Chris@16:       detail::check_scale("boost::math::lognormal_distribution<%1%>::lognormal_distribution", l_scale, &result, Policy());
Chris@16:       detail::check_location("boost::math::lognormal_distribution<%1%>::lognormal_distribution", l_location, &result, Policy());
Chris@16:    }
Chris@16: 
Chris@16:    RealType location()const
Chris@16:    {
Chris@16:       return m_location;
Chris@16:    }
Chris@16: 
Chris@16:    RealType scale()const
Chris@16:    {
Chris@16:       return m_scale;
Chris@16:    }
Chris@16: private:
Chris@16:    //
Chris@16:    // Data members:
Chris@16:    //
Chris@16:    RealType m_location;  // distribution location.
Chris@16:    RealType m_scale;     // distribution scale.
Chris@16: };
Chris@16: 
Chris@16: typedef lognormal_distribution<double> lognormal;
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline const std::pair<RealType, RealType> range(const lognormal_distribution<RealType, Policy>& /*dist*/)
Chris@16: { // Range of permissible values for random variable x is >0 to +infinity.
Chris@16:    using boost::math::tools::max_value;
Chris@16:    return std::pair<RealType, RealType>(static_cast<RealType>(0), max_value<RealType>());
Chris@16: }
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline const std::pair<RealType, RealType> support(const lognormal_distribution<RealType, Policy>& /*dist*/)
Chris@16: { // Range of supported values for random variable x.
Chris@16:    // This is range where cdf rises from 0 to 1, and outside it, the pdf is zero.
Chris@16:    using boost::math::tools::max_value;
Chris@16:    return std::pair<RealType, RealType>(static_cast<RealType>(0),  max_value<RealType>());
Chris@16: }
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: RealType pdf(const lognormal_distribution<RealType, Policy>& dist, const RealType& x)
Chris@16: {
Chris@16:    BOOST_MATH_STD_USING  // for ADL of std functions
Chris@16: 
Chris@16:    RealType mu = dist.location();
Chris@16:    RealType sigma = dist.scale();
Chris@16: 
Chris@16:    static const char* function = "boost::math::pdf(const lognormal_distribution<%1%>&, %1%)";
Chris@16: 
Chris@16:    RealType result = 0;
Chris@16:    if(0 == detail::check_scale(function, sigma, &result, Policy()))
Chris@16:       return result;
Chris@16:    if(0 == detail::check_location(function, mu, &result, Policy()))
Chris@16:       return result;
Chris@16:    if(0 == detail::check_lognormal_x(function, x, &result, Policy()))
Chris@16:       return result;
Chris@16: 
Chris@16:    if(x == 0)
Chris@16:       return 0;
Chris@16: 
Chris@16:    RealType exponent = log(x) - mu;
Chris@16:    exponent *= -exponent;
Chris@16:    exponent /= 2 * sigma * sigma;
Chris@16: 
Chris@16:    result = exp(exponent);
Chris@16:    result /= sigma * sqrt(2 * constants::pi<RealType>()) * x;
Chris@16: 
Chris@16:    return result;
Chris@16: }
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline RealType cdf(const lognormal_distribution<RealType, Policy>& dist, const RealType& x)
Chris@16: {
Chris@16:    BOOST_MATH_STD_USING  // for ADL of std functions
Chris@16: 
Chris@16:    static const char* function = "boost::math::cdf(const lognormal_distribution<%1%>&, %1%)";
Chris@16: 
Chris@16:    RealType result = 0;
Chris@16:    if(0 == detail::check_scale(function, dist.scale(), &result, Policy()))
Chris@16:       return result;
Chris@16:    if(0 == detail::check_location(function, dist.location(), &result, Policy()))
Chris@16:       return result;
Chris@16:    if(0 == detail::check_lognormal_x(function, x, &result, Policy()))
Chris@16:       return result;
Chris@16: 
Chris@16:    if(x == 0)
Chris@16:       return 0;
Chris@16: 
Chris@16:    normal_distribution<RealType, Policy> norm(dist.location(), dist.scale());
Chris@16:    return cdf(norm, log(x));
Chris@16: }
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline RealType quantile(const lognormal_distribution<RealType, Policy>& dist, const RealType& p)
Chris@16: {
Chris@16:    BOOST_MATH_STD_USING  // for ADL of std functions
Chris@16: 
Chris@16:    static const char* function = "boost::math::quantile(const lognormal_distribution<%1%>&, %1%)";
Chris@16: 
Chris@16:    RealType result = 0;
Chris@16:    if(0 == detail::check_scale(function, dist.scale(), &result, Policy()))
Chris@16:       return result;
Chris@16:    if(0 == detail::check_location(function, dist.location(), &result, Policy()))
Chris@16:       return result;
Chris@16:    if(0 == detail::check_probability(function, p, &result, Policy()))
Chris@16:       return result;
Chris@16: 
Chris@16:    if(p == 0)
Chris@16:       return 0;
Chris@16:    if(p == 1)
Chris@16:       return policies::raise_overflow_error<RealType>(function, 0, Policy());
Chris@16: 
Chris@16:    normal_distribution<RealType, Policy> norm(dist.location(), dist.scale());
Chris@16:    return exp(quantile(norm, p));
Chris@16: }
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline RealType cdf(const complemented2_type<lognormal_distribution<RealType, Policy>, RealType>& c)
Chris@16: {
Chris@16:    BOOST_MATH_STD_USING  // for ADL of std functions
Chris@16: 
Chris@16:    static const char* function = "boost::math::cdf(const lognormal_distribution<%1%>&, %1%)";
Chris@16: 
Chris@16:    RealType result = 0;
Chris@16:    if(0 == detail::check_scale(function, c.dist.scale(), &result, Policy()))
Chris@16:       return result;
Chris@16:    if(0 == detail::check_location(function, c.dist.location(), &result, Policy()))
Chris@16:       return result;
Chris@16:    if(0 == detail::check_lognormal_x(function, c.param, &result, Policy()))
Chris@16:       return result;
Chris@16: 
Chris@16:    if(c.param == 0)
Chris@16:       return 1;
Chris@16: 
Chris@16:    normal_distribution<RealType, Policy> norm(c.dist.location(), c.dist.scale());
Chris@16:    return cdf(complement(norm, log(c.param)));
Chris@16: }
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline RealType quantile(const complemented2_type<lognormal_distribution<RealType, Policy>, RealType>& c)
Chris@16: {
Chris@16:    BOOST_MATH_STD_USING  // for ADL of std functions
Chris@16: 
Chris@16:    static const char* function = "boost::math::quantile(const lognormal_distribution<%1%>&, %1%)";
Chris@16: 
Chris@16:    RealType result = 0;
Chris@16:    if(0 == detail::check_scale(function, c.dist.scale(), &result, Policy()))
Chris@16:       return result;
Chris@16:    if(0 == detail::check_location(function, c.dist.location(), &result, Policy()))
Chris@16:       return result;
Chris@16:    if(0 == detail::check_probability(function, c.param, &result, Policy()))
Chris@16:       return result;
Chris@16: 
Chris@16:    if(c.param == 1)
Chris@16:       return 0;
Chris@16:    if(c.param == 0)
Chris@16:       return policies::raise_overflow_error<RealType>(function, 0, Policy());
Chris@16: 
Chris@16:    normal_distribution<RealType, Policy> norm(c.dist.location(), c.dist.scale());
Chris@16:    return exp(quantile(complement(norm, c.param)));
Chris@16: }
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline RealType mean(const lognormal_distribution<RealType, Policy>& dist)
Chris@16: {
Chris@16:    BOOST_MATH_STD_USING  // for ADL of std functions
Chris@16: 
Chris@16:    RealType mu = dist.location();
Chris@16:    RealType sigma = dist.scale();
Chris@16: 
Chris@16:    RealType result = 0;
Chris@16:    if(0 == detail::check_scale("boost::math::mean(const lognormal_distribution<%1%>&)", sigma, &result, Policy()))
Chris@16:       return result;
Chris@16:    if(0 == detail::check_location("boost::math::mean(const lognormal_distribution<%1%>&)", mu, &result, Policy()))
Chris@16:       return result;
Chris@16: 
Chris@16:    return exp(mu + sigma * sigma / 2);
Chris@16: }
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline RealType variance(const lognormal_distribution<RealType, Policy>& dist)
Chris@16: {
Chris@16:    BOOST_MATH_STD_USING  // for ADL of std functions
Chris@16: 
Chris@16:    RealType mu = dist.location();
Chris@16:    RealType sigma = dist.scale();
Chris@16: 
Chris@16:    RealType result = 0;
Chris@16:    if(0 == detail::check_scale("boost::math::variance(const lognormal_distribution<%1%>&)", sigma, &result, Policy()))
Chris@16:       return result;
Chris@16:    if(0 == detail::check_location("boost::math::variance(const lognormal_distribution<%1%>&)", mu, &result, Policy()))
Chris@16:       return result;
Chris@16: 
Chris@16:    return boost::math::expm1(sigma * sigma, Policy()) * exp(2 * mu + sigma * sigma);
Chris@16: }
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline RealType mode(const lognormal_distribution<RealType, Policy>& dist)
Chris@16: {
Chris@16:    BOOST_MATH_STD_USING  // for ADL of std functions
Chris@16: 
Chris@16:    RealType mu = dist.location();
Chris@16:    RealType sigma = dist.scale();
Chris@16: 
Chris@16:    RealType result = 0;
Chris@16:    if(0 == detail::check_scale("boost::math::mode(const lognormal_distribution<%1%>&)", sigma, &result, Policy()))
Chris@16:       return result;
Chris@16:    if(0 == detail::check_location("boost::math::mode(const lognormal_distribution<%1%>&)", mu, &result, Policy()))
Chris@16:       return result;
Chris@16: 
Chris@16:    return exp(mu - sigma * sigma);
Chris@16: }
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline RealType median(const lognormal_distribution<RealType, Policy>& dist)
Chris@16: {
Chris@16:    BOOST_MATH_STD_USING  // for ADL of std functions
Chris@16:    RealType mu = dist.location();
Chris@16:    return exp(mu); // e^mu
Chris@16: }
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline RealType skewness(const lognormal_distribution<RealType, Policy>& dist)
Chris@16: {
Chris@16:    BOOST_MATH_STD_USING  // for ADL of std functions
Chris@16: 
Chris@16:    //RealType mu = dist.location();
Chris@16:    RealType sigma = dist.scale();
Chris@16: 
Chris@16:    RealType ss = sigma * sigma;
Chris@16:    RealType ess = exp(ss);
Chris@16: 
Chris@16:    RealType result = 0;
Chris@16:    if(0 == detail::check_scale("boost::math::skewness(const lognormal_distribution<%1%>&)", sigma, &result, Policy()))
Chris@16:       return result;
Chris@16:    if(0 == detail::check_location("boost::math::skewness(const lognormal_distribution<%1%>&)", dist.location(), &result, Policy()))
Chris@16:       return result;
Chris@16: 
Chris@16:    return (ess + 2) * sqrt(boost::math::expm1(ss, Policy()));
Chris@16: }
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline RealType kurtosis(const lognormal_distribution<RealType, Policy>& dist)
Chris@16: {
Chris@16:    BOOST_MATH_STD_USING  // for ADL of std functions
Chris@16: 
Chris@16:    //RealType mu = dist.location();
Chris@16:    RealType sigma = dist.scale();
Chris@16:    RealType ss = sigma * sigma;
Chris@16: 
Chris@16:    RealType result = 0;
Chris@16:    if(0 == detail::check_scale("boost::math::kurtosis(const lognormal_distribution<%1%>&)", sigma, &result, Policy()))
Chris@16:       return result;
Chris@16:    if(0 == detail::check_location("boost::math::kurtosis(const lognormal_distribution<%1%>&)", dist.location(), &result, Policy()))
Chris@16:       return result;
Chris@16: 
Chris@16:    return exp(4 * ss) + 2 * exp(3 * ss) + 3 * exp(2 * ss) - 3;
Chris@16: }
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline RealType kurtosis_excess(const lognormal_distribution<RealType, Policy>& dist)
Chris@16: {
Chris@16:    BOOST_MATH_STD_USING  // for ADL of std functions
Chris@16: 
Chris@16:    // RealType mu = dist.location();
Chris@16:    RealType sigma = dist.scale();
Chris@16:    RealType ss = sigma * sigma;
Chris@16: 
Chris@16:    RealType result = 0;
Chris@16:    if(0 == detail::check_scale("boost::math::kurtosis_excess(const lognormal_distribution<%1%>&)", sigma, &result, Policy()))
Chris@16:       return result;
Chris@16:    if(0 == detail::check_location("boost::math::kurtosis_excess(const lognormal_distribution<%1%>&)", dist.location(), &result, Policy()))
Chris@16:       return result;
Chris@16: 
Chris@16:    return exp(4 * ss) + 2 * exp(3 * ss) + 3 * exp(2 * ss) - 6;
Chris@16: }
Chris@16: 
Chris@16: } // namespace math
Chris@16: } // namespace boost
Chris@16: 
Chris@16: // This include must be at the end, *after* the accessors
Chris@16: // for this distribution have been defined, in order to
Chris@16: // keep compilers that support two-phase lookup happy.
Chris@16: #include <boost/math/distributions/detail/derived_accessors.hpp>
Chris@16: 
Chris@16: #endif // BOOST_STATS_STUDENTS_T_HPP
Chris@16: 
Chris@16: