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 = 0;
if(0 == detail::check_scale(function, sigma, &result, Policy()))
return result;
if(0 == detail::check_location(function, mu, &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;
}
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 = 0;
if(0 == detail::check_scale("lslboost::math::mode(const lognormal_distribution<%1%>&)", sigma, &result, Policy()))
return result;
return exp(mu - sigma * sigma);
}
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 = 0;
if(0 == detail::check_scale("boost::math::variance(const lognormal_distribution<%1%>&)", sigma, &result, Policy()))
return result;
if(0 == detail::check_location("boost::math::variance(const lognormal_distribution<%1%>&)", mu, &result, Policy()))
return result;
return boost::math::expm1(sigma * sigma, Policy()) * exp(2 * mu + sigma * sigma);
}
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 = "lslboost::math::cdf(const lognormal_distribution<%1%>&, %1%)";
RealType result = 0;
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));
}
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 = "lslboost::math::quantile(const lognormal_distribution<%1%>&, %1%)";
RealType result = 0;
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));
}
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 = 0;
if(0 == detail::check_scale("lslboost::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;
}
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 = 0;
if(0 == detail::check_scale("lslboost::math::skewness(const lognormal_distribution<%1%>&)", sigma, &result, Policy()))
return result;
return (ess + 2) * sqrt(lslboost::math::expm1(ss, 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
}
