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- #ifndef BOOST_STATS_PARETO_HPP
- #define BOOST_STATS_PARETO_HPP
- #include <boost/math/distributions/fwd.hpp>
- #include <boost/math/distributions/complement.hpp>
- #include <boost/math/distributions/detail/common_error_handling.hpp>
- #include <boost/math/special_functions/powm1.hpp>
- #include <utility>
- namespace boost
- {
- namespace math
- {
- namespace detail
- {
- template <class RealType, class Policy>
- inline bool check_pareto_scale(
- const char* function,
- RealType scale,
- RealType* result, const Policy& pol)
- {
- if((boost::math::isfinite)(scale))
- {
- if (scale > 0)
- {
- return true;
- }
- else
- {
- *result = policies::raise_domain_error<RealType>(
- function,
- "Scale parameter is %1%, but must be > 0!", scale, pol);
- return false;
- }
- }
- else
- {
- *result = policies::raise_domain_error<RealType>(
- function,
- "Scale parameter is %1%, but must be finite!", scale, pol);
- return false;
- }
- }
- template <class RealType, class Policy>
- inline bool check_pareto_shape(
- const char* function,
- RealType shape,
- RealType* result, const Policy& pol)
- {
- if((boost::math::isfinite)(shape))
- {
- if (shape > 0)
- {
- return true;
- }
- else
- {
- *result = policies::raise_domain_error<RealType>(
- function,
- "Shape parameter is %1%, but must be > 0!", shape, pol);
- return false;
- }
- }
- else
- {
- *result = policies::raise_domain_error<RealType>(
- function,
- "Shape parameter is %1%, but must be finite!", shape, pol);
- return false;
- }
- }
- template <class RealType, class Policy>
- inline bool check_pareto_x(
- const char* function,
- RealType const& x,
- RealType* result, const Policy& pol)
- {
- if((boost::math::isfinite)(x))
- {
- if (x > 0)
- {
- return true;
- }
- else
- {
- *result = policies::raise_domain_error<RealType>(
- function,
- "x parameter is %1%, but must be > 0 !", x, pol);
- return false;
- }
- }
- else
- {
- *result = policies::raise_domain_error<RealType>(
- function,
- "x parameter is %1%, but must be finite!", x, pol);
- return false;
- }
- }
- template <class RealType, class Policy>
- inline bool check_pareto(
- const char* function,
- RealType scale,
- RealType shape,
- RealType* result, const Policy& pol)
- {
- return check_pareto_scale(function, scale, result, pol)
- && check_pareto_shape(function, shape, result, pol);
- }
- }
- template <class RealType = double, class Policy = policies::policy<> >
- class pareto_distribution
- {
- public:
- typedef RealType value_type;
- typedef Policy policy_type;
- pareto_distribution(RealType l_scale = 1, RealType l_shape = 1)
- : m_scale(l_scale), m_shape(l_shape)
- {
- RealType result = 0;
- detail::check_pareto("boost::math::pareto_distribution<%1%>::pareto_distribution", l_scale, l_shape, &result, Policy());
- }
- RealType scale()const
- {
- return m_scale;
- }
- RealType shape()const
- {
- return m_shape;
- }
- private:
-
- RealType m_scale;
- RealType m_shape;
- };
- typedef pareto_distribution<double> pareto;
- template <class RealType, class Policy>
- inline const std::pair<RealType, RealType> range(const pareto_distribution<RealType, Policy>& )
- {
- 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 pareto_distribution<RealType, Policy>& dist)
- {
-
- using boost::math::tools::max_value;
- return std::pair<RealType, RealType>(dist.scale(), max_value<RealType>() );
- }
- template <class RealType, class Policy>
- inline RealType pdf(const pareto_distribution<RealType, Policy>& dist, const RealType& x)
- {
- BOOST_MATH_STD_USING
- static const char* function = "boost::math::pdf(const pareto_distribution<%1%>&, %1%)";
- RealType scale = dist.scale();
- RealType shape = dist.shape();
- RealType result = 0;
- if(false == (detail::check_pareto_x(function, x, &result, Policy())
- && detail::check_pareto(function, scale, shape, &result, Policy())))
- return result;
- if (x < scale)
- {
- return 0;
- }
- result = shape * pow(scale, shape) / pow(x, shape+1);
- return result;
- }
- template <class RealType, class Policy>
- inline RealType cdf(const pareto_distribution<RealType, Policy>& dist, const RealType& x)
- {
- BOOST_MATH_STD_USING
- static const char* function = "boost::math::cdf(const pareto_distribution<%1%>&, %1%)";
- RealType scale = dist.scale();
- RealType shape = dist.shape();
- RealType result = 0;
- if(false == (detail::check_pareto_x(function, x, &result, Policy())
- && detail::check_pareto(function, scale, shape, &result, Policy())))
- return result;
- if (x <= scale)
- {
- return 0;
- }
-
- result = -boost::math::powm1(scale/x, shape, Policy());
- return result;
- }
- template <class RealType, class Policy>
- inline RealType quantile(const pareto_distribution<RealType, Policy>& dist, const RealType& p)
- {
- BOOST_MATH_STD_USING
- static const char* function = "boost::math::quantile(const pareto_distribution<%1%>&, %1%)";
- RealType result = 0;
- RealType scale = dist.scale();
- RealType shape = dist.shape();
- if(false == (detail::check_probability(function, p, &result, Policy())
- && detail::check_pareto(function, scale, shape, &result, Policy())))
- {
- return result;
- }
- if (p == 0)
- {
- return scale;
- }
- if (p == 1)
- {
- return policies::raise_overflow_error<RealType>(function, 0, Policy());
- }
- result = scale /
- (pow((1 - p), 1 / shape));
-
- return result;
- }
- template <class RealType, class Policy>
- inline RealType cdf(const complemented2_type<pareto_distribution<RealType, Policy>, RealType>& c)
- {
- BOOST_MATH_STD_USING
- static const char* function = "boost::math::cdf(const pareto_distribution<%1%>&, %1%)";
- RealType result = 0;
- RealType x = c.param;
- RealType scale = c.dist.scale();
- RealType shape = c.dist.shape();
- if(false == (detail::check_pareto_x(function, x, &result, Policy())
- && detail::check_pareto(function, scale, shape, &result, Policy())))
- return result;
- if (x <= scale)
- {
- return 1;
- }
- result = pow((scale/x), shape);
- return result;
- }
- template <class RealType, class Policy>
- inline RealType quantile(const complemented2_type<pareto_distribution<RealType, Policy>, RealType>& c)
- {
- BOOST_MATH_STD_USING
- static const char* function = "boost::math::quantile(const pareto_distribution<%1%>&, %1%)";
- RealType result = 0;
- RealType q = c.param;
- RealType scale = c.dist.scale();
- RealType shape = c.dist.shape();
- if(false == (detail::check_probability(function, q, &result, Policy())
- && detail::check_pareto(function, scale, shape, &result, Policy())))
- {
- return result;
- }
- if (q == 1)
- {
- return scale;
- }
- if (q == 0)
- {
- return policies::raise_overflow_error<RealType>(function, 0, Policy());
- }
- result = scale / (pow(q, 1 / shape));
-
- return result;
- }
- template <class RealType, class Policy>
- inline RealType mean(const pareto_distribution<RealType, Policy>& dist)
- {
- RealType result = 0;
- static const char* function = "boost::math::mean(const pareto_distribution<%1%>&, %1%)";
- if(false == detail::check_pareto(function, dist.scale(), dist.shape(), &result, Policy()))
- {
- return result;
- }
- if (dist.shape() > RealType(1))
- {
- return dist.shape() * dist.scale() / (dist.shape() - 1);
- }
- else
- {
- using boost::math::tools::max_value;
- return max_value<RealType>();
- }
- }
- template <class RealType, class Policy>
- inline RealType mode(const pareto_distribution<RealType, Policy>& dist)
- {
- return dist.scale();
- }
- template <class RealType, class Policy>
- inline RealType median(const pareto_distribution<RealType, Policy>& dist)
- {
- RealType result = 0;
- static const char* function = "boost::math::median(const pareto_distribution<%1%>&, %1%)";
- if(false == detail::check_pareto(function, dist.scale(), dist.shape(), &result, Policy()))
- {
- return result;
- }
- BOOST_MATH_STD_USING
- return dist.scale() * pow(RealType(2), (1/dist.shape()));
- }
- template <class RealType, class Policy>
- inline RealType variance(const pareto_distribution<RealType, Policy>& dist)
- {
- RealType result = 0;
- RealType scale = dist.scale();
- RealType shape = dist.shape();
- static const char* function = "boost::math::variance(const pareto_distribution<%1%>&, %1%)";
- if(false == detail::check_pareto(function, scale, shape, &result, Policy()))
- {
- return result;
- }
- if (shape > 2)
- {
- result = (scale * scale * shape) /
- ((shape - 1) * (shape - 1) * (shape - 2));
- }
- else
- {
- result = policies::raise_domain_error<RealType>(
- function,
- "variance is undefined for shape <= 2, but got %1%.", dist.shape(), Policy());
- }
- return result;
- }
- template <class RealType, class Policy>
- inline RealType skewness(const pareto_distribution<RealType, Policy>& dist)
- {
- BOOST_MATH_STD_USING
- RealType result = 0;
- RealType shape = dist.shape();
- static const char* function = "boost::math::pdf(const pareto_distribution<%1%>&, %1%)";
- if(false == detail::check_pareto(function, dist.scale(), shape, &result, Policy()))
- {
- return result;
- }
- if (shape > 3)
- {
- result = sqrt((shape - 2) / shape) *
- 2 * (shape + 1) /
- (shape - 3);
- }
- else
- {
- result = policies::raise_domain_error<RealType>(
- function,
- "skewness is undefined for shape <= 3, but got %1%.", dist.shape(), Policy());
- }
- return result;
- }
- template <class RealType, class Policy>
- inline RealType kurtosis(const pareto_distribution<RealType, Policy>& dist)
- {
- RealType result = 0;
- RealType shape = dist.shape();
- static const char* function = "boost::math::pdf(const pareto_distribution<%1%>&, %1%)";
- if(false == detail::check_pareto(function, dist.scale(), shape, &result, Policy()))
- {
- return result;
- }
- if (shape > 4)
- {
- result = 3 * ((shape - 2) * (3 * shape * shape + shape + 2)) /
- (shape * (shape - 3) * (shape - 4));
- }
- else
- {
- result = policies::raise_domain_error<RealType>(
- function,
- "kurtosis_excess is undefined for shape <= 4, but got %1%.", shape, Policy());
- }
- return result;
- }
- template <class RealType, class Policy>
- inline RealType kurtosis_excess(const pareto_distribution<RealType, Policy>& dist)
- {
- RealType result = 0;
- RealType shape = dist.shape();
- static const char* function = "boost::math::pdf(const pareto_distribution<%1%>&, %1%)";
- if(false == detail::check_pareto(function, dist.scale(), shape, &result, Policy()))
- {
- return result;
- }
- if (shape > 4)
- {
- result = 6 * ((shape * shape * shape) + (shape * shape) - 6 * shape - 2) /
- (shape * (shape - 3) * (shape - 4));
- }
- else
- {
- result = policies::raise_domain_error<RealType>(
- function,
- "kurtosis_excess is undefined for shape <= 4, but got %1%.", dist.shape(), Policy());
- }
- return result;
- }
- template <class RealType, class Policy>
- inline RealType entropy(const pareto_distribution<RealType, Policy>& dist)
- {
- using std::log;
- RealType xm = dist.scale();
- RealType alpha = dist.shape();
- return log(xm/alpha) + 1 + 1/alpha;
- }
- }
- }
-
-
-
- #include <boost/math/distributions/detail/derived_accessors.hpp>
- #endif
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