You cannot select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and dots ('.'), can be up to 35 characters long. Letters must be lowercase.
444 lines
15 KiB
444 lines
15 KiB
// Copyright John Maddock 2007. |
|
// Copyright Paul A. Bristow 2007, 2009 |
|
// 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_PARETO_HPP |
|
#define BOOST_STATS_PARETO_HPP |
|
|
|
// http://en.wikipedia.org/wiki/Pareto_distribution |
|
// http://www.itl.nist.gov/div898/handbook/eda/section3/eda3661.htm |
|
// Also: |
|
// Weisstein, Eric W. "Pareto Distribution." |
|
// From MathWorld--A Wolfram Web Resource. |
|
// http://mathworld.wolfram.com/ParetoDistribution.html |
|
// Handbook of Statistical Distributions with Applications, K Krishnamoorthy, ISBN 1-58488-635-8, Chapter 23, pp 257 - 267. |
|
// Caution KK's a and b are the reverse of Mathworld! |
|
|
|
#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> // for BOOST_CURRENT_VALUE? |
|
|
|
namespace boost |
|
{ |
|
namespace math |
|
{ |
|
namespace detail |
|
{ // Parameter checking. |
|
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)) |
|
{ // any > 0 finite value is OK. |
|
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 |
|
{ // Not finite. |
|
*result = policies::raise_domain_error<RealType>( |
|
function, |
|
"Scale parameter is %1%, but must be finite!", scale, pol); |
|
return false; |
|
} |
|
} // bool check_pareto_scale |
|
|
|
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)) |
|
{ // Any finite value > 0 is OK. |
|
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 |
|
{ // Not finite. |
|
*result = policies::raise_domain_error<RealType>( |
|
function, |
|
"Shape parameter is %1%, but must be finite!", shape, pol); |
|
return false; |
|
} |
|
} // bool check_pareto_shape( |
|
|
|
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 |
|
{ // Not finite.. |
|
*result = policies::raise_domain_error<RealType>( |
|
function, |
|
"x parameter is %1%, but must be finite!", x, pol); |
|
return false; |
|
} |
|
} // bool check_pareto_x |
|
|
|
template <class RealType, class Policy> |
|
inline bool check_pareto( // distribution parameters. |
|
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); |
|
} // bool check_pareto( |
|
|
|
} // namespace detail |
|
|
|
template <class RealType = double, class Policy = policies::policy<> > |
|
class pareto_distribution |
|
{ |
|
public: |
|
typedef RealType value_type; |
|
typedef Policy policy_type; |
|
|
|
pareto_distribution(RealType scale = 1, RealType shape = 1) |
|
: m_scale(scale), m_shape(shape) |
|
{ // Constructor. |
|
RealType result = 0; |
|
detail::check_pareto("boost::math::pareto_distribution<%1%>::pareto_distribution", scale, shape, &result, Policy()); |
|
} |
|
|
|
RealType scale()const |
|
{ // AKA Xm and Wolfram b and beta |
|
return m_scale; |
|
} |
|
|
|
RealType shape()const |
|
{ // AKA k and Wolfram a and alpha |
|
return m_shape; |
|
} |
|
private: |
|
// Data members: |
|
RealType m_scale; // distribution scale (xm) or beta |
|
RealType m_shape; // distribution shape (k) or alpha |
|
}; |
|
|
|
typedef pareto_distribution<double> pareto; // Convenience to allow pareto(2., 3.); |
|
|
|
template <class RealType, class Policy> |
|
inline const std::pair<RealType, RealType> range(const pareto_distribution<RealType, Policy>& /*dist*/) |
|
{ // Range of permissible values for random variable x. |
|
using boost::math::tools::max_value; |
|
return std::pair<RealType, RealType>(static_cast<RealType>(0), max_value<RealType>()); // scale zero to + infinity. |
|
} // range |
|
|
|
template <class RealType, class Policy> |
|
inline const std::pair<RealType, RealType> support(const pareto_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>(dist.scale(), max_value<RealType>() ); // scale to + infinity. |
|
} // support |
|
|
|
template <class RealType, class Policy> |
|
inline RealType pdf(const pareto_distribution<RealType, Policy>& dist, const RealType& x) |
|
{ |
|
BOOST_MATH_STD_USING // for ADL of std function pow. |
|
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) |
|
{ // regardless of shape, pdf is zero (or should be disallow x < scale and throw an exception?). |
|
return 0; |
|
} |
|
result = shape * pow(scale, shape) / pow(x, shape+1); |
|
return result; |
|
} // pdf |
|
|
|
template <class RealType, class Policy> |
|
inline RealType cdf(const pareto_distribution<RealType, Policy>& dist, const RealType& x) |
|
{ |
|
BOOST_MATH_STD_USING // for ADL of std function pow. |
|
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) |
|
{ // regardless of shape, cdf is zero. |
|
return 0; |
|
} |
|
|
|
// result = RealType(1) - pow((scale / x), shape); |
|
result = -boost::math::powm1(scale/x, shape, Policy()); // should be more accurate. |
|
return result; |
|
} // cdf |
|
|
|
template <class RealType, class Policy> |
|
inline RealType quantile(const pareto_distribution<RealType, Policy>& dist, const RealType& p) |
|
{ |
|
BOOST_MATH_STD_USING // for ADL of std function pow. |
|
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; // x must be scale (or less). |
|
} |
|
if (p == 1) |
|
{ |
|
return tools::max_value<RealType>(); // x = + infinity. |
|
} |
|
result = scale / |
|
(pow((1 - p), 1 / shape)); |
|
// K. Krishnamoorthy, ISBN 1-58488-635-8 eq 23.1.3 |
|
return result; |
|
} // quantile |
|
|
|
template <class RealType, class Policy> |
|
inline RealType cdf(const complemented2_type<pareto_distribution<RealType, Policy>, RealType>& c) |
|
{ |
|
BOOST_MATH_STD_USING // for ADL of std function pow. |
|
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) |
|
{ // regardless of shape, cdf is zero, and complement is unity. |
|
return 1; |
|
} |
|
result = pow((scale/x), shape); |
|
|
|
return result; |
|
} // cdf complement |
|
|
|
template <class RealType, class Policy> |
|
inline RealType quantile(const complemented2_type<pareto_distribution<RealType, Policy>, RealType>& c) |
|
{ |
|
BOOST_MATH_STD_USING // for ADL of std function pow. |
|
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; // x must be scale (or less). |
|
} |
|
if (q == 0) |
|
{ |
|
return tools::max_value<RealType>(); // x = + infinity. |
|
} |
|
result = scale / (pow(q, 1 / shape)); |
|
// K. Krishnamoorthy, ISBN 1-58488-635-8 eq 23.1.3 |
|
return result; |
|
} // quantile complement |
|
|
|
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>(); // +infinity. |
|
} |
|
} // mean |
|
|
|
template <class RealType, class Policy> |
|
inline RealType mode(const pareto_distribution<RealType, Policy>& dist) |
|
{ |
|
return dist.scale(); |
|
} // mode |
|
|
|
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())); |
|
} // median |
|
|
|
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; |
|
} // variance |
|
|
|
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; |
|
} // skewness |
|
|
|
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; |
|
} // kurtosis |
|
|
|
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; |
|
} // kurtosis_excess |
|
|
|
} // 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_PARETO_HPP |
|
|
|
|
|
|