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