FM / distributions

/usr/include/boost/math/distributions

Name	Size	Mode	Actions
detail/	-	0755	rm
arcsine.hpp	18797	0644	edit dl rm
bernoulli.hpp	12143	0644	edit dl rm
beta.hpp	18807	0644	edit dl rm
binomial.hpp	28654	0644	edit dl rm
cauchy.hpp	12310	0644	edit dl rm
chi_squared.hpp	12242	0644	edit dl rm
complement.hpp	5978	0644	edit dl rm
empirical_cumulative_distribution_function.hpp	1886	0644	edit dl rm
exponential.hpp	8944	0644	edit dl rm
extreme_value.hpp	10491	0644	edit dl rm
find_location.hpp	6713	0644	edit dl rm
find_scale.hpp	9674	0644	edit dl rm
fisher_f.hpp	14391	0644	edit dl rm
fwd.hpp	5461	0644	edit dl rm
gamma.hpp	10660	0644	edit dl rm
geometric.hpp	21156	0644	edit dl rm
hyperexponential.hpp	21887	0644	edit dl rm
hypergeometric.hpp	12220	0644	edit dl rm
inverse_chi_squared.hpp	15202	0644	edit dl rm
inverse_gamma.hpp	15389	0644	edit dl rm
inverse_gaussian.hpp	19760	0644	edit dl rm
laplace.hpp	10580	0644	edit dl rm
logistic.hpp	11273	0644	edit dl rm
lognormal.hpp	11714	0644	edit dl rm
negative_binomial.hpp	26139	0644	edit dl rm
non_central_beta.hpp	35837	0644	edit dl rm
non_central_chi_squared.hpp	40704	0644	edit dl rm
non_central_f.hpp	15848	0644	edit dl rm
non_central_t.hpp	47973	0644	edit dl rm
normal.hpp	10768	0644	edit dl rm
pareto.hpp	15516	0644	edit dl rm
poisson.hpp	20267	0644	edit dl rm
rayleigh.hpp	10344	0644	edit dl rm
skew_normal.hpp	25646	0644	edit dl rm
students_t.hpp	18476	0644	edit dl rm
triangular.hpp	18407	0644	edit dl rm
uniform.hpp	12963	0644	edit dl rm
weibull.hpp	12081	0644	edit dl rm

Edit: /usr/include/boost/math/distributions/pareto.hpp (15516B)

//  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 l_scale = 1, RealType l_shape = 1)
        : m_scale(l_scale), m_shape(l_shape)
      { // Constructor.
        RealType result = 0;
        detail::check_pareto("boost::math::pareto_distribution<%1%>::pareto_distribution", l_scale, l_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 policies::raise_overflow_error<RealType>(function, 0, Policy()); // 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 policies::raise_overflow_error<RealType>(function, 0, Policy()); // 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

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;
    }

} // 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

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