Added boost header

test/external/boost/math/distributions/pareto.hpp

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+//  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
+
+