Added boost header

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

@@ -0,0 +1,458 @@
+// inverse_gamma.hpp
+
+//  Copyright Paul A. Bristow 2010.
+//  Copyright John Maddock 2010.
+//  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_INVERSE_GAMMA_HPP
+#define BOOST_STATS_INVERSE_GAMMA_HPP
+
+// Inverse Gamma Distribution is a two-parameter family
+// of continuous probability distributions
+// on the positive real line, which is the distribution of
+// the reciprocal of a variable distributed according to the gamma distribution.
+
+// http://en.wikipedia.org/wiki/Inverse-gamma_distribution
+// http://rss.acs.unt.edu/Rdoc/library/pscl/html/igamma.html
+
+// See also gamma distribution at gamma.hpp:
+// http://www.itl.nist.gov/div898/handbook/eda/section3/eda366b.htm
+// http://mathworld.wolfram.com/GammaDistribution.html
+// http://en.wikipedia.org/wiki/Gamma_distribution
+
+#include <boost/math/distributions/fwd.hpp>
+#include <boost/math/special_functions/gamma.hpp>
+#include <boost/math/distributions/detail/common_error_handling.hpp>
+#include <boost/math/distributions/complement.hpp>
+
+#include <utility>
+
+namespace boost{ namespace math
+{
+namespace detail
+{
+
+template <class RealType, class Policy>
+inline bool check_inverse_gamma_shape(
+      const char* function, // inverse_gamma
+      RealType shape, // shape aka alpha
+      RealType* result, // to update, perhaps with NaN
+      const Policy& pol)
+{  // Sources say shape argument must be > 0
+   // but seems logical to allow shape zero as special case,
+   // returning pdf and cdf zero (but not < 0).
+   // (Functions like mean, variance with other limits on shape are checked
+   // in version including an operator & limit below).
+   if((shape < 0) || !(boost::math::isfinite)(shape))
+   {
+      *result = policies::raise_domain_error<RealType>(
+         function,
+         "Shape parameter is %1%, but must be >= 0 !", shape, pol);
+      return false;
+   }
+   return true;
+} //bool check_inverse_gamma_shape
+
+template <class RealType, class Policy>
+inline bool check_inverse_gamma_x(
+      const char* function,
+      RealType const& x,
+      RealType* result, const Policy& pol)
+{
+   if((x < 0) || !(boost::math::isfinite)(x))
+   {
+      *result = policies::raise_domain_error<RealType>(
+         function,
+         "Random variate is %1% but must be >= 0 !", x, pol);
+      return false;
+   }
+   return true;
+}
+
+template <class RealType, class Policy>
+inline bool check_inverse_gamma(
+      const char* function, // TODO swap these over, so shape is first.
+      RealType scale,  // scale aka beta
+      RealType shape, // shape aka alpha
+      RealType* result, const Policy& pol)
+{
+   return check_scale(function, scale, result, pol)
+     && check_inverse_gamma_shape(function, shape, result, pol);
+} // bool check_inverse_gamma
+
+} // namespace detail
+
+template <class RealType = double, class Policy = policies::policy<> >
+class inverse_gamma_distribution
+{
+public:
+   typedef RealType value_type;
+   typedef Policy policy_type;
+
+   inverse_gamma_distribution(RealType shape = 1, RealType scale = 1)
+      : m_shape(shape), m_scale(scale)
+   {
+      RealType result;
+      detail::check_inverse_gamma(
+        "boost::math::inverse_gamma_distribution<%1%>::inverse_gamma_distribution",
+        scale, shape, &result, Policy());
+   }
+
+   RealType shape()const
+   {
+      return m_shape;
+   }
+
+   RealType scale()const
+   {
+      return m_scale;
+   }
+private:
+   //
+   // Data members:
+   //
+   RealType m_shape;     // distribution shape
+   RealType m_scale;     // distribution scale
+};
+
+typedef inverse_gamma_distribution<double> inverse_gamma;
+// typedef - but potential clash with name of inverse gamma *function*.
+// but there is a typedef for gamma
+//   typedef boost::math::gamma_distribution<Type, Policy> gamma;
+
+// Allow random variable x to be zero, treated as a special case (unlike some definitions).
+
+template <class RealType, class Policy>
+inline const std::pair<RealType, RealType> range(const inverse_gamma_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>());
+}
+
+template <class RealType, class Policy>
+inline const std::pair<RealType, RealType> support(const inverse_gamma_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;
+   using boost::math::tools::min_value;
+   return std::pair<RealType, RealType>(static_cast<RealType>(0),  max_value<RealType>());
+}
+
+template <class RealType, class Policy>
+inline RealType pdf(const inverse_gamma_distribution<RealType, Policy>& dist, const RealType& x)
+{
+   BOOST_MATH_STD_USING  // for ADL of std functions
+
+   static const char* function = "boost::math::pdf(const inverse_gamma_distribution<%1%>&, %1%)";
+
+   RealType shape = dist.shape();
+   RealType scale = dist.scale();
+
+   RealType result = 0;
+   if(false == detail::check_inverse_gamma(function, scale, shape, &result, Policy()))
+   { // distribution parameters bad.
+      return result;
+   } 
+   if(x == 0)
+   { // Treat random variate zero as a special case.
+      return 0;
+   }
+   else if(false == detail::check_inverse_gamma_x(function, x, &result, Policy()))
+   { // x bad.
+      return result;
+   }
+   result = scale / x;
+   if(result < tools::min_value<RealType>())
+      return 0;  // random variable is infinite or so close as to make no difference.
+   result = gamma_p_derivative(shape, result, Policy()) * scale;
+   if(0 != result)
+   {
+      if(x < 0)
+      {
+         // x * x may under or overflow, likewise our result,
+         // so be extra careful about the arithmetic:
+         RealType lim = tools::max_value<RealType>() * x;
+         if(lim < result)
+            return policies::raise_overflow_error<RealType, Policy>(function, "PDF is infinite.", Policy());
+         result /= x;
+         if(lim < result)
+            return policies::raise_overflow_error<RealType, Policy>(function, "PDF is infinite.", Policy());
+         result /= x;
+      }
+      result /= (x * x);
+   }
+   // better than naive
+   // result = (pow(scale, shape) * pow(x, (-shape -1)) * exp(-scale/x) ) / tgamma(shape);
+   return result;
+} // pdf
+
+template <class RealType, class Policy>
+inline RealType cdf(const inverse_gamma_distribution<RealType, Policy>& dist, const RealType& x)
+{
+   BOOST_MATH_STD_USING  // for ADL of std functions
+
+   static const char* function = "boost::math::cdf(const inverse_gamma_distribution<%1%>&, %1%)";
+
+   RealType shape = dist.shape();
+   RealType scale = dist.scale();
+
+   RealType result = 0;
+   if(false == detail::check_inverse_gamma(function, scale, shape, &result, Policy()))
+   { // distribution parameters bad.
+      return result;
+   }
+   if (x == 0)
+   { // Treat zero as a special case.
+     return 0;
+   }
+   else if(false == detail::check_inverse_gamma_x(function, x, &result, Policy()))
+   { // x bad
+      return result;
+   }
+   result = boost::math::gamma_q(shape, scale / x, Policy());
+   // result = tgamma(shape, scale / x) / tgamma(shape); // naive using tgamma
+   return result;
+} // cdf
+
+template <class RealType, class Policy>
+inline RealType quantile(const inverse_gamma_distribution<RealType, Policy>& dist, const RealType& p)
+{
+   BOOST_MATH_STD_USING  // for ADL of std functions
+   using boost::math::gamma_q_inv;
+
+   static const char* function = "boost::math::quantile(const inverse_gamma_distribution<%1%>&, %1%)";
+
+   RealType shape = dist.shape();
+   RealType scale = dist.scale();
+
+   RealType result = 0;
+   if(false == detail::check_inverse_gamma(function, scale, shape, &result, Policy()))
+      return result;
+   if(false == detail::check_probability(function, p, &result, Policy()))
+      return result;
+   if(p == 1)
+   {
+      return policies::raise_overflow_error<RealType>(function, 0, Policy());
+   }
+   result = gamma_q_inv(shape, p, Policy());
+   if((result < 1) && (result * tools::max_value<RealType>() < scale))
+      return policies::raise_overflow_error<RealType, Policy>(function, "Value of random variable in inverse gamma distribution quantile is infinite.", Policy());
+   result = scale / result;
+   return result;
+}
+
+template <class RealType, class Policy>
+inline RealType cdf(const complemented2_type<inverse_gamma_distribution<RealType, Policy>, RealType>& c)
+{
+   BOOST_MATH_STD_USING  // for ADL of std functions
+
+   static const char* function = "boost::math::quantile(const gamma_distribution<%1%>&, %1%)";
+
+   RealType shape = c.dist.shape();
+   RealType scale = c.dist.scale();
+
+   RealType result = 0;
+   if(false == detail::check_inverse_gamma(function, scale, shape, &result, Policy()))
+      return result;
+   if(false == detail::check_inverse_gamma_x(function, c.param, &result, Policy()))
+      return result;
+
+   //result = 1. - gamma_q(shape, c.param / scale, Policy());
+   result = gamma_p(shape, scale/c.param, Policy());
+   return result;
+}
+
+template <class RealType, class Policy>
+inline RealType quantile(const complemented2_type<inverse_gamma_distribution<RealType, Policy>, RealType>& c)
+{
+   BOOST_MATH_STD_USING  // for ADL of std functions
+
+   static const char* function = "boost::math::quantile(const inverse_gamma_distribution<%1%>&, %1%)";
+
+   RealType shape = c.dist.shape();
+   RealType scale = c.dist.scale();
+   RealType q = c.param;
+
+   RealType result = 0;
+   if(false == detail::check_inverse_gamma(function, scale, shape, &result, Policy()))
+      return result;
+   if(false == detail::check_probability(function, q, &result, Policy()))
+      return result;
+
+   if(q == 0)
+   {
+      return policies::raise_overflow_error<RealType>(function, 0, Policy());
+   }
+   result = gamma_p_inv(shape, q, Policy());
+   if((result < 1) && (result * tools::max_value<RealType>() < scale))
+      return policies::raise_overflow_error<RealType, Policy>(function, "Value of random variable in inverse gamma distribution quantile is infinite.", Policy());
+   result = scale / result;
+   return result;
+}
+
+template <class RealType, class Policy>
+inline RealType mean(const inverse_gamma_distribution<RealType, Policy>& dist)
+{
+   BOOST_MATH_STD_USING  // for ADL of std functions
+
+   static const char* function = "boost::math::mean(const inverse_gamma_distribution<%1%>&)";
+
+   RealType shape = dist.shape();
+   RealType scale = dist.scale();
+
+   RealType result = 0;
+
+   if(false == detail::check_scale(function, scale, &result, Policy()))
+   {
+     return result;
+   }
+   if((shape <= 1) || !(boost::math::isfinite)(shape))
+   {
+     result = policies::raise_domain_error<RealType>(
+       function,
+       "Shape parameter is %1%, but for a defined mean it must be > 1", shape, Policy());
+     return result;
+   }
+  result = scale / (shape - 1);
+  return result;
+} // mean
+
+template <class RealType, class Policy>
+inline RealType variance(const inverse_gamma_distribution<RealType, Policy>& dist)
+{
+   BOOST_MATH_STD_USING  // for ADL of std functions
+
+   static const char* function = "boost::math::variance(const inverse_gamma_distribution<%1%>&)";
+
+   RealType shape = dist.shape();
+   RealType scale = dist.scale();
+
+   RealType result = 0;
+      if(false == detail::check_scale(function, scale, &result, Policy()))
+   {
+     return result;
+   }
+   if((shape <= 2) || !(boost::math::isfinite)(shape))
+   {
+     result = policies::raise_domain_error<RealType>(
+       function,
+       "Shape parameter is %1%, but for a defined variance it must be > 2", shape, Policy());
+     return result;
+   }
+   result = (scale * scale) / ((shape - 1) * (shape -1) * (shape -2));
+   return result;
+}
+
+template <class RealType, class Policy>
+inline RealType mode(const inverse_gamma_distribution<RealType, Policy>& dist)
+{
+   BOOST_MATH_STD_USING  // for ADL of std functions
+
+   static const char* function = "boost::math::mode(const inverse_gamma_distribution<%1%>&)";
+
+   RealType shape = dist.shape();
+   RealType scale = dist.scale();
+
+   RealType result = 0;
+   if(false == detail::check_inverse_gamma(function, scale, shape, &result, Policy()))
+   {
+      return result;
+   }
+   // Only defined for shape >= 0, but is checked by check_inverse_gamma.
+   result = scale / (shape + 1);
+   return result;
+}
+
+//template <class RealType, class Policy>
+//inline RealType median(const gamma_distribution<RealType, Policy>& dist)
+//{  // Wikipedia does not define median,
+     // so rely on default definition quantile(0.5) in derived accessors.
+//  return result.
+//}
+
+template <class RealType, class Policy>
+inline RealType skewness(const inverse_gamma_distribution<RealType, Policy>& dist)
+{
+   BOOST_MATH_STD_USING  // for ADL of std functions
+
+   static const char* function = "boost::math::skewness(const inverse_gamma_distribution<%1%>&)";
+
+   RealType shape = dist.shape();
+   RealType scale = dist.scale();
+   RealType result = 0;
+
+   if(false == detail::check_scale(function, scale, &result, Policy()))
+   {
+     return result;
+   }
+   if((shape <= 3) || !(boost::math::isfinite)(shape))
+   {
+     result = policies::raise_domain_error<RealType>(
+       function,
+       "Shape parameter is %1%, but for a defined skewness it must be > 3", shape, Policy());
+     return result;
+   }
+   result = (4 * sqrt(shape - 2) ) / (shape - 3);
+   return result;
+}
+
+template <class RealType, class Policy>
+inline RealType kurtosis_excess(const inverse_gamma_distribution<RealType, Policy>& dist)
+{
+   BOOST_MATH_STD_USING  // for ADL of std functions
+
+   static const char* function = "boost::math::kurtosis_excess(const inverse_gamma_distribution<%1%>&)";
+
+   RealType shape = dist.shape();
+   RealType scale = dist.scale();
+
+   RealType result = 0;
+   if(false == detail::check_scale(function, scale, &result, Policy()))
+   {
+     return result;
+   }
+   if((shape <= 4) || !(boost::math::isfinite)(shape))
+   {
+     result = policies::raise_domain_error<RealType>(
+       function,
+       "Shape parameter is %1%, but for a defined kurtosis excess it must be > 4", shape, Policy());
+     return result;
+   }
+   result = (30 * shape - 66) / ((shape - 3) * (shape - 4));
+   return result;
+}
+
+template <class RealType, class Policy>
+inline RealType kurtosis(const inverse_gamma_distribution<RealType, Policy>& dist)
+{
+  static const char* function = "boost::math::kurtosis(const inverse_gamma_distribution<%1%>&)";
+   RealType shape = dist.shape();
+   RealType scale = dist.scale();
+
+   RealType result = 0;
+
+  if(false == detail::check_scale(function, scale, &result, Policy()))
+   {
+     return result;
+   }
+   if((shape <= 4) || !(boost::math::isfinite)(shape))
+   {
+     result = policies::raise_domain_error<RealType>(
+       function,
+       "Shape parameter is %1%, but for a defined kurtosis it must be > 4", shape, Policy());
+     return result;
+   }
+  return kurtosis_excess(dist) + 3;
+}
+
+} // 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_INVERSE_GAMMA_HPP